CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations

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CPGRec+: A Balance-oriented Framework for Personalized Video Game
Recommendations
XIPING LI, Harbin Institute of Technology, China
AIER YANG, Harbin Institute of Technology, China
JIANGHONG MA∗,Harbin Institute of Technology, China
KANGZHE LIU, Harbin Institute of Technology, China
SHANSHAN FENG
∗
,Centre for Frontier AI Research, A*STAR, Singapore Institute of High-Performance Computing,
A*STAR, Singapore, Singapore
HAIJUN ZHANG, Harbin Institute of Technology, China
YI ZHAO, Harbin Institute of Technology, China
The rapid expansion of gaming industry requires advanced recommender systems tailored to its dynamic landscape. Existing Graph
Neural Network (GNN)-based methods primarily prioritize accuracy over diversity, overlooking their inherent trade-o. To address
this, we previously proposed CPGRec, a balance-oriented gaming recommender system. However, CPGRec fails to account for critical
disparities in player-game interactions, which carry varying signicance in reecting players’ personal preferences and may exacerbate
over-smoothness issues inherent in GNN-based models. Moreover, existing approaches underutilize the reasoning capabilities and
extensive knowledge of large language models (LLMs) in addressing these limitations. To bridge this gap, we propose two new modules.
First, Preference-informed Edge Reweighting (PER) module assigns signed edge weights to qualitatively distinguish signicant player
interests and disinterests while then quantitatively measuring preference strength to mitigate over-smoothing in graph convolutions.
Second, Preference-informed Representation Generation (PRG) module leverages LLMs to generate contextualized descriptions of
games and players by reasoning personal preferences from comparing global and personal interests, thereby rening representations
of players and games. Experiments on Steam dataset demonstrate CPGRec+’s superior accuracy and diversity over state-of-the-art
models. The code is accessible at https://github.com/HsipingLi/CPGRec-Plus.
CCS Concepts: •Information systems →Recommender systems;Information extraction; Personalization;
Additional Key Words and Phrases: video game recommendation, accuracy-diversity tradeo, personal preferences, long-tail games
ACM Reference Format:
Xiping Li, Aier Yang, Jianghong Ma, Kangzhe Liu, Shanshan Feng, Haijun Zhang, and Yi Zhao. 2018. CPGRec+: A Balance-oriented
Framework for Personalized Video Game Recommendations. In Proceedings of Make sure to enter the correct conference title from your
rights conrmation email (Conference acronym ’XX). ACM, New York, NY, USA, 35 pages. https://doi.org/XXXXXXX.XXXXXXX
∗Corresponding author
Authors’ Contact Information: Xiping Li, Harbin Institute of Technology, Shenzhen, Guangdong, China, lihsiping@gmail.com; Aier Yang, Harbin Institute
of Technology, Shenzhen, China, yangaier0920@gmail.com; Jianghong Ma, Harbin Institute of Technology, Shenzhen, China, majianghong@hit.edu.cn;
Kangzhe Liu, Harbin Institute of Technology, Shenzhen, China, kangzheliu@foxmail.com; Shanshan Feng, Centre for Frontier AI Research, A*STAR,
Singapore and Institute of High-Performance Computing, A*STAR, Singapore, Singapore, Singapore, victor_fengss@foxmail.com; Haijun Zhang, Harbin
Institute of Technology, Shenzhen, China, hjzhang@hit.edu.cn; Yi Zhao, Harbin Institute of Technology, Shenzhen, China, zhao.yi@hit.edu.cn.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not
made or distributed for prot or commercial advantage and that copies bear this notice and the full citation on the rst page. Copyrights for components
of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on
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©2018 Copyright held by the owner/author(s). Publication rights licensed to ACM.
Manuscript submitted to ACM
Manuscript submitted to ACM 1

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2 Xiping Li et al.
1 Introduction
Recommender systems, pivotal in the customization of digital media content, have gained signicant traction across
a spectrum of industries, including e-commerce [
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,
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,
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–
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,
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], news [
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,
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,
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,
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,
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,
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,
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,
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], and music
[
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,
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,
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,
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,
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,
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,
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,
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,
85
]. Notably, the gaming sector has witnessed an extraordinary surge in recent years. A
compelling example is provided by the data from SteamDB
1
, which indicates a remarkable proliferation of games on
the Steam platform: by 2024, the total number of game titles released had reached 14,310, representing an astonishing
33-fold increase over the past decade. This expansive selection of games highlights the substantial potential and the
pressing need for the development of recommendation algorithms tailored for the gaming industry. These algorithms
are poised to elevate user engagement and bolster nancial performance for platforms, developers, and publishers alike,
thus creating a symbiotic relationship.
The domain of game recommendation studies has recently attracted considerable academic attention, primarily
focusing on developing accuracy-oriented recommender systems to provide tailored game suggestions [
5
,
8
,
12
,
27
,
52
,
82
].
Despite the considerable advancements these models have achieved in enhancing accuracy, they usually neglect the
essential diversity of the recommendation lists, raising concerns about the lter bubble eect [
24
,
34
,
46
,
75
], where
users are conned to a narrow selection of popular games. This limitation may curtail users’ exposure to a variety of
perspectives and potentially exacerbate pre-existing biases. By integrating diversity into recommendations, the user
experience can be signicantly enriched, introducing fresh and unexpected choices that broaden horizons and cater to
a wider demographic. Against this background, the domain of game recommendation studies is currently facing several
key obstacles:
•
Limitations of Accuracy-Focused Methods. Traditional accuracy-centric game recommendation algorithms
[
3
,
5
,
12
,
52
] emphasize transformantions from spatial domain but underutilize rich categorical game data.
Notably, games with similar genres can originate from various publishers and development studios, which
signicantly inuence user preferences. SCGRec [
82
] leverages category-based connections within game
graphs to improve accuracy but relies on single-category associations, which may not always reect true game
similarities, potentially reducing recommendation accuracy.
•
Challenges in Diversity-Focused Methods. Graph Neural Network (GNN)-based diversity-focused methods
have introduced techniques like dynamic neighbor sampling [
84
,
95
], neighbor selection [
83
], and BPR loss
modications [
56
] to enhance diversity. However, these approaches face two challenges: (1) complexity risks
and suboptimal use of item details in neighbor modeling, and (2) the challenge of long-tail distribution in the
spread of messages. Neighbor sampling strategies can become overly intricate or sparse, neglecting key item
features like categories. Additionally, most methods ignore item popularity, disproportionately favoring popular
items and limiting exposure to niche or long-tail games.
•
Balancing Accuracy and Diversity. The trade-o between accuracy and diversity is a persistent challenge, as
these objectives often conict. Accuracy-focused methods like BPR loss [
67
,
72
,
82
] rene models using negative
examples, while diversity-oriented methods employ loss rescaling or likelihood adjustments [
11
,
83
,
87
,
95
].
However, these approaches predominantly favor one objective, grappling with the achievement of a harmonious
accuracy-diversity balance.
In prior work [
39
], we have addressed the outlined challenges by introducing a novel model, termed Category-based
and Popularity-guided Video Game Recommendation (CPGRec). As part of that study, we explored a strategy for
1https://steamdb.info/stats/releases/
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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 3
constructing a graph structure by explicitly encoding the semantic information of game categories and popularity into
the graph. Particularly, (1) when it comes to accuracy, based on the local smoothness of GNNs, CPGRec retains links
exclusively between games that share a strong similarity in their categories, emphasizing the rationale for inferring
content similarity from category similarity. (2) Regarding diversity, CPGRec allows information to ow freely between
games across dierent categories, breaking the representation clustering of same-category games in high-dimensional
space. Furthermore, by limiting the inuence of popular game nodes while emphasizing their propagation capability,
CPGRec facilitates the widespread dissemination of feature information for long-tail games. (3) Overall, regarding
the trade-o between accuracy and diversity, CPGRec infers the relationship between representations and popularity
information based on the rating scores of negative samples extracted from the BPR loss, allowing for the reweighting of
BPR loss. Experimental results demonstrate that CPGRec outperforms baseline models in both accuracy and diversity.
Despite its success, CPGRec neglects the disparities among observed historical player-game interactions, i.e., it
assumes that all these interactions reect the players’ interest equally. However, in real-world scenarios, it is more
reasonable to acknowledge the disparities of historical interactions, as they may have dierent importance in reecting
the player’s personal preferences. Intuitively, a player’s personal preferences are more pronounced in their historical
interactions that signicantly dier from those of the broader player base, rather than in interactions that show
indistinguishable interest from global interests, considering both positive (interest) and negative (disinterest) aspects
(which is analyzed in detail in Section 5.3). Based on this, two points should be highlighted: (1) Considering CPGRec’s
employment of graph convolutional layers with non-interaction-specic edge weights in bipartite graphs, ignoring
these disparities in interactions may cause the smoothness of GCNs (i.e., low-pass ltering in the spectral domain,
which leads the adjacent nodes’ representations to become similar gradually) to become a trigger, leading to suboptimal
modeling of players and games, as well as the resulting representations. (2) Furthermore, although the eectiveness of
Large Language Models (LLMs) has been demonstrated in existing works, their great potential in lling the above gap,
such as their rich knowledge about the game and powerful reasoning ability for understanding the above disparities of
player-game interactions, has not yet been explored.
To address these problems, we newly propose two modules in this study. They both incorporate both the dwelling
time and average ratings, which respectively reect the personal interest and public interests, to rene the representation
of player-game interactions. First, we design a module, namely Preference-informed Edge Reweighting (PER), an
edge reweighting method with sign design to address the above-mentioned over-smoothing risk arising from the neglect.
Both the sign and edge weight are proposed to model the personal preferences indicated by historical interactions,
where the sign qualitatively reects whether signicant interest or disinterest is indicated in each interaction, while the
edge weight further quantitatively measures the extent of signicant preference. Specically, a two-level approach is
adopted: (1) Fisher Distribution-based Sign Decision: Using the Fisher statistic and Fisher distribution, we compare
personal and global interests, uncovering both interests and disinterests, which inform the directional ow of messages
on each edge, i.e., the sign of messages. (2) Information Content-based Volume Evaluation: We introduce the
concept of “information content” [
35
,
40
,
60
,
62
] to quantify the signicance of each interaction, thereby determining
the magnitude of propagated messages. Second, inspired by the outstanding performance of existing recommender
systems that integrate LLMs, CPGRec+ further proposes a Preference-informed Representation Generation (PRG)
module. PRG leverages the broad knowledge as well as powerful reasoning capabilities to generate game descriptions
and player descriptions as supplementary representations to polish game representation while further capturing the
personal preferences of players. Particularly, PRG operates in two steps: (1) Rating-informed Game Description
Generation: This step leverages the broad knowledge of LLMs by explicitly instructing them to reason from the average
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4 Xiping Li et al.
rating of each game, which is highlighted by our designed game prompt. This ensures that the generated descriptions
eectively capture and reect the global interest of the general players toward the game. (2) Preference-informed
Player Description Generation: This step utilizes the reasoning capabilities of LLMs, explicitly instructing them to
infer player preferences by comparing personal interests with global interests. Jointly, these two preference-informed
modules prioritize interactions that better reect player interest to solve these aforementioned problems, thereby
improving the accuracy of our enhanced model, CPGRec+. Experimental results conrm that CPGRec+ outperforms
CPGRec and remains competitive with state-of-the-art benchmarks.
Building upon our previous work [39], this study presents the following contributions:
•
We extend CPGRec by newly incorporating both Preference-informed Edge Reweighting (PER) and Preference-
informed Representation Generation (PRG), enabling ner-grained modeling for player-game historical inter-
actions and personalized preferences. This integration empowers the system’s capability of delivering more
tailored and satisfactory recommendations.
•
We propose a methodology to map video-game-related distributions to standard normal distributions using
the Box-Cox transformation, which facilitates deeper theoretical analysis of personal preferences embedded
within historical interactions and is experimentally validated through hypothesis testing, providing a robust
foundation for future game recommendation research.
•
We propose a novel approach to enhance recommender systems by leveraging LLMs to generate game de-
scriptions based on global interests, and generate player descriptions by reasoning individual preferences from
comparing personal interest and global interest, subsequently embedding these descriptions to rene player
and game representations for improved recommendation quality.
•
Experimental results highlight the superior accuracy of the enhanced model, CPGRec+, while maintaining the
diversity strengths of CPGRec, thereby attaining an ideal equilibrium for the trade-o task.
2 RELATED WORK
2.1 Video Game Recommendation
The escalating growth of the video game industry has drawn signicant scholarly interest in the eld of video game
recommendation algorithms. Initial scholarly investigations primarily focused on approaches grounded in Collaborative
Filtering (CF) and Content-Based Filtering (CBF). Anwar et al. presented a CF strategy that addresses the distinct
proles of games and users for the purpose of personalized game endorsements [
3
]. BharathiPriya et al. expanded on
this by merging CF and CBF to deduce implicit hierarchies, with a focus on elements such as the duration of play [
5
].
Pérez-Marcos et al., in a related approach, proposed a hybrid recommendation framework for gaming, drawing on
methodologies from the music sector to optimize the usage of playtime [52].
Recently, there has been a discernible trend towards exploring innovative deep learning methodologies for game
recommendation studies. These innovative strategies have consistently surpassed conventional methods, which are
largely based on implicit user feedback. A case in point is the comprehensive study by Cheuque et al., which evaluated
the traditional Factorization Machine, DeepNN and hybrid DeepFM [12].
Their outcomes, notably when utilized with data from the Steam platform, indicated that DeepNN and DeepFM models
outperformed the FM model. The integration of GNNs into game recommender systems has also gained considerable
traction. Graph Neural Networks (GNNs) excel at capturing intricate connections and dependencies in graph-based data
[
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,
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,
33
,
44
,
51
,
66
,
73
,
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,
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,
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,
87
–
89
], positioning them as a strong choice for advancing recommendation systems
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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 5
in the gaming sector. Yang et al. introduced SCGRec, a novel system that uses a GNN architecture to incorporate game
context and social interactions [82].
Discussion. CPGRec+ apart from prior research in two key aspects: (1) Unlike traditional game recommendation
models overlook the disparities of player-game historical interactions, CPGRec+ deeply mines the rich semantics of
interaction-level to provide more accurate recommendations. Building on our earlier work [
39
], it integrates inter-
category linkages within the graph structure and employs the Fisher distribution and entropy metrics to enhance
player modeling by analyzing personal preferences from historical interactions. Besides, CPGRec+ further leverages the
extensive knowledge and advanced reasoning capabilities of LLMs to rene game and player representations, incorpo-
rating global interests and conducting a comparative analysis between individual and global interests, respectively.
(2) In contrast to prior studies that often overlook diversity, leading to homogeneous recommendations, CPGRec+
incorporates both accuracy and diversity, ensuring a more balanced and varied recommendation output.
2.2 Diversified Recommendation
Pioneers like Ziegler et al. [
96
] initially brought the concept of diversity into the domain of recommender systems.
This sparked extensive scholarly exploration into diversifying recommendation algorithms. Yin et al. [
86
] delved
into diversity challenges within session-based recommender systems with a thorough study. Liang et al. [
41
]’s EDUA
employs a dual-path network with adaptive balancing and dual-metric learning to boost both the accuracy and diversity
of recommendations. Zheng et al.’s DGCN, a strategy based on GCN [
33
], boosts diversity by selecting neighbors,
reweighting samples, as well as the employment of adversarial learning [
95
]. Ye et al. [
84
]’s DDGraph employs a
diversifying selector to update the user-item graph, ensuring neighbor diversity. Yang et al. [
83
]’s DGRec uses a
submodular function for diverse neighbor selection and employs multi-layer attention and adjusts loss weights to
glean more detailed insights from higher-order neighbors. The EXPLORE framework [
13
] presents a probabilistic user-
behavior model that maximizes recommendation diversity while maintaining relevance, balancing user engagement
and exploration.
Discussion. Collectively, the above studies advance the incorporation of diversity in recommender systems. However,
most of these works sacrice accuracy for diversity, use complex dynamic methods ineciently, and inadequately
leverage game category information for neighbor selection. To this end, our recently proposed CPGRec boosts recom-
mendation accuracy by tightly linking games, enhances diversity by connecting varied game categories and leveraging
popular games for long-tail visibility, and balances both through a novel negative-sample reweighting approach.
2.3 LLM for Recommendation
Recent research has explored the application of LLMs to enhance recommendation systems in various ways [
42
]. A-
LLMRec proposes an ecient LLM-based recommender system that leverages collaborative knowledge from pre-trained
CF-RecSys to excel in both cold and warm scenarios [
32
]. CoLLM introduces an innovative LLMRec approach that
explicitly integrates collaborative information by encoding it from traditional collaborative models and aligning it with
the LLM’s input text token space [
93
]. CUP addresses the challenge of sparse user interactions by using Transformer-
based representation learning and selecting informative cues from review texts to construct concise user proles for
recommendations [
68
]. KAR proposes an open-world knowledge-augmented recommendation framework that acquires
reasoning knowledge on user preferences and factual knowledge on items from LLMs [
77
]. RLMRec introduces a
model-agnostic framework that enhances existing recommenders with LLM-empowered representation learning to
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6 Xiping Li et al.
capture intricate semantic aspects and address challenges like scalability and text-only reliance [
55
]. SAGCN harnesses
the sentiment analysis capabilities of LLMs to uncover semantic aspect-aware interactions from user reviews, enhancing
the accuracy and interpretability of conventional recommendation methods [43].
Discussion. Although these latest methods have attempted to leverage the rich knowledge of LLM to generate
rich descriptions for users or items, or to encode collaborative ltering signals into representations, they still have
some key deciencies. (1) Existing LLM-based recommender systems often overlook the importance of average ratings,
which reect the preferences of a large number of players, in the process of generating detailed game descriptions. This
omission may lead to game descriptions that fail to reect the aspects most relevant to players’ interests. While a game’s
description may accurately portray its content and initially appear to align with a player’s preferences—prompting
them to select it—its actual content may fall short of expectations, as indicated by a persistently low average rating. In
such cases, despite a supercial alignment based on textual description alone, the game should not be recommended, as
the collective feedback from the broader player community reveals a fundamental mismatch. (2) Existing works fail to
fully harness the powerful reasoning capabilities of LLMs to extract individual preferences from historical interaction
data, particularly by using dwelling time and average ratings as key indicators. These two factors, when combined,
provide valuable insights into a player’s unique interests, as discussed in Section 5.3. To overcome these limitations,
CPGRec+ employs large language models (LLMs) to integrate average ratings and dwelling time into the prompting
process, enabling the generation of rened game and player descriptions. By explicitly capturing both global player
preferences and individual interests, this approach enhances the alignment between game content and user experience,
leading to more accurate and personalized recommendations.
3 Investigating GNN-based Video Game Recommendation
3.1 Preliminaries
3.1.1 DEFINITION(Game Graphs with Raw Connections).In this study, we explore the interconnections among
video games by categorizing them based on three fundamental types of categories: genre, developer, and publisher.
This framework enables the establishment of raw connections between games. Specically, in a game graph with
genre-based raw connections, a connection forms when two games share overlapping genres; similar approaches dene
connections based on shared developer and publisher aliations. By identifying games linked through shared genre
(g), developer (d), and publisher (p) characteristics, we create three separate game networks based on these categories,
denoted as G𝑔,G𝑑, and G𝑝.
3.1.2 DEFINITION(Player-Game Bipartite Graph).In game recommendations, we dene a group of players as
U={𝑢1,𝑢 2, . . . , 𝑢|U|}
and a set of games as
I={𝑖1, 𝑖2, . . . , 𝑖 |I| }
. The subset
I(𝑢) ⊂ I
signies the games that the
player uhas played. To model these historical interactions between players and games, we construct a player-game
bipartite graph, represented as
G=(V,E)
, where
V=U ∪ I
. An edge is established between player uand game iif
the player has previously engaged with the game.
3.1.3 Problem Statement.The central objective of this study is to develop a system for game recommendations
for each player
𝑢∈ U
by generating a top Klist of games, denoted as
I(𝑢)
𝐾={𝑖(𝑢)
1, 𝑖 (𝑢)
2, . .., 𝑖 (𝑢)
𝐾}
, which player uhas
not yet engaged with. Furthermore, this study introduces a multifaceted task that integrates considerations of both
accuracy and diversity, requiring that the recommended lists of
𝐾
games not only match the interests of the players but
also maintain sucient diversity.
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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 7
3.2 Discovering the Long-tail Nature of Video Games
In various real-world recommendation scenarios, such as short videos, movies, and products, user feedback on items is
a critical reection of user interest. This feedback is often quantied through metrics such as user clicks, downloads,
and purchase counts, serving as proxies for item popularity within the recommendation framework. The long-tail eect
describes the signicant imbalance in the popularity distribution among items. Specically, a limited number of items
capture the majority of user engagement, while a substantial proportion of items, commonly referred to as “long-tail
items”, receive minimal attention.
The long-tail eect can adversely aect user satisfaction with recommender systems by impairing their ability to
model user preferences eectively. This phenomenon arises because popular items, characterized by extensive historical
interactions with a broad user base, intensify the high-dimensional similarity representations between these items
and users. Consequently, popular items tend to dominate the ranking process, overshadowing long-tail items. Thus, a
signicant challenge for recommender systems is disrupting this cycle and ensuring long-tail items are recommended
with sucient frequency despite the prevailing long-tail eect.
We highlight that the evident long-tail eect in video games is a crucial motivation and signicant practical
foundation for this study. Specically, the following intuitive depiction and quantitative analysis of the long-tail
distribution observed on the Steam platform provide an illustration of the long-tail phenomenon.
Intuitive depiction: As demonstrated in Fig. 1(a), games are organized in descending order based on the number of
players to eectively illustrate the long-tail phenomenon. This phenomenon is characterized by (1) a limited number
of highly popular games, often referred to as the “head”, which dominate the market, and (2) a signicantly larger
number of less popular games, known as the “long tail”, each commanding smaller individual shares.
Quantitative analysis: Building on the concept of long-tail phenomenon, we propose the statistic Top Ratio
𝑇 𝑅 (𝑝)
to quantitatively capture the long-tail characteristics of video games. This statistic is dened as:
𝑇 𝑅 (𝑝)=#of top-𝑝popular games’ players
#of all games’ players ,(1)
where
𝑝
is a fraction in [0.1,1] with increments of 0.1. It is evident that
𝑇 𝑅 (𝑝)
represents the cumulative share of the
top-
𝑝
most popular games on Steam; thus, a larger
𝑇 𝑅 (𝑝)
for a smaller
𝑝
indicates a more pronounced long-tail eect.
Additionally, we introduce Δ𝑇𝑅 (𝑝), dened as 𝑇 𝑅(𝑝) − 𝑇𝑅 (𝑝−0.1), to show the growth of 𝑇𝑅 (𝑝)as 𝑝increases.
The
𝑇 𝑅 (𝑝)
and
Δ𝑇𝑅 (𝑝)
presented in Fig. 1(b) illustrate the signicant long-tail property of Steam video games.
(1) Even when
𝒑
is small (specically, limited to 0.3),
𝑻 𝑹 (𝒑)
achieves a high value of 0.93, indicating that the most
popular games account for a substantial majority of the total player base. (2) As
𝒑
increases, the incremental gain in
𝑻 𝑹 (𝒑)
diminishes sharply. These two observations quantitatively provide an intuitive understanding of the long-tail
distribution characteristic of Steam video games.
3.3 Discovering the Categorical Semantics of Video Games
The categorical information of games is intricately linked to ner details of game content such as visual and musical
styles, containing rich semantics and therefore profoundly inuencing players. This enables category information to
serve as a form of prior knowledge and empower the inference that the representations of games aliated with similar
categories should be positioned closer together in the high-dimensional space, and vice versa, which can be classied
as one of the common ideas for Content-Based Filtering (CBF) [4,16,80].
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8 Xiping Li et al.
(a) Games sorted in descending order of num-
ber of players.
(b) A quantitative depiction based on
𝑇 𝑅 (𝑝),Δ𝑇𝑅 (𝑝).
Fig. 1. The long-tail phenomenon in the number of players across all games within Steam platform, with quantitative analysis via
𝑇 𝑅 (𝑝)and Δ𝑇𝑅 (𝑝).
Following such ideas, GNNs have become one of the most commonly used basic frameworks in the eld of recom-
mender systems, one of the reasons being that they can explicitly exploit the above-mentioned category information to
learn game representations in a spatial way, including by building edges based on the category information. Specically,
a general approach [
11
,
82
,
95
] is to establish a connection between any two items on the item graph based on a specic
category, provided that they share similarities in this category. For example, RIP-Trilogy (casual, indie) and RoboBlitz
(action, indie) are linked via the shared “indie” category.
However, the above strategy is limited by the uncertain reliability of category semantics—when category similarity
fails to reect true content similarity, it introduces noise, degrading recommendation quality. To mitigate this, our
previous work [
39
] introduced strict connections, requiring item pairs to share similarities in two categories to ensure
stronger content alignment, in contrast to the raw connections used in conventional approaches. For instance, Counter-
Strike: Source and Day of Defeat: Source (both action games developed by Valve) exhibit high content similarity, unlike
Amnesia: The Dark Descent, which, despite being categorized as action, has distinct horror-themed graphics and
puzzle-based gameplay.
To validate the eectiveness of strict connections, we analyze the Steam network by comparing edge quantity, Eu-
clidean distance, and cosine similarity of game description embeddings under raw and strict connections. Descriptions
are generated using Qwen2.5 [81] for contextual understanding and M3-Embedding [9] for capturing semantic mean-
ing—both chosen for their strong performance, accessibility, and cost-eectiveness. As shown in Fig. 2(a), introducing
a second category condition signicantly reduces edge quantity, ltering out noisy connections and enhancing CBF
signal quality. In Fig. 2(b), the larger main diagonal elements indicate that strict connections link games with more
similar content, as they exhibit smaller Euclidean distances. Likewise, Fig. 2(c) shows larger main diagonal elements,
conrming higher cosine similarity and stronger content alignment under strict connections.
4 Review of CPGRec
This section reviews our model CPGRec proposed in conference work [
39
], which is composed of four essential modules:
Stringency-improved Game Connection (SGC), Connectivity-enhanced Neighbor Aggregation (CNA), Popularity-guided
Edges and Nodes Reweighting (PENR), and Combined Training with Negative-sample Score Reweighting (NSR). As
these methods have been detailed in prior work [39], this study provides only a concise overview.
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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 9
(a) antity of edges (b) Average euclidean distance (c) Average cosine similarity
Fig. 2. Figure (a) presents the number of edges in the Steam game network. Figures (b) and (c) show the average Euclidean distance
and cosine similarity of game description embeddings, respectively. These descriptions are generated using a large language model
(LLM), and embeddings are obtained via an embedding model. The main diagonal elements reflect the Steam game network based on
raw connections, while other elements are based on strict connections.
4.1 Stringency-improved Game Connection
As detailed in Section 3.3, category information is rich in semantics. Since games within the same category are expected
to share similar content, eective game representations should capture this insight. Category information thus serves
as a key semantic guidance in video game modeling.
Based on this insight, the concept of strict connections is proposed to preserve connections only between games that
share at least two categories among genre, developer, and publisher. This approach provides a more solid guarantee
for the rationality of our inference from category similarity to the similarity of learned representation. Subsequently,
LightGCN [
25
] with category-wise self-attention [
70
] is employed to learn the representation, which is dened as
follows:
𝑒𝐶𝑎
𝑖=Graphwise Attention(𝑒𝑔&𝑑
𝑖, 𝑒𝑔&𝑝
𝑖, 𝑒𝑑&𝑝
𝑖),(2)
where
𝑒𝑔&𝑑
𝑖
,
𝑒𝑔&𝑝
𝑖
, and
𝑒𝑑&𝑝
𝑖
denote the learned representations obtained using LightGCN on
G𝑔&𝑑
,
G𝑔&𝑝
, and
G𝑑&𝑝
,
the three game graphs with strict connections dened in Section 3.1.1, respectively.
4.2 Connectivity-enhanced Neighbor Aggregation
To enhance diversity, we promote message propagation and aggregation across dierent game categories on a game
graph constructed by strengthening the game graph’s connectivity. Specically, we rstly construct a game graph
G𝐶𝑜
where neighboring games are only required to share at least one common category but are allowed to dier signicantly
in others. For instance, adjacent games might share the same genre but have dierent developers and publishers. Second,
to boost cross-category message interaction, we apply multi-layer LightGCN for message propagation and aggregation
within
G𝐶𝑜
, and use an attention mechanism to weight embeddings from dierent layers, reducing over-smoothing
risks. Third, we introduce a layer-wise reweighting parameter:
𝑤𝑙=1− (𝑘−𝑙)𝛽, (3)
where
𝑤𝑙
is the reweighting parameter for the
𝑙
-th layer,
𝑘
is the number of LightGCN layers, and
𝛽
is the decay
parameter assigning higher weights to deeper layers’ embeddings. Specically,
𝑤𝑙
weights the
𝑙
-th layer’s game
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embedding to emphasize those from deeper layers, which capture messages from more distant and diverse games.
Formally, the embedding of game 𝑖is obtained by:
𝑒𝐶𝑜
𝑖=Layerwise Attention(𝑤1𝑒(1)
𝑖, 𝑤2𝑒(2)
𝑖, . .., 𝑤𝑘𝑒(𝑘)
𝑖),(4)
where 𝑒(𝑙)
𝑖is the output embedding of game 𝑖from the 𝑙-th layer.
4.3 Popularity-guided Edges and Nodes Reweighting
To emphasize diversity, the aim of this module is to create a situation where, although under normal circumstances,
long-tail game nodes on player-game bipartite graphs have insucient connectivity to inuence the nal learned
player representation. In contrast, with the design of this link, in the alternating process of message propagation and
aggregation, once messages from long-tail games ow through popular games, they can be widely disseminated to
player nodes with the help of the latter’s advantageous connectivity; at the same time, the inuence of popular game
nodes themselves should also be limited. To achieve this, we increase the weights of out edges from popular games and
those of long-tail game nodes, while decreasing the weights of popular game nodes. Formally, the edge weight function
Θ𝑃𝑜
𝑒(·) is specied as follows:
Θ𝑃𝑜
𝑒(𝑖)=





Θℎ𝑜𝑡
𝑒𝑖∈ I
ℎ𝑜𝑡
1𝑖∉I
ℎ𝑜𝑡
,(5)
and similarly a node weight mapping Θ𝑃𝑜
𝑛(·) is dened as:
Θ𝑃𝑜
𝑛(𝑖)=











Θℎ𝑜𝑡
𝑛𝑖∈ I
ℎ𝑜𝑡
1𝑖∉I
ℎ𝑜𝑡 ∪ I
𝑐𝑜𝑙𝑑
Θ𝑐𝑜𝑙𝑑
𝑛𝑖∈ I
𝑐𝑜𝑙𝑑
,(6)
where
I
ℎ𝑜𝑡
and
I
𝑐𝑜𝑙𝑑
are respectively the sets of popular games and long-tail games. Then, multiple graph convolution
layers which integrate the aforementioned reweighting mechanism are characterized by:
𝑒(𝑙+1)
𝑢=1
|N𝑢||N𝑢|𝑒(𝑙)
𝑢+
𝑖∈N𝑢
Θ𝑃𝑜
𝑒(𝑖)Θ𝑃𝑜
𝑛(𝑖)
|N𝑢||N𝑖|𝑒(𝑙)
𝑖,(7)
𝑒(𝑙+1)
𝑖=
Θ𝑃𝑜
𝑛(𝑖)
|N𝑖||N𝑖|𝑒(𝑙)
𝑖+
𝑢∈N𝑖
1
|N𝑖||N𝑢|𝑒(𝑙)
𝑢.(8)
Here,
N𝑖
denotes the set of neighbors for game
𝑖
, while
N𝑢
denotes the set for player
𝑢
. The terms
𝑒(𝑙)
𝑖
and
𝑒(𝑙)
𝑢
are the
embeddings output by the
𝑙
-th layer of LightGCN for game
𝑖
and player
𝑢
, respectively. After processing through
𝑘
layers, the embeddings for player 𝑢and game 𝑖in this module are determined by the following calculation:
𝑒𝑃𝑜
𝑢=𝑒(𝑘)
𝑢, 𝑒𝑃 𝑜
𝑖=𝑒(𝑘)
𝑖.(9)
4.4 Combined Training with Negative-sample Score Reweighting
The key consideration in delivering a satisfying gaming experience to players is achieving a balance between accuracy
and diversity. The rst module (SGC) and the last two modules (CNA, PENR) proposed above form the accuracy-oriented
and diversity-oriented modules of our framework, respectively. To integrate these aspects, CPGRec adopts a weighted
combination method governed by learnable parameters
𝑤𝐶𝑎,𝑤𝐶𝑜, 𝑤𝑃 𝑜
to obtain the nal representations for each
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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 11
player 𝑢and game 𝑖, which is dened as
𝑒𝑢=𝑒𝑃𝑜
𝑢,
𝑒𝑖=𝑤𝐶𝑎𝑒𝐶 𝑎
𝑖+𝑤𝐶𝑜 𝑒𝐶𝑜
𝑖+𝑤𝑃𝑜 𝑒𝑃𝑜
𝑖,
𝑤𝐶𝑎 +𝑤𝐶𝑜 +𝑤𝑃 𝑜 =1,
(10)
where
𝑤𝐶𝑎,𝑤𝐶𝑜, 𝑤𝑃 𝑜
are the weights for the embeddings of game
𝑖
obtained in modules SGC, CNA, and PENR,
respectively. By adjusting these weights, we can adapt the model to meet various requirements. Moreover, CPGRec
further enhances both accuracy and diversity by rening the rating scores for negative samples to facilitate more
ecient learning from samples, which is expressed as:
∼
𝐿𝐵𝑃𝑅 =−
𝑢∈U,𝑖∈I(𝑢),
𝑗∉I(𝑢)
log 𝜎(𝑟𝑢,𝑖 −∼
𝑟𝑢, 𝑗 ) +𝜆∥Θ∥2
2,(11)
where 𝜎(·) is the sigmoid function, 𝑟𝑢,𝑖 =𝑒𝑢·𝑒𝑖is the rating score of positive sample 𝑖, and
∼
𝑟𝑢, 𝑗 =𝑚·𝜎(𝑟𝑢,𝑗 ) · 𝑟𝑢,𝑗 ,(12)
is the reweighted rating score of negative sample 𝑗, with 𝑚controlling the reweighting intensity.
From the perspective of enhancing accuracy, a negative sample predicted with a high rating score could be deceptive,
i.e., it can easily be mistaken for a positive sample. Thus, the increased loss through negative-sample score reweighting
compels an improvement in the model’s recognition capabilities, aiming to achieve more accurate predictions in such
cases.
From the perspective of promoting diversity, a low score assigned to a negative sample implies substantial dissimi-
larity between that sample and players in terms of their representations. This could indicate limited interactions due
to the game’s poor exposure to players, suggesting it might be a long-tail game. By increasing the rating score, this
module enhances their chances of being recommended.
5 Motivation for New Module
5.1 Preliminary: Smoothness Nature of GCNs
In the eld of graph learning, the concept of smoothness refers to a property of GNN models (e.g., Graph Convolutional
Network (GCN)). It means that the representations learned by a GNN-based model with smoothness of nodes that are
close to each other on a graph (i.e., connected or in close proximity) tend to be similar (e.g., their cosine similarity is much
higher, or their Euclidean distance is much lower). The vast majority of GNN-based models, especially the most widely
used GCN, possess the property of smoothness, which has a dual nature: (1) Smoothness can be leveraged to capture
commonalities between nodes. When nodes are connected or part of the same neighborhood in a graph, they often share
similar characteristics or roles. By enforcing smoothness, GNNs can eectively propagate and aggregate information
between neighboring nodes, leading to more coherent and consistent representations; (2) However, excessive smoothness
can lead to the problem of over-smoothness, where the representations of nodes may become too similar, losing the
distinctiveness needed for eective learning and prediction.
In CPGRec, smoothness is utilized to capture the commonalities between games sharing similar categories in the
module SGC, based on the belief that games with similar categories are expected to have similar content, eectively
enhancing the recommendation accuracy. Nonetheless, as mentioned earlier, the direct application of GCN layers may
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12 Xiping Li et al.
lead to the over-smoothness issue. To better leverage smoothness while mitigating over-smoothness, it is essential to
understand the smoothness property of GCN.
From a spatial domain perspective, smoothness is relatively straightforward to understand, as feature interactions
occur through message propagation and aggregation between adjacent nodes, resulting in greater similarity among
neighboring nodes. However, this intuitive perspective is insucient, as it fails to adequately explain why certain
GNNs, particularly those designed from the spectral domain, hold the potential to address over-smoothness. Therefore,
a spectral perspective is provided in Appendix Afor a deeper understanding of smoothness.
5.2 Motivation 1: Smoothness of GCN Layer within CPGRec
The GCN [
25
,
33
] serves as a foundational framework in CPGRec, facilitating representation learning for players and
video games within game graphs and the bipartite graph. Nevertheless, it is essential to recognize that the role of GCN
in CPGRec is not uniformly advantageous.
On one hand, the smoothness property of GCNs enhances game representation learning by eectively capturing
the rich semantics of various categories in the context of the SGC module. Discussions in Section 3.3 introduce the
rationality of the belief that categorically similar games should share similar representations, which serves as a principle
that oers guidance to game modeling, and can be eectively implemented through the smoothness property of GCNs.
Conversely, the smoothness property introduces the risk of compromising accuracy in module PENR, which is based
on the player-game graph. The tendency for representations of players and games to converge towards similarity
poses a signicant challenge to the eectiveness of CPGRec, as it neglects the consideration of diverse preferences and
behavioral patterns among dierent players. Furthermore, while popularity-guided weights are introduced to enhance
long-tail inuence and diversify recommendations, the experimental results of the ablation study in our conference
work [
39
] have demonstrated that they may even impair accuracy, albeit to an acceptable degree. Potential reasons are
that these popularity-guided weights are not conducive to learning complex interaction patterns in the player-game
context, as the popularity information solely reveals nothing about the player-game interactions.
(a) Dwelling time of all players for game Elec-
tronic Super Joy
(b) Dwelling time of the player 320’s for histor-
ical games
Fig. 3. Two concrete examples for illustrating the disparities of historical interactions.
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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 13
5.3 Motivation 2: Disparities of Historical Interactions in Player-Game Graph
In this section, we conduct several data explorations to illustrate the problems arising from edge weights derived from
the PENR module (introduced in Section 4.3) in the context of the player-game bipartite graph. This analysis reveals the
underlying causes of over-smoothness and highlights the motivations and foundations of this study. Specically, we
discuss the unequal importance and rich semantics of historical interactions from two perspectives:
•
From the viewpoint of a specic game, the duration of engagement by historical players exhibits considerable
variation, indicative of diering levels of enthusiasm among players for that game.
•
From the viewpoint of a specic player, engagement time across historical games varies signicantly, reecting
the player’s unique preferences for dierent games.
To provide a more intuitive illustration, we oer concrete examples for both scenarios: from the game perspective,
we use the game Electronic Super Joy as an example; from the player perspective, we focus on the player with ID=320.
These examples are depicted in Fig. 3.
Fig. 3.(a) shows the dwelling time of all 76 players for the game Electronic Super Joy. Despite their observed historical
interactions with the game, dwelling times exhibit considerable variability. Notably, one player has amassed an impressive
177,260 hours of playtime, while another player has not engaged with the game at all since its acquisition. We contend
that only the former’s substantial engagement accurately reects genuine interest, whereas the latter’s inactivity does
not.
Fig. 3.(b) illustrates the Z-score-normalized dwelling times for the player with ID=320 across their 90 historical games.
Although the player has interacted with these games, dwelling times vary signicantly. For instance, after Z-score
normalization, the player’s engagement with certain games approaches nearly 1.0, indicating a strong alignment with
their interests. In contrast, a dwelling time close to 0.0 for other games suggests minimal engagement post-purchase,
leading us to classify these games as unrepresentative of the player’s preferences.
Summary. Considering the smoothness property of GCNs, neglecting the critical disparities in historical interactions
can cause the representations of players and games to become overly similar, potentially hindering CPGRec’s capability
to provide more accurate recommendations. To address this issue, we propose integrating a new module called
Preference-informed Edge Reweighting (PER), which aims to model the personal preference of each player by factoring in
interaction-wise semantics, where both signicant interest and disinterest are included. Moreover, current recommender
systems fail to fully utilize LLMs’ potential in deeply mining players’ personal preferences. To bridge this gap, we
introduce the Preference-informed Representation Generation (PRG) module, which leverages LLMs to enhance the
modeling of players’ preferences by rening game descriptions based on average ratings (global interest) and generating
player descriptions through a comparative analysis of dwelling time (personal interest) and global interest.
6 CPGRec+: Towards Preference-informed Recommendation
In this section, we begin by analyzing the interest and disinterest in our study. Subsequently, we propose two novel
modules, PER and PRG, to capture these preferences with edge reweighting and LLMs respectively. Both modules
address the challenge of interaction disparities, while PER further mitigates the risk of over-smoothing inherent in
CPGRec. Finally, we show the overview of the improved CPGRec+ model and its detailed analysis.
Player’s preference. A player’s personal preference is manifested in the discrepancies between his or her preference
and those of the broader player base. Specically, each historical interaction potentially reects a player’s personal
preference from two perspectives: (1) interest: a player may exhibit greater interest than the general player base on the
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Fig. 4. Illustration of the CPGRec+ framework, comprising three modules: Accuracy-driven module (Stringency-improved Game
Connection, Preference-informed Edge Reweighting, and Preference-informed Representation Generation), Diversity-driven module
(Connectivity-enhanced Neighbor Aggregation, Popularity-guided Edges and Nodes Reweighting), and Comprehensive module.
observed interactions with a non-popular game, reecting his or her personal interest in that game, in stark contrast to
the general historical players of this involved game; (2) disinterest: conversely, a player may demonstrate signicantly
less interest than the general player in a popular game, indicating his or her disinterest. To this end, PER and PRG
are proposed in this paper to detect these informative interactions, and leverage them to rene the representations of
games and players.
6.1 New Module: Preference-informed Edge Reweighting
A player-game bipartite graph that neglects the disparities of observed player-game interactions is an under-improved
modeling of player-game history relationships. This is because it does not fully consider real-world situations, leading
to suboptimal collaborative ltering signals. Furthermore, such neglect may trigger problems arising from the inherent
smoothness of GCN, which results in increased similarity among node representations. These factors ultimately lead
to suboptimal modeling for players and games. To address this problem, we propose the PER module, which solves
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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 15
this problem in two steps. First, inspired by existing works in anomaly detection eld to address over-smoothing
problem [
15
,
21
,
64
], we design a sign decision mapping for player-game edges within the bipartite graph to dierentiate
between interest and disinterest of player. Then, we further introduce information content [
62
] to carefully quantify
the signicant preferences identied in the previous step.
6.1.1 Fisher Distribution-based Sign Decision. We propose introducing a sign decision mapping for edges within
the player-game bipartite graph, which dierentiates between interest and disinterest as revealed by each historical
interaction. Such sign mapping for messages can be seamlessly integrated into graph convolutional layers and has
demonstrated ecacy in mitigating over-smoothness in the eld of data mining, such as anomaly detection [
15
,
21
,
64
].
Specically, we detect those interactions that show signicant player preferences (including both interest and
disinterest) based on the involved dwelling time and the average ratings of the involved games. Then, we assign a
positive sign to edges representing interest and a negative sign to those indicating disinterest. This approach allows us
to convey messages with a positive sign through the former and messages with a negative sign through the latter. As a
result, we expect a reduction in the high-dimensional representation similarities between players and the games they
show signicant disinterest in, while simultaneously increasing similarities with games they show signicant interest
in.
To achieve this, we construct the sign mapping by employing both the dwelling time and average ratings as metrics.
The reason for adopting them is that dwelling time revealed by each single historical interaction reects this particular
player’s interest in this specic game; in contrast, the average rating of this game reects the interest of general players
in this game. By comparing these two indicators, they jointly reect the personal preference of this player indicated by
each historical interaction. However, this raises two critical questions:
•
The dwelling time and average ratings should be from dierent spaces, prohibiting comparisons between them
(our goal). How to transform dwelling time and ratings into the same space?
•
How can we dene a method that compares dwelling time and average ratings to eectively infer the personal
preferences of each player?
To solve the rst question, we propose to introduce the Box-Cox transformation [
6
]. Box-Cox transformation is a
statistical method that can eectively map any input data into an approximately normal distribution while maintaining
its relative relationship, and has been widely employed in various elds, such as anomaly detection [
26
,
94
], fuzzy
systems [
92
], and Monte Carlo denoising [
58
]. Then, we nest a Z-score normalization to further turn the data output by
Box-Cox transformation into approximately standard normal distribution, which eventually maps both the dwelling
time and average ratings to the same space (standard normal space).
Formally, for any input data 𝑦(i.e., dwelling time or average ratings), the transformed data 𝑦(𝜆)is computed by:
𝑦(𝜆)=





𝑦𝜆−1
𝜆if 𝜆≠0,
ln(𝑦)if 𝜆=0,
(13)
where
𝜆
is a hyper-parameter that controls the skewness and kurtosis of the transformed distribution. Subsequently,
the Z-score transformation is introduced to further turn 𝑦(𝜆)into 𝑧by:
𝑧=𝑦(𝜆)−E[𝑦(𝜆)]
Var[𝑦(𝜆)]
,(14)
Manuscript submitted to ACM

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16 Xiping Li et al.
which approximately follows the standard normal distribution.
E
and
Var
are the expectation and variance of data
𝑦(𝜆)
,
respectively. Moreover, we demonstrate the eectiveness of our proposed composite mapping (Box-Cox transformation
followed by Z-score normalization) in transforming dwelling time and average ratings into the same standard normal
space by employing One Sample Kolmogorov-Smirnov Test [1] in Section 6.4.
The standard normality of the transformed data inspires us to design a comparison method to solve the second
problem: modeling the personal preferences of each player. Specically, Fisher [
17
] proposed the concept of Fisher
distribution, which can be regarded as the square of the ratio of two independent standard normal distributions, and the
distribution characteristics of Fisher distribution are clearly known. This allows us to use the square of the ratio between
the transformed dwelling time and the average rating as the result of the comparison, and use Fisher distribution as the
basis for measuring the signicance of this comparison result, to obtain a qualitative comparison result.
Formally, given that the observed dwelling time of player
𝑢
on game
𝑖
is denoted as
𝑡𝑢,𝑖
, and the average rating of
game
𝑖
is denoted as
𝑟𝑖
, we know that the mapped dwelling time
𝑇
for each video game and the mapped average ratings
𝑅of all games respectively follow a standard normal distribution, which are expressed as:
𝑓𝑇(𝑡𝑢,𝑖)=1
√2𝜋exp(−𝑡2
𝑢,𝑖 ), 𝑡𝑢,𝑖 ∈ R,(15)
𝑓𝑅(𝑟𝑖)=1
√2𝜋exp(−𝑟2
𝑖), 𝑟𝑖∈ R.(16)
According to the denition of Fisher distribution, the statistic
𝐹=𝑇2
𝑅2
follows a Fisher distribution with parameters
(𝑑1, 𝑑2)=(1,1)[17], whose cumulative distribution function of 𝐹is dened as:
𝑃(𝐹≤𝑥)=I𝑥
𝑥+1(1
2,1
2),(17)
where Iis the regularized incomplete beta function as:
I𝑥(𝑎, 𝑏)=𝐵(𝑥;𝑎, 𝑏 )
𝐵(𝑎, 𝑏),(18)
𝐵(𝑥;𝑎, 𝑏)=∫𝑥
0
𝑡𝑎−1(1−𝑡)𝑏−1𝑑𝑡 . (19)
Thus, we can directly obtain the upper quantile
𝑄𝛼∈ R
of
𝐹
(hyper-parameter
𝛼
controls the signicance level) and
take it as a clear criterion for whether 𝑇2is signicantly greater than 𝑅2, considering
𝐹≫𝑄𝛼⇐⇒ 𝑇2≫𝑅2, 𝐹 =𝑇2
𝑅2.(20)
It is noteworthy that the condition
𝐹≫𝑄𝛼
highlights the two very dierent cases
𝑇≫
0
, 𝑅 ≈
0and
𝑇≪
0
, 𝑅 ≈
0,
which respectively show the signicant interest and disinterest of the player revealed in the particular interaction:
•𝑇≫
0
, 𝑅 ≈
0respectively indicate that the player has a strong interest for this game (indicated by a fairly long
dwelling time) while the global interest of all players for this game is at a mediocre level (indicated by the
average rating of the game), which together reect the player’s signicant interest in the game.
•𝑇≪
0
, 𝑅 ≈
0respectively indicate that the player has a strong disinterest for this game (indicated by a fairly
short dwelling time) while the global interest of all players for this game is at a mediocre level (indicated by the
average rating of the game), which together reect the player’s signicant disinterest in the game.
Manuscript submitted to ACM

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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 17
This inspires us to construct the preference-informed sign mapping for the historical interaction between player
𝑢
and
game 𝑖by:
𝑠𝑖𝑔𝑛𝑃 𝑟
𝑒(𝑢, 𝑖)=













1if 𝐹=𝑡2
𝑢,𝑖
𝑟2
𝑖
>𝑄𝛼and 𝑡𝑢,𝑖 >0,
−1if 𝐹=𝑡2
𝑢,𝑖
𝑟2
𝑖
>𝑄𝛼and 𝑡𝑢,𝑖 ≤0,
0else,
(21)
which rst determines whether each historical interaction shows a signicant personal preference, and if so, determines
whether the preference is interest or disinterest: if it is interest, a positive sign is given to increase the similarity between
the player and game representations; if it is disinterest, a negative sign is given to explicitly reduce the similarity
between the two.
6.1.2 Information Content-based Volume Evaluation. Although preference-informed sign mapping provides a macro-
scopic perspective on players’ personal preferences, there remains a need for a more detailed quantication of the
disparities present in dierent historical interactions.
Inspired by existing research [
35
,
40
,
60
], we propose to introduce information content [
62
] as the metric to solve this
problem. As an important concept of information theory, information content
I(·)
quanties the amount of surprise or
unexpectedness associated with an observed event A, which is formally computed by:
I(A)=−log(𝑃(A)),(22)
where
𝑃(A)
is the probability that
A
occurs. As seen, a rarer event
A
has higher information content
I(A)
since
its probability
𝑃(A)
is low, and vice versa. This enables us to quantitatively describe the intensity of each observed
signicant personal preference in a similar way. Specically, for a historical interaction involving a player with an
observed dwelling time of 𝑡𝑢,𝑖 and an observed game rating of 𝑟𝑖, the information content is dened as:
I𝑃𝑟
𝑒(𝑡𝑢,𝑖, 𝑟 𝑖)=−log 𝑃(𝑇=𝑡𝑢,𝑖, 𝑅 =𝑟𝑖).(23)
Given 𝑇and 𝑅are independent, we have
𝑃(𝑇=𝑡𝑢,𝑖, 𝑅 =𝑟𝑖)=𝑃(𝑇=𝑡𝑢,𝑖 )𝑃(𝑅=𝑟𝑖)(24)
and
I𝑃𝑟
𝑒(𝑡𝑢,𝑖, 𝑟 𝑖)=−log 𝑃(𝑇=𝑡𝑢,𝑖 )𝑃(𝑅=𝑟𝑖).(25)
Eventually, the preference-informed edge weight Θ𝑃𝑟
𝑒(𝑢, 𝑖)is dened as:
Θ𝑃𝑟
𝑒(𝑢, 𝑖)=𝑠𝑖𝑔𝑛𝑃𝑟
𝑒(𝑢, 𝑖) · I𝑃 𝑟
𝑒(𝑡𝑢,𝑖, 𝑟 𝑖),(26)
which provides a detailed, interaction-focused characterization of each historical interaction. The PER algorithm is
summarized in Algorithm 1.
6.2 New Module: Preference-informed Representation Generation
Large language models (LLMs) have been widely used in the eld of recommender systems recently due to their
rich knowledge and powerful reasoning ability. However, their potential for generating informative descriptions and
comprehending historical interactions has yet to be fully leveraged in uncovering players’ personal preferences. To
Manuscript submitted to ACM

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18 Xiping Li et al.
Algorithm 1: Preference-informed Edge Reweighting
Input: edge set E, game average rating mapping 𝑅, player dwelling time mapping 𝑇, signicance level 𝛼
Output: preference-informed edge weight mapping Θ𝑃𝑟
𝑒(e)for input edge e∈ E
1𝑄𝑢
𝛼←1−𝛼
𝛼
2for 𝑒in Edo
3(𝑢, 𝑖) ← 𝑒
4𝑅𝑖,𝑇𝑢←𝑅(𝑖), 𝑇 (𝑒)
5𝐹←𝑇2
𝑢
𝑅2
𝑖
6𝐼𝑇,𝑅 (𝑇𝑢, 𝑅𝑖) ← − log(1
2𝜋exp(−(𝑇2
𝑢+𝑅2
𝑖))
7if 𝐹>𝑄𝛼then
8if 𝑇𝑢>0then
9Θ𝑃𝑟
𝑒(𝑒) ← 𝐼𝑇 ,𝑅 (𝑇𝑢, 𝑅𝑖)
10 else
11 Θ𝑃𝑟
𝑒(𝑒) ← −𝐼𝑇 ,𝑅 (𝑇𝑢, 𝑅𝑖)
12 else
13 Θ𝑃𝑟
𝑒(𝑒) ← 0
14 return Θ𝑃𝑟
𝑒(e)
address this gap, this study rst employs LLMs to generate game descriptions that emphasize players’ global interests,
which are indicated by the average ratings of involved games. Subsequently, LLMs are further utilized to extract player
descriptions that capture individual preferences. Finally, both types of descriptions are embedded into representations
to rene player and game embeddings, enhancing the overall recommendation quality.
6.2.1 Rating-informed Game Description Generation. PRG enables LLM to deeply understand the content of each game
at a semantic level by constructing textual prompts that include key game information, such as the title, rating, price,
and release time (since the comparison between ratings and time is not directly addressed here, the original 100-point
rating scale is retained). Specically, PRG directs the LLM to focus on deriving insights from the average rating, which
reects the preferences of the majority of players, serving as an indicator of global interest. This approach leverages
the LLM’s capabilities in reasoning, natural language understanding, and generation to create high-quality textual
descriptions for each game, which later facilitates further reasoning involving the joint evaluation of rating and dwelling
time.
Formally, PRG designs an input prompt
P(𝑖)
𝑔
for each game
𝑖∈ I
by combining two key components: (1) critical
textual information about the game and (2) explicit instructions. The textual information includes the game title
𝛼𝑔
, the
average rating
𝑟𝑔
(as a reection of global interest), and supplementary data such as price
𝑝𝑔
and release date
𝑡𝑔
. The
explicit requirements instruct the LLM to generate the description with particular emphasis on
𝑟𝑔
, as it reects the
global interest of general player base for this game. This can be formally expressed as:
Manuscript submitted to ACM

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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 19
P(𝑖)
𝑔=


















𝑓𝑔([𝛼𝑔, 𝑟𝑔, 𝑝𝑔, 𝑡𝑔]),if 𝑟𝑔, 𝑝𝑔, 𝑡𝑔exist,
𝑓𝑔([𝛼𝑔,¯
𝑟𝑔, 𝑝𝑔, 𝑡𝑔]),else if 𝑝𝑔, 𝑡𝑔exist,
𝑓𝑔([𝛼𝑔, 𝑟𝑔]),else if 𝑟𝑔exist,
𝑓𝑔([𝛼𝑔,¯
𝑟𝑔]),otherwise,
(27)
where
𝑓𝑔(·)
is a game-specic function that combines the textual information with the explicit requirements into a single
string. Missing game ratings are substituted with the average rating of available games, while missing supplementary
information is omitted as it is non-essential.
Based on this, a state-of-the-art LLM can be leveraged to generate high-quality description as textual representation
in natural language for each game 𝑖∈ I, which is expressed as:
D(𝑖)
𝑔=LLM(P(𝑖)
𝑔),(28)
where
D(𝑖)
𝑔
indicates the textual description of game
𝑖
, which highlights the global interest of players. In this study, the
LLM Qwen2.5 [81] is utilized considering its excellent ability to understand context and generate human-like text.
Additionally, building on the success of LLMs in generating user and item proles in recommender systems [
42
,
90
,
97
],
we integrate an embedding model
EMB
to map
D(𝑖)
𝑔
into a numerical semantic space. This complements the game
representation, as expressed by the following equations:
𝑒D
𝑖=EMB(D(𝑖)
𝑔),
𝑒D−𝐴𝑙𝑖𝑔𝑛
𝑖=𝑀𝐿 𝑃 D−𝐴𝑙𝑖𝑔𝑛 (𝑒D
𝑖),
𝑒𝑖=𝑀𝐿 𝑃 D−𝐼𝑛𝑡𝑒𝑔
𝑔([𝑒𝑖,𝑒 D−𝐴𝑙𝑖𝑔𝑛
𝑖]),(29)
where
EMB
(M3-Embedding [
9
] is adopted due to its eectiveness in capturing semantic meaning) embeds the textual
description
D(𝑖)
𝑔
for game
𝑖
into the numerical semantic space to obtain
𝑒D
𝑖
,
𝑀𝐿 𝑃 D−𝐴𝑙𝑖𝑔𝑛
is a Multilayer Perceptron
[
57
] that aligns
𝑒D
𝑖
from the semantic space with
𝑒𝑖
from the original game representation space, and
𝑀𝐿 𝑃 D−𝐼𝑛𝑡𝑒𝑔
𝑔
updates the game representation
𝑒𝑖
by integrating
𝑒D−𝐴𝑙𝑖𝑔𝑛
𝑖
, encapsulating the LLM-derived knowledge about the game
(with the MLP depth set to 2 by default in this study). We provide an example in Appendix B(Fig. 8) that specically
shows how to generate a description for a game following the above steps.
6.2.2 Preference-informed Player Description Generation. Furthermore, PRG leverages the meticulously generated
game descriptions
{D(𝑖)
𝑔}𝑖∈I
to construct personalized prompts aimed at deeply exploring players’ preferences by
reasoning from the comparison between the dwelling time and the average ratings of games. Specically, PRG designs
a personal prompt for each player, which includes the descriptions of its historical games, the personal interest of this
player in these games (represented by the normalized dwelling time
𝑡𝑢,𝑖
) and the global interest (represented by the
normalized average rating
𝑟𝑖
). By explicitly instructing the LLM to compare personal and global interests as the
primary focus, PRG compels the LLM to extract and highlight the most relevant information that reects the player’s
unique preferences from the previously generated high-quality game descriptions.
It is worth noting that, since the rating and dwelling time obtained in Equation 14 have been carefully mapped to
follow a standard normal distribution, they can be directly compared and serve as quantitative indicators of personal
preference. This enables the LLM to interpret and understand these features more eectively.
Manuscript submitted to ACM

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Formally, the structure of the input player prompt 𝑃𝑝for player-description generation is outlined as follows:
P(𝑢)
𝑝=𝑓𝑝([𝑓ℎ𝑔(D(𝑖)
𝑔, 𝑡𝑢,𝑖, 𝑟 𝑖)]), 𝑖 ∈ I(𝑢),(30)
where
𝑓ℎ𝑔
combines the generated game description
D(𝑖)
𝑔
with both the normalized dwelling time
𝑡𝑢,𝑖
and average
rating
𝑟𝑖
;
𝑓𝑝
integrates all the historical games of player
𝑢
and explicitly requires the language model LLM to infer the
player’s personal preferences by comparing time and average rating based on our analysis detailed in Section 5.3 and
the transformed data obtained in Section 6.1. Then, with the help of LLM, we obtain the description for each player
𝑢
by:
D(𝑢)
𝑝=LLM(P(𝑢)
𝑝),(31)
where
D(𝑢)
𝑝
indicates the textual description of player
𝑢
, emphasizing the personal interest of the player. In this context,
we also utilize the LLM Qwen2.5 [81] to generate these descriptions.
Similar to Equation 29, we use a state-of-the-art embedding model
EMB
(i.e., M3-Embedding [
9
]) to integrate the
preference-informed player description D(𝑢)
𝑝into the player representation by:
𝑒D
𝑢=EMB(D(𝑢)
𝑝),
𝑒D−𝐴𝑙𝑖𝑔𝑛
𝑢=𝑀𝐿 𝑃 D−𝐴𝑙𝑖𝑔𝑛 (𝑒D
𝑢),
𝑒𝑢=𝑀𝐿𝑃 D−𝐼𝑛𝑡 𝑒𝑔
𝑝([𝑒𝑢,𝑒 D−𝐴𝑙𝑖𝑔𝑛
𝑢]).(32)
Appendix B(Fig. 9) provides a specic example illustrating how to generate a description for a player following the
above steps.
6.3 Overview of CPGRec+
In summary, the two newly introduced modules (PER and PRG) attempt to bridge the gap resulting from our proposed
model CPGRec’s insucient consideration of the disparities of observed player-game historical interactions, where
disparities refer to the dierent importance of each player’s interactions in reecting this player’s personal interest.
To solve this problem, both PER and PRG attempt to better model the personal preference of each player by deeply
capturing the player’s interest or disinterest exhibited in each historical interaction. Methodologically, PER renes
the modeling of player-game interactions by reweighting edges based on the comparison between personal interest
and global interests, whereas PRG leverages LLMs to generate more informative game and player representations by
explicitly guiding the model to reason from both the personal and global interests as key factors in preference inference.
Although both the PER and PENR modules reweight the player-game edge weights, the newly proposed PER serves as
an accuracy-driven module, whereas the PENR functions as a diversity-driven module. Collectively, these two modules
facilitate balance-oriented recommendations through the formulation of a balance-oriented edge weight dened as:
Θ𝑅𝑊𝑇
𝑒(𝑒)=Θ𝑃𝑟
𝑒(𝑒) + Θ𝑃𝑜
𝑒(𝑒),(33)
which is employed in Equation 7to replace the former edge weight Θ𝑃𝑜
𝑒(𝑒).
The newly introduced PRG module, by contrast, harnesses the powerful generative and reasoning capabilities of
LLMs, along with their rich knowledge, as a crucial source of supplementary information. This information is seamlessly
integrated into the representations of both games and players through Equations 29 and 32, ensuring that both global
interests and the personal interests are eectively captured within the game and player representations,
respectively.
Manuscript submitted to ACM

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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 21
As depicted in Fig. 4, the proposed framework, CPGRec+, consists of ve core modules designed to deliver balance-
oriented recommendations for players as follows:
Accuracy-Driven Module (SGC+PER+PRG): SGC module leverages cross-category associations to establish strict
connections among games within the game graph, enhancing accuracy.
By employing a comparison method based on the Fisher distribution and information content, PER captures player
preferences from historical interactions that signicantly indicate the personal preferences of players. Interaction-wise
edge weights are then applied to the player-game graph to rene player modeling. Following a similar insight, PRG
leverages LLMs to enrich player and game representations by incorporating complementary information, specically,
both the players’ average ratings (represent global interests) and the dwelling time (represent personal interests). First,
it prompts LLMs to generate game descriptions that encapsulate global interest. Subsequently, it constructs detailed
player descriptions by inferring personal preferences through a comparative analysis of individual interest and global
interest.
Diversity-Driven Module (CNA+PENR): In contrast to SGC, CNA emphasizes diverse-category neighbors to
strengthen the connectivity of the game graph, promoting diversity. Unlike PER, PENR adjusts the weights of nodes and
edges in the player-game graph based on game popularity, transforming popular games into conduits for disseminating
messages from long-tail games, thereby enhancing diversity.
Comprehensive Module: It harmonizes accuracy and diversity by employing Combined Training with NSR.
Together, these modules enable CPGRec+ to achieve a balance between accuracy and diversity in recommendations.
6.4 Detailed Analysis of CPGRec+
In this section, we conduct a detailed analysis of CPGRec+, including both the validation of the standard normality of
transformed dwelling time and average ratings involved in PER module and a case study for previously proposed PENR
module.
6.4.1 Validation of the Statistical Basis of PER Module. In this section, we employ the Kolmogorov-Smirnov Test for
one sample to validate the ecacy of applying Box-Cox and Z-score transformation in mapping the dwelling time and
average ratings to the standard normal distribution.
Kolmogorov-Smirnov Test (KS Test) for one sample estimates the likelihood that a given sample is drawn from a
specied reference distribution. Specically, the KS Test introduces the KS-statistic, formally dened as:
𝐷𝑛=𝑠𝑢𝑝𝑥|𝐹𝑛(𝑥) − 𝐹(𝑥)|,(34)
where 𝑛is the size of sample, and
𝐹𝑛(𝑥)=#of sample points ≤𝑥
𝑛(35)
is the empirical cumulative distribution function, which measures the distance between the empirical distribution of the
sample and that of the reference distribution, denoted as
𝐹
. According to the Kolmogorov theorem,
√𝑛𝐷𝑛
converges to
the Kolmogorov distribution, whose cumulative distribution is given by
𝐹𝐾(𝑥)=√2𝜋
𝑥
∞

𝑘=1
exp(−(2𝑘−1)2𝜋2
8𝑥2),(36)
which quanties the probability that the given sample originates from the reference distribution.
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22 Xiping Li et al.
In our analysis, the empirical sample consists of the dwelling times and average ratings transformed via Box-Cox
and Z-score transformations, while the reference distribution is the standard normal distribution. The experimental
results are shown in Fig. 5and Table 1. Among the 2,675 Steam video games with varying player dwelling times, we
examine the game Electronic Super Joy as a representative example.
As illustrated in Fig. 5, the mapped dwelling times of players for Electronic Super Joy and the average ratings of
all games closely resemble the standard normal distribution in terms of probability density, providing an intuitive
perspective on the eectiveness of the transformations. Furthermore, as shown in Table 1, the p-values for dwelling
time and average ratings are 0
.
5950 and 0
.
5024, respectively, both of which exceed the commonly used signicance
level of
𝛼=
0
.
05. This indicates that the transformed data are statistically indistinguishable from the standard
normal distribution.
Fig. 5. Illustration of the probability density of dwelling time of players of Electronic Super Joy and average ratings of all video games
mapped by Box-Cox and Z-score transformations, which is intuitively highly close to standard normal distribution.
Table 1. Experimental results of Kolmogorov-Smirnov test.
Feature KS-statistic P-value Size of Sample
Dwelling Time 0.0861 0.5950 76
Average Rating 0.0159 0.5024 2675
6.4.2 Case Study for PENR Module. In our conference paper [
39
], we propose the PENR module, aimed at enhancing
diversity by leveraging popular game nodes to propagate messages for long-tail games. This section includes a case
study of the PENR module to provide a clearer and more intuitive understanding of its functionality.
Consider a simplied scenario with only 2video games and 2players, denoted as
𝑖0, 𝑖1
and
𝑢0, 𝑢1
, respectively. To
show the role of PENR module in amplifying the inuence of long-tail game nodes, we assume that
𝑖0
is a long-tail game,
while
𝑖1
is popular. The existing historical interactions are
(𝑢0, 𝑖0),(𝑢0, 𝑖1),(𝑢1, 𝑖1)
. Let
𝑒(𝑙)
𝑢0, 𝑒 (𝑙)
𝑢1, 𝑒 (𝑙)
𝑖0, 𝑒 (𝑙)
𝑖1
represent the
representations of
𝑢0, 𝑢1, 𝑖0, 𝑖 1
respectively obtained from the
𝑙
-th layer. According to the PENR module’s denition, the
operations of the graph convolutional layers are as follows:
𝑒(𝑙+1)
𝑢1=𝐶𝑢1𝑢1·𝑒(𝑙)
𝑢1+𝑒ℎ𝑛ℎ·𝐶𝑢1𝑖1·𝑒(𝑙)
𝑖1,
𝑒(𝑙+1)
𝑖1=𝑛ℎ·𝐶𝑖1𝑖1·𝑒(𝑙)
𝑖1+𝐶𝑢1𝑖1·𝑒(𝑙)
𝑢1+𝐶𝑢0𝑖1·𝑒(𝑙)
𝑢0,
𝑒(𝑙+1)
𝑢0=𝑛𝑙·𝐶𝑢0𝑖0·𝑒(𝑙)
𝑖0+𝑒ℎ𝑛ℎ𝐶𝑢0𝑖1·𝑒(𝑙)
𝑖1+𝐶𝑢0𝑢0·𝑒(𝑙)
𝑢0,
𝑒(𝑙+1)
𝑖0=𝑛𝑙·𝐶𝑖0𝑖0·𝑒(𝑙)
𝑖0+𝐶𝑢0𝑖0·𝑒(𝑙)
𝑢0,
(37)
Manuscript submitted to ACM

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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 23
where the normalization term is dened as:
𝐶𝑎𝑚𝑏𝑛=1
|𝑁𝑎𝑚||𝑁𝑏𝑛|, 𝑎, 𝑏 ∈ {𝑢, 𝑖 },𝑚, 𝑛 ∈ {0,1},(38)
and
𝑒ℎ=𝜃ℎ𝑜𝑡
𝑒, 𝑛ℎ=𝜃ℎ𝑜𝑡
𝑛, 𝑛𝑙=𝜃𝑐𝑜𝑙𝑑
𝑛
are popularity-guided weights for edges and nodes. Consequently, the
representation for 𝑢1derived from the 3𝑟𝑑 layer could be obtained by recursion of Equation 37, formally denoted as:
𝑒(𝑙+3)
𝑢1=𝐴𝑒 (𝑙)
𝑖0+𝐵𝑒 (𝑙)
𝑖1+𝐶𝑒 (𝑙)
𝑢0+𝐷𝑒 (𝑙)
𝑢1,(39)
where
𝐴=𝑒ℎ𝑛ℎ𝑛𝑙𝐶𝑢1𝑖1𝐶𝑢0𝑖1𝐶𝑢0𝑖0,
𝐵=𝑒ℎ𝑛ℎ𝐶2
𝑢1𝑢1𝐶𝑢1𝑖1+𝑒ℎ𝑛2
ℎ𝐶𝑢1𝑖1𝐶𝑖1𝑖1𝐶𝑢1𝑢1,
+𝑒ℎ𝑛3
ℎ𝐶𝑢1𝑖1𝐶2
𝑖1𝑖1+𝑒2
ℎ𝑛2
ℎ𝐶3
𝑢1𝑖1+𝑒2
ℎ𝑛2
ℎ𝐶2
𝑢0𝑖1𝐶𝑢1𝑖1
𝐶=𝑒ℎ𝑛ℎ𝐶𝑢1𝑖1𝐶𝑢0𝑖1𝐶𝑢1𝑢1+𝑒ℎ𝑛2
ℎ𝐶𝑢1𝑖1𝐶𝑖1𝑖1𝐶𝑢0𝑖1
+𝑒ℎ𝑛ℎ𝐶𝑢1𝑖1𝐶𝑢0𝑖1𝐶𝑢0𝑢0,
𝐷=𝐶3
𝑢1𝑢1+𝑒ℎ𝑛ℎ𝐶𝑢1𝑢1𝐶2
𝑢1𝑖1
+𝑒ℎ𝑛2
ℎ𝐶2
𝑢1𝑖1𝐶𝑖1𝑖1+𝑒ℎ𝑛ℎ𝐶2
𝑢1𝑖1𝐶𝑢1𝑢1.
(40)
To explore the function of the PENR module in enhancing the inuences of long-tail games, we dene the inuence
index 𝐼 𝑁 𝐹 to quantify the inuence of each node on 𝑢1:
𝐼 𝑁 𝐹𝑖0=𝐴
𝐴+𝐵+𝐶+𝐷,
𝐼 𝑁 𝐹𝑖1=𝐵
𝐴+𝐵+𝐶+𝐷,
𝐼 𝑁 𝐹𝑢0=𝐶
𝐴+𝐵+𝐶+𝐷,
𝐼 𝑁 𝐹𝑢1=𝐷
𝐴+𝐵+𝐶+𝐷.
(41)
Table 2. Influence factors.
𝑒ℎ/𝑛ℎ/𝑛𝑙𝐼 𝑁 𝐹𝑖0𝐼 𝑁 𝐹𝑖1𝐼 𝑁 𝐹𝑢0𝐼𝑁 𝐹𝑢1
1/1/1 0.0747 0.3796 0.1966 0.3491
1/1/6 0.3263 0.2764 0.1432 0.2542
1/0.2/1 0.0864 0.2549 0.1922 0.4665
5/1/1 0.0486 0.6439 0.1280 0.1796
5/0.2/1 0.0966 0.3379 0.1912 0.3742
5/0.2/6 0.3908 0.2279 0.1290 0.2523
Based on Equation 41, we conduct the following case study as shown in Table 2by varying the popularity-guided
weights
𝑛ℎ, 𝑛𝑙, 𝑒ℎ
. It is worth noting that
𝑛ℎ=𝑛𝑙=𝑒ℎ=
1means that the PENR module is removed. From the results,
there are several observations:
•
Eectiveness of Popularity-guided Reweighting: Compared to the scenario without PENR module (i.e.
𝑒ℎ/𝑛ℎ/𝑛𝑙=
1
/
1
/
1), the
𝐼 𝑁 𝐹𝑖0
with PENR module (i.e.
𝑒ℎ/𝑛ℎ/𝑛𝑙=
5
/
0
.
2
/
6) signicantly increases from 0
.
0747
to 0.3908, which proves the eectiveness of popularity-guided reweighting.
Manuscript submitted to ACM

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24 Xiping Li et al.
•
Increase of Long-Tail Game Node Weight: The setup
𝑒ℎ/𝑛ℎ/𝑛𝑙=
1
/
1
/
6enlarges the eectiveness of long-tail
game node
𝑖0
by amplifying its node weight, resulting in an increase in the inuence index
𝐼 𝑁 𝐹𝑖0
to 0
.
3263,
while concurrently reducing the inuence index of the popular game node 𝑖1by approximately 27.19%.
•
Decrease of Popular Game Node Weight: The setup
𝑒ℎ/𝑛ℎ/𝑛𝑙=
1
/
0
.
2
/
1reduces the node weight of the
popular game
𝑖1
, thereby signicantly constraining its inuence; consequently,
𝐼 𝑁 𝐹𝑖1
decreases by about 32
.
85%,
while the inuence index of all other nodes increase.
•
Increase of Popular Game Edge Weight: The setup
𝑒ℎ/𝑛ℎ/𝑛𝑙=
5
/
1
/
1enlarges the weight of outgoing edges
from the popular game node
𝑖1
, thereby enhancing its capacity to propagate messages. This transformation
leads to an expansion of the inuence of the popular game 𝑖1.
•
Combined Eect of Increasing Popular Game Edge Weight and Decreasing Popular Game Node
Weight: The setup
𝑒ℎ/𝑛ℎ/𝑛𝑙=
5
/
0
.
2
/
1further reduces
𝑛ℎ
compared to the last setup, thereby limiting the
eectiveness of 𝑖1, and resulting in a decrease in 𝐼 𝑁 𝐹𝑖1by 47.52%.
The aforementioned examples intuitively illustrate and substantiate the importance of the popularity-guided weight
introduced by the PENR module. Together, these mechanisms enhance the inuence of long-tail games while simultane-
ously mitigating the predominance of popular games.
7 Experiments
In this section, we conduct comprehensive experiments to evaluate the performance of CPGRec+, focusing on its
accuracy and diversity.
7.1 Experimental Setup
7.1.1 Dataset. Building upon our previous conference research [
39
], we have evaluated the performance of CPGRec+
using experimental results derived from the Steam dataset, as contributed by Mark et al. [
49
] and Yang et al. [
82
]. Table
3succinctly presents the basic statistics of the Steam dataset, oering a clear overview of its features.
Table 3. Statistics of the Steam dataset.
Dataset Steam
# Players 3,908,744
# Games 2,675
# Interactions 95,208,806
# Genre 22
# Developer 1,170
# Publisher 688
In accordance with the partition setting of previous studies [
39
], the observed historical interactions are split into
train, valid, and test sets, following a ratio of 0.8/0.1/0.1.
7.1.2 Evaluation Metrics. For accuracy assessment, we employ NDCG@K, Recall@K, Hit@K, and Precision@K as our
metrics; for diversity, in addition to Coverage@K and Entropy@K, which were employed in our previous conference
Manuscript submitted to ACM

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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 25
work [39], we introduce Conventional Coverage@K, dened as:
Conventional Coverage@𝐾=| ∪𝑢∈U I(𝑢)
𝐾|
|I| ,(42)
where
I(𝑢)
𝐾
is the top-K recommended list for each user
𝑢∈ U
, and
𝐾
takes values in
{
5
,
10
}
. It is crucial to note
that Coverage@K and Entropy@K evaluate individual diversity, whereas Conventional Coverage@K assesses global
diversity. Specically, Coverage@K measures diversity across genres, developers, publishers, and their combined total
in the top-
𝐾
recommendations; Entropy@K evaluates the entropy of recommendation lists based on these categories;
Conventional Coverage@K assesses the variety of unique video games present in the top-K recommendations.
7.2 Baselines
In order to thoroughly assess the performance of CPGRec+, we carried out comparisons against a variety of established
recommender systems.
In terms of accuracy, we compared CPGRec+ with two models: the widely-used GNN-based model LightGCN [
25
],
and SCGRec [82], which leads accuracy-oriented game recommender systems.
In terms ofdiversity, CPGRec+ is evaluated in comparison to ve distinguished diversity-focused models: MMR [
7
],
EDUA [41], DDGraph [84], DGCN [95], and DGRec [83].
In terms of balance, EXPLORE [
13
] and the prior work CPGRec[
39
] were introduced as trade-o-focused baselines.
7.3 Performance Evaluation
Table 4. Accuracy-focus performance comparison of dierent accuracy-, diversity- and balance-driven recommender systems in terms
of NDGC, Recall, Hit, Precision.
Methods NDGC Recall Hit Precision
@5 @10 @5 @10 @5 @10 @5 @10
Accuracy-driven
Methods
LightGCN 0.1861 0.2100 0.2452 0.3174 0.2849 0.3784 0.0637 0.0447
SCGRec 0.4351 0.4660 0.5385 0.6311 0.6519 0.7535 0.1508 0.0969
Accuracy-focused CPGRec 0.4796 0.5000 0.5746 0.6387 0.6983 0.7659 0.1625 0.0989
Accuracy-focused CPGRec+ 0.4805 0.5029 0.5768 0.6413 0.6993 0.7674 0.1637 0.0993
Diversity-driven
Methods
MMR 0.3259 0.3871 0.2768 0.3420 0.3522 0.4302 0.0684 0.0623
EDUA 0.3839 0.4072 0.4746 0.5545 0.5808 0.6936 0.1149 0.0826
DDGraph 0.3997 0.4298 0.4949 0.5883 0.6059 0.7094 0.1399 0.0894
DGCN 0.3732 0.4025 0.4536 0.5523 0.6056 0.7123 0.1129 0.0806
DGRec 0.3546 0.3982 0.4293 0.5434 0.5791 0.7126 0.1041 0.0786
Diversity-focused CPGRec 0.4285 0.4547 0.5168 0.5990 0.6390 0.7292 0.1469 0.0922
Diversity-focused CPGRec+ 0.4312 0.4570 0.5221 0.6029 0.6439 0.7322 0.1485 0.0930
Balance-driven
Methods
EXPLORE 0.4126 0.4381 0.5002 0.5895 0.6187 0.7177 0.1398 0.0916
CPGRec(trade-o framework) 0.4320 0.4547 0.5168 0.5990 0.6390 0.7292 0.1469 0.0922
CPGRec+(trade-o framework) 0.4422 0.4691 0.5347 0.6192 0.6590 0.7473 0.1538 0.0967
An exhaustive comparison of CPGRec+ against various baseline models is detailed in Table 4and Table 5. The
superior and runner-up outcomes are distinctively highlighted in bold and underlined text, respectively. Drawing from
these experimental ndings, we can distill the following insights:
•
Superiority of the Proposed Method w.r.t Accuracy or Diversity. (1) CPGRec+, in its accuracy-focused
form, outperforms all other accuracy-centric methods across all metrics. (2) Similarly, the diversity-focused
CPGRec+ surpasses all diversity-centric approaches except for CPGRec, which serves as a variant of CPGRec+
by removing the two newly proposed modules (both PER and PRG), on every metric. Moreover, CPGRec+
Manuscript submitted to ACM

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26 Xiping Li et al.
Table 5. Diversity-focus performance comparison of dierent accuracy-, diversity- and balance-driven recommender systems in terms
of Conventional Coverage (CC), Coverage (C) and Entropy (E).
Methods CC C(genre) C(developer) C(publisher) C(total) E(genre) E(developer) E(publisher)
@5 @10 @5 @10 @5 @10 @5 @10 @5 @10 @5 @10 @5 @10 @5 @ 10
Accuracy-driven
Methods
LightGCN 0.2373 0.2848 2.2839 3.2916 3.0915 5.1401 2.2818 4.3852 7.6572 12.8169 0.9409 0.9011 0.7030 1.4600 1.4820 1.2652
SCGRec 0.2416 0.2785 2.3871 3.3754 3.1898 5.4122 2.3708 4.1812 7.9477 12.9688 0.9766 0.9118 0.7297 1.4773 1.5383 1.2802
Accuracy-focused CPGRec 0.2685 0.3188 2.7509 4.3680 3.1800 6.2738 2.5783 4.8981 8.5092 15.5399 1.0455 1.0926 0.7812 1.7702 1.6470 1.5340
Accuracy-focused CPGRec+ 0.2757 0.3291 2.7491 4.3640 3.1768 6.2719 2.5674 4.8931 8.4933 15.5290 1.0404 1.0899 0.7692 1.7685 1.6431 1.5328
Diversity-driven
Methods
MMR 0.2719 0.3284 2.5928 3.8183 3.5418 5.4192 3.0945 4.8985 9.2291 14.1360 1.0783 1.0708 0.7778 1.7142 1.6190 1.4657
EDUA 0.2496 0.2925 2.1285 3.2491 3.2595 5.4325 2.3465 5.2056 7.7345 13.8872 0.9900 0.9821 0.7077 1.5624 1.4660 1.3385
DDGraph 0.2871 0.3033 2.3905 3.7699 3.0540 5.4324 2.6843 4.6402 8.1288 13.8425 0.9956 0.8848 0.8078 1.4931 1.5679 1.4212
DGCN 0.2602 0.3090 2.4069 4.2905 3.2863 5.8637 2.4981 3.9211 8.1913 14.0753 1.0133 1.0086 0.7301 1.5127 1.5708 1.3987
DGRec 0.2964 0.3047 2.5203 3.8800 3.6386 5.5896 2.6931 4.8046 8.8520 14.2742 1.0708 1.0633 0.7719 1.7013 1.6061 1.4549
Diversity-focused CPGRec 0.3173 0.3740 3.0929 4.7109 3.8044 6.9557 3.2404 5.9743 10.1377 17.6409 1.2602 1.1937 0.9054 2.1125 2.0886 1.6275
Diversity-focused CPGRec+ 0.3252 0.3845 3.0915 4.6929 3.7941 6.9465 3.2352 5.9678 10.1208 17.6072 1.2571 1.1921 0.9009 2.1083 2.0848 1.6254
Balance-driven
Methods
EXPLORE 0.2952 0.3508 2.6180 4.2931 3.3212 5.9811 2.6833 5.2119 8.6225 15.4861 1.0622 1.1423 0.8942 1.4428 1.7854 1.5612
CPGRec(trade-o framework) 0.2963 0.3515 2.8635 4.5731 3.7032 6.8842 2.6864 5.2506 9.2530 16.7079 1.0971 1.1697 0.9070 1.8828 1.9418 1.6297
CPGRec+(trade-o framework) 0.3047 0.3611 2.7820 4.3553 3.6859 6.6449 2.7582 5.2616 9.2261 16.2618 1.0835 1.1873 1.0680 1.8666 1.9095 1.6171
consistently outperforms CPGRec in Conventional Coverage due to its personal-preference-centeredness, which
mitigates the dominance of popular games and enhances global diversity while restricting the individual
diversity of each recommended list, as indicated by Coverage and Entropy. In essence, these results underscore
CPGRec+’s superior performance in both accuracy and diversity.
•
Superiority of the Proposed Method w.r.t Capability of Flexible Adjusting. CPGRec+ along with CPGRec
have outperformed the SOTA in the domains of accuracy, diversity, and balance, respectively. This demonstrates
that the supposed dichotomy between accuracy and diversity is not inevitable. A well-calibrated recommender
system like CPGRec+ can eectively harmonize these two aspects, precisely capturing user preferences while
delivering a diverse selection that enriches the player experience.
•
Double-Edged Nature of Graph Convolutional Smoothness. (1) On one hand, eectively leveraging
smoothness encodes category information into the representations of video games through graph structural
transformations, thereby enhancing accuracy. This strategy is evident in SCGRec and both the SGC and CNA
modules of CPGRec+; (2) On the other hand, the smoothness resulting from stacking GCN layers reduces
the distinctiveness of representations between neighboring games, which in turn aects the improvement of
accuracy, as seen in diversity-driven baselines like DGRec. The stark contrast between the aforementioned two
aspects is not surprising, as the latter’s design motivation is diversity rather than accuracy.
On top of that, by comparing CPGRec+ and CPGRec, it is worth noting that our newly introduced modules (PER and
PRG) show signicant empowerment of accuracy. Detailed analysis is deferred to the following ablation study presented
in Section 7.4.
7.4 Ablation Study
Within this segment, we conduct an ablation analysis on CPGRec+ by methodically removing each of its ve modules.
For the SGC module, we introduce two variants: one involves the complete removal of the SGC module, while the other
substitutes strict connections with raw ones. For the PER module, we nullify its eect by assigning a preference-informed
weight of 0 to each edge within the player-game graph. Our observations from the experimental results, presented in
Table 6, are as follows:
•
Eectiveness of Existing Four Modules. The observations from removing each of the existing four modules
(SGC, CNA, PENR, and NSR), as presented in our conference work [
39
], are consistent with the results from that
publication, so a redundant analysis is omitted here. However, it is important to note that these results not only
Manuscript submitted to ACM

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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 27
validate the ecacy of the existing four modules but also conrm the compatibility of the newly introduced
PER and PRG modules with them.
•
Eectiveness of PER Module w.r.t Accuracy. The removal of the PER module signicantly degraded CP-
GRec+’s performance across all accuracy metrics, underscoring PER’s pivotal role in tailoring recommendations
to player interests. This indicates that PER eectively provides a granular modeling of a player’s preferences by
contrasting the personal interest in each historical record with the global interests of the public.
•
Eectiveness of PRG Module w.r.t Accuracy. Similarly, removing PRG results in a signicant decline in the
accuracy of CPGRec+. This is expected, as the rich knowledge embedded in LLMs enables the generation of
more comprehensive game descriptions beyond the dataset. Additionally, the reasoning capabilities of LLMs not
only identify deep commonalities among games from multiple perspectives but also infer a player’s personal
preferences, eectively constructing a more informative player prole.
•
Both PER and PRG Enable Broader Game Recommendations. The removals of the PER and PRG both
result in a modest enhancement in Coverage@10 relative to CPGRec+, which aligns with the anticipated
trade-o between accuracy and diversity observed in numerous empirical studies [
10
,
28
,
36
,
50
,
65
]. Conversely,
a marked reduction is evident in Conventional Coverage. This nding highlights the critical role of comparing
individual player preferences with public interests, which are employed in both PER and PRG, broadly enabling
a wider range of games to be recommended.
Table 6. Ablation study. We show CPGRec+’s performance when removing each of the modules.
Method Recall@5 Recall@10 Hit@5 Hit@10 Precision@5 Precision@10 C(total)@5 C(total)@10 CC@5 CC@10
CPGRec+ (trade-o framework) 0.5347 0.6192 0.6590 0.7473 0.1538 0.0967 9.2261 16.2618 0.3047 0.3611
w/o SGC (1st accuracy-driven module) 0.5284 0.6114 0.6506 0.7404 0.1508 0.0947 9.7154 17.3755 0.3076 0.3654
CPGRec+ (SGC with raw connections) 0.5275 0.6114 0.6502 0.7407 0.1499 0.0941 8.4256 15.6349 0.2959 0.3490
w/o PER (2nd accuracy-driven module) 0.5277 0.6119 0.6498 0.7406 0.1501 0.0946 9.2041 16.7189 0.2924 0.3468
w/o PRG (3rd accuracy-driven module) 0.5252 0.6101 0.6481 0.7402 0.1498 0.0944 9.0745 16.5235 0.2895 0.3402
w/o CNA (1st diversity-driven module) 0.5311 0.6106 0.6545 0.7393 0.1518 0.0947 8.3133 14.3171 0.2799 0.3318
w/o PENR (2nd diversity-driven module) 0.5794 0.6376 0.7055 0.7629 0.1630 0.0989 8.7021 16.3384 0.3148 0.3765
w/o NSR (comprehensive module) 0.5131 0.6018 0.6333 0.7330 0.1491 0.0924 7.8537 13.2116 0.2832 0.3348
Fig. 6. Parameter sensitivity on 𝛼, which is the significance level applied in PER module.
7.5 Parameter Sensitivity
To evaluate the eectiveness of
𝛼
, we conducted experiments by varying its value within the range
[
0
.
001
,
0
.
01
,
0
.
05
,
0
.
1
,
0
.
2
,
0
.
4
]
.
For accuracy assessment, we utilized Recall@5 and Precision@5; for diversity evaluation, we employed Coverage@5 and
Conventional Coverage@5. The experimental results, presented in Fig. 6, demonstrate that
𝛼
signicantly inuences
both accuracy and diversity, with optimal performance observed at moderate values of 𝛼.
For accuracy, the analysis reveals two distinct trends:
Manuscript submitted to ACM

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28 Xiping Li et al.
Input of CPGRec+
(Raw Features)
Spectral Energy
Distribution
Output of CPGRec+
(w/o PER)
Spectral Energy
Distribution
Smoothness ofOutput Representations of CPGRec+ (w/o PER)
Output of CPGRec+
(w/ PER)
Spectral Energy
Distribution
Smoothness ofOutput Representations of CPGRec+ (w/ PER)
Smoothness of Players’ and
Games’ Raw Features
Node Feature
Node FeatureNode Feature
2
1
0
-1
-2
2
1
0
-1
-2
2
1
0
-1
-2
0.2
0.15
0.1
0.05
0.0
0.45
0.3
0.15
0.0
0.2
0.15
0.1
0.05
0.0
1.61.20.8
0.40.0 2.0
1.61.20.8
0.40.0 2.0
1.6
1.20.80.4
0.0 2.0




(,)
(,)

(,)
Fig. 7. Spectral energy distribution of node representations on the player-game
game. The representations on the le figure is the raw feature of players and games,
and those on the right are respectively processed by CPGRec+ w/o PER and w/
PER.
(1)
When
𝛼
is small (specically,
𝛼∈ {
0
.
001
,
0
.
01
,
0
.
05
}
), both Recall and Precision increase as
𝛼
rises. Notably, a
fairly small
𝛼
imposes strict conditions for using the PER module, similar to not applying it, while increasing
𝛼
moderately broadens the scope for preference-informed weights. This underscores the critical role of
𝛼
in
enhancing recommendation accuracy.
(2)
However, as
𝛼
grows larger (
𝛼∈ {
0
.
05
,
0
.
1
,
0
.
2
,
0
.
4
}
), both Recall and Precision decline. A larger
𝛼
makes PER’s
conditions too lenient, including less reliable preferences, which adds noise and reduces accuracy.
For diversity, the metrics Coverage and Conventional Coverage behave dierently as 𝛼changes:
(1)
As
𝛼
increases, Coverage rst decreases, then rises. This diers from accuracy trends, showing a trade-o:
wider-ranging recommendations can improve diversity but may lower accuracy.
(2)
Meanwhile, Conventional Coverage rises initially with
𝛼
, then slightly drops, similar to Recall and Precision.
This occurs because the PER module uses dwelling time and game ratings to better model players and games,
making recommendations more unique and globally diverse.
7.6 Intuitive Understanding of the Functionality of PER
In this section, we provide a detailed explanation to enhance understanding of the PER module’s role within CPGRec+.
We use a subgraph from the player-game bipartite graph as an illustrative example. This subgraph consists of 50 nodes
representing players or games, with edges denoting historical interactions. Each node is assigned a 1-dimensional
simulated feature. To demonstrate CPGRec+’s functionality, we compare it to a variant without the PER module, focusing
on how each processes input features. Fig. 7presents the subgraph details, including spectral energy distributions as a
Manuscript submitted to ACM

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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 29
quantitative supplement. The spectral energy distribution is dened as:
𝑓𝐺(Λ,𝑋 )=𝑓𝐺(𝜆1, 𝑋 ), 𝑓𝐺(𝜆2, 𝑋 ),· · · , 𝑓𝐺(𝜆N, 𝑋 )(43)
=he𝑥𝑇
1e𝑥1
ÍN
𝑖=1e𝑥𝑇
𝑖e𝑥𝑖
,e𝑥𝑇
2e𝑥2
ÍN
𝑖=1e𝑥𝑇
𝑖e𝑥𝑖
,·· · ,e𝑥𝑇
Ne𝑥N
ÍN
𝑖=1e𝑥𝑇
𝑖e𝑥𝑖i,(44)
where
e𝑥𝑖
is the dot product of the
𝑖
-th normalized eigenvector
𝑢𝑖
dened as Equation 48 and the nodes’ feature
𝑋∈ RN
.
Smaller
𝜆𝑖
values correspond to low-frequency components, and vice versa. The smoothness of
𝑋
is characterized by
the spectral energy distribution’s emphasis on low-frequency parts: higher
𝑓𝐺(𝜆𝑖, 𝑋 )
values for smaller
𝜆𝑖
indicate
greater smoothness, while higher weights in mid to high frequencies suggest less smoothness.
The left gure in Fig. 7illustrates the raw feature smoothness, showing distinct node features with non-uniform
colors. The spectral energy distribution suggests a signicant distribution across low and mid frequencies.
The right gures in Fig. 7compare representations processed by CPGRec+ without and with the PER module, with
observations as follows:
(1) The rst row shows that without the PER module, representations exhibit over-smoothness, as indicated by uniform
node colors (e.g., red) and concentrated low-frequency spectral energy. This aligns with Section 5.3’s analysis, where
neglecting interaction disparities leads to over-smoothness due to graph convolutional layers’ inherent smoothness.
(2) Conversely, the second row demonstrates that incorporating the PER module helps CPGRec+ avoid over-
smoothness, evident from varied node colors. The spectral energy distribution retains high-frequency components,
indicating that CPGRec+ captures preference-informed personal interest and disinterest, extending beyond a low-pass
lter to address personalized player needs.
8 Conclusion
To address the accuracy-diversity trade-o in video game recommendation, we identify two key limitations in GCN-
based models: oversmoothing, which homogenizes recommendations, and the neglect of interaction-level disparities,
which weakens personalization. This motivates enhancements to our prior framework, CPGRec, resulting in CPGRec+.
Motivated by these ndings, we proposed CPGRec+, which introduces two novel modules to address interaction
disparities and balance competing objectives. The Preference-informed Edge Reweighting (PER) module leverages
dwell time and ratings—transformed via Box-Cox and Fisher distribution linkages—to dierentiate player interests and
disinterests, mitigating over-smoothing by reweighting edges with information-theoretic condence scores. Comple-
menting this, the Preference-informed Representation Generation (PRG) module harnesses LLMs to synthesize
game descriptions enriched by global ratings and infer personalized player preferences through comparative reasoning
to generate player descriptions, rening embeddings with semantic insights. Experiments on real-world data demon-
strated CPGRec+’s superiority: it achieves signicantly better accuracy than state-of-the-art accuracy-focused models
while maintaining diversity metrics comparable to specialized baselines. Ablation studies underscore the necessity of
PER and PRG, with their removal causing signicant accuracy drops and reduced global coverage.
Future work will explore dynamic graph updates to handle evolving player preferences and cold-start scenarios.
Additionally, integrating LLMs for cross-modal game understanding could further bridge semantic gaps, advancing
toward truly adaptive recommendation ecosystems.
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9 Appendices
A Introduction to Smoothness from a Spectral Perspective
From a spectral perspective, a graph learning task can be viewed as a graph signal processing task, where Graph Neural
Networks (GNNs) act as lters. Given a specic homogeneous graph
G
with
N
nodes, denoted as
V={𝑣1, 𝑣2, . . . , 𝑣 N}
,
whose edges are represented by an adjacency matrix 𝐴=[𝑎𝑖𝑗 ]N×N, where
𝑎𝑖 𝑗 =





1if there is an edge between 𝑣𝑖and 𝑣𝑗,
0otherwise,
(45)
these nodes are characterized by
𝑑
features, represented as
X=[𝑋1, 𝑋2, . . . , 𝑋𝑑] ∈ RN×𝑑
. Each column
𝑋𝑗=
[𝑥𝑗1, 𝑥 𝑗2, . . . , 𝑥 𝑗N]𝑇
, for
𝑗∈ {
1
,
2
, . . . , 𝑑 }
, constitutes a graph signal dened on
G
, with
𝑥𝑗𝑖 ∈R
denoting the
𝑗
-th
feature value of node 𝑣𝑖.
The Laplacian matrix 𝐿is a fundamental element in analyzing graph structures and is dened as:
𝐿=𝐷−𝐴, (46)
Manuscript submitted to ACM

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34 Xiping Li et al.
where
𝐷
is the diagonal degree matrix with
𝐷𝑖𝑖 =ÍN
𝑗=1𝐴𝑖 𝑗
. Being real and symmetric,
𝐿
admits an orthogonal
diagonalization:
𝐿=UΛU𝑇=U

𝜆1
𝜆2
...
𝜆N

U𝑇,(47)
where {𝜆𝑖}N
𝑖=1are the eigenvalues of 𝐿, satisfying 𝜆1≤𝜆2≤ ··· ≤ 𝜆N, and
U=[𝑢1, 𝑢2, . . . , 𝑢N](48)
is the matrix whose columns are the normalized eigenvectors of 𝐿.
Eigenvalues carry rich semantic information, bridging the spectral and spatial domains. Specically, eigenvectors
corresponding to small eigenvalues represent low-frequency components of the graph signal, meaning the signal varies
slowly across the graph, which results in neighboring nodes having similar feature values, thus indicating greater
smoothness.
Based on these denitions, the general formulation of a GNN is given by:
𝑥out =U𝑓(Λ)U𝑇𝑥in,(49)
where
𝑥in
and
𝑥out
denote the input and output graph signals, respectively. The function
𝑓(Λ)
represents the GNN’s
frequency response function, serving as the convolutional kernel. By designing dierent
𝑓(Λ)
, researchers develop
various GNN-based models tailored to specic tasks.
For instance, in the Graph Convolutional Network (GCN), a widely used GNN model, the frequency response function
is dened as:
𝑓(Λ)=𝜃(𝐼−Λ),(50)
which simplies to
𝑓(Λ)=𝐼−Λ
when
𝜃=
1. This formulation highlights the low-pass nature of GCNs, as the kernel
amplies low-frequency signals while suppressing high-frequency ones. Since emphasizing low-frequency components
in the spectral domain increases the similarity of feature representations between neighboring nodes in the spatial
domain, this accounts for the smoothness property observed in GCNs.
B Prompts for Generating Descriptions
This section provides two examples, which show how to generate descriptions for a game and a player, respectively.
Specically, Fig. 8shows the process of generating a description for the game Ducati World Championship, whose
average rating on the scale 100 is 35. Both Game Instruction and Game Prompt are input to the LLMs, which
accordingly outputs the Game Description for Ducati World Championship. Fig. 9shows how to generate a description
for a player who has played three games whose ID=40, 79, and 456, respectively. Similarly, both Player Instruction
and Player Prompt are input to the LLMs, which outputs Player Description.
Received 20 February 2007; revised 12 March 2009; accepted 5 June 2009
Manuscript submitted to ACM

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CPGRec+: A Balance-oriented Framework for Personalized Video Game Recommendations 35
You will serve as an assistant with rich knowledge about the video games released on Steam platform, who are required to providea description
possessing the most key information for each video game. I will provide you with the title of video game, as well as the average rating by players on it.
Here are some instructions:
1. The provided information of video game is in the form of a JSON string that contains its title and average rating:
{"title": "the title of the video game",
"average rating": "the average rating (100-scale) of historical players on the video game",
"supplementary information": "supplementary information of the video game, including its price(US dollar) and released time(Year-
Month-Day), (price=0 indicates this game is free)}
Requirements:
1. Please provide your answer in a JSON format, following this structure:
{"description": "the most valuable information as a description for the video game, taking both its inherent information and the plays"
average rating on it as important factors into consideration",
"reasoning": "briefly explain your reasoning for the description taking average rating into account"}
2. Please ensure that the "description" is no longer than 500 words.
3. You are not required to include the information about the developer, publisher, price and released time into the description.
4. Please ensure that the "reasoning" is no longer than 200 words.
5. Please do not provide any text within your answer in any form out of JSON string.
6. Your answer must be in English.
7. If the title of video game is null, just leave each term of your answer "None" Game Instruction
{"title": "Ducati World Championship",
"average rating": "35",
"supplementary information": "its price is 4.99 dollars and released time is 2007-09-21"} Game Prompt
LLMs
{"description": "Ducati World Championship is a motorcycle racing simulation game released in 2007. Players can experience the thrill of
racing with Ducati motorcycles in various tracks. However, it has received mixed reviews from players, with an average rating of 35 out of
100, indicating that it may not fully meet the expectations of all players.",
"reasoning": "The game's average rating of 35 suggests that it has some issues that players find unsatisfactory, such as gameplay
mechanics, graphics, or overall experience. Despite its historical significance and the excitement of motorcycle racing, the low rating
implies that players may face challenges or disappointments while playing.”} Game Description
Fig. 8. An example of generating a game description.
Player Instruction
LLMs
Player Description
You will serve as an assistant to profile a player’s personal interest based on meticulous comparisonbetween his or her personal interest and global interest, and your rich knowledge about the video games. I will provide you
with the historical gaming records of each player along with his or her personal interest for each according game and the global interest, which represents the interest of general players.
Here are some instructions:
1. The provided information of this player is in the form of a JSON string:
{"information of historical games": "the historical gaming records of a player"},
2. To be more detailed, the aforementioned historical records of a player is in the form of a JSON string:
{"historical game i": {"description": "descriptionfor game i", "reasoning": "explanation for the generation of description for game i",
"personal interest": "a float number represents the personal interest of this player for game i, which follows the standard normal distribution", (A higher value indicates a greater degree of personal interest)."
"global interest": "a float number represents the global interest of general players for game i, which follows the standard normal distribution", (A higher value indicates a greater degree of personal interest)."}
{"historical game j": {... (which is the same as the aforementioned case of game i)}}, ...(Similarly, all the video games played by this player will be included)}
Requirements:
1. Please provide your answer in a JSON format, following this structure:
{"description": "the most valuable description for this player based on meticulous comparison between his or her personal interest and global interest along with your knowledge about the historical video games",
"reasoning": "briefly explain your reasoning for the description, taking the meticulous person-globality comparison as the most important factor"}
2. Please ensure that the "description" is no longer than 200 words.
3. Please ensure that the "reasoning" is no longer than 100 words.
4. Please do not provide any text within your answer in any form out of JSON string.
5. Your answer must be in English.
6. As for the comparison between this player’s personal interest and the general players’ global interest: Apersonal interest significantly
larger than global interest well reflects this particular player’s personal interest, while one smaller than global interest obviously shows his or her disinterest.
The knowledge of historical games that this player has shown a significant personal interest in serves as more crucial information for the profiling of this player,
in contrast, the information of games played that this player has shown witnessed disinterest also effectively reflects the personal preference of this player from an opposite side.
{"description": "This player exhibits a strong personal interest in first-person shooter games, particularly those with a focus on teamwork, strategy, and customization. Team Fortress 2, with its vibrant characters
and humorous dialogue, resonates well with the player's preferences, as evidenced by a personal interest score of 2.1, which is higher than the global interest score of 1.6. The player also shows a keen interest
in games like Loadout, which offers a blend of strategy and action, with a personal interest score of 0.3, despite a lower global interest score of -0.9.",
"reasoning": "The player's personal interest in Team Fortress 2 and Loadout, both first-person shooter games with elements of teamwork, strategy, and customization, supports the observation that the player
prefers this genre. The higher personal interest compared to global interest suggests a strong individual preference for these types of games."}
Player Prompt
Fig. 9. An example of generating a player description.
Manuscript submitted to ACM