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Complex & Intelligent Systems
https://doi.org/10.1007/s40747-022-00873-9
ORIGINAL ARTICLE
Evolutionary game analysis of three parties in logistics platforms
and freight transportation companies’ behavioral strategies
for horizontal collaboration considering vehicle capacity utilization
Shuai Deng1,2 ·Duohong Zhou1·Guohua Wu2·Ling Wang3·Ge You4,5
Received: 16 January 2022 / Accepted: 4 September 2022
© The Author(s) 2022
Abstract
In China, logistics platforms are an effective way to solve vehicle capacity utilization using information sharing. However, most
logistics platforms do not possess operational sustainability due to excessive profit-seeking. To address this problem, conflicts
of interest among freight transportation participants are discussed using a stakeholder approach. A three-player evolutionary
game model (TEGM) is developed to analyze the interactions among freight carriers, freight shippers, and logistics platforms.
Then, the asymptotic equilibrium and evolutionary stability strategies of the three-player game are analyzed. The results
indicate that a high-level positive network externality is the driving force behind the logistics platform’s “high-level service”.
A fairness payment incentive guarantees a “sharing” strategy for freight carriers and shippers. When the high-level positive
network externality is limited and lower than a threshold value, there is no stable equilibrium point in the TEGM. A government
tax incentive cannot change the freight carriers’ and shippers’ strategy to participate in this horizontal collaboration system,
except for the logistics platform’s probability of providing “high-level service”. However, the behavioral strategies of the
freight transportation participants can be changed to achieve the sustainability of freight transportation by reducing the value-
added tax rate through the logistics platform and increasing the high-level positive network externality of the logistics platform
and other participants’ perceived fairness through a payment incentive. Finally, suggestions for regulating the behaviors of
freight transportation participants and promoting the sustainability of freight transportation are discussed.
Keywords Evolutionary game ·Logistics platform ·Freight transportation ·Horizontal collaboration ·Vehicle
capacity utilization
Introduction
The low-capacity utilization of vehicles and empty mileage
leads to a high freight transportation cost [1]. Inefficient
transportation has a negative impact on the environment and
society, which has attracted increasing attention, and many
BGuohua Wu
guohuawu@csu.edu.cn
1School of Safety and Management Engineering, Hunan
Institute of Technology, Hengyang 421001, China
2School of Transportation Engineering, Central South
University, Changsha 410083, China
3Department of Automation, Tsinghua University, Beijing,
China
4School of Management, Jinan University, Guangzhou
510632, China
5Nanfang College Guangzhou, Guangzhou 510970, China
scholars have studied ways to improve vehicle capacity uti-
lization [2]. The level of empty running and the capacity
utilization of freight vehicles have hardly changed. EU statis-
tics show that in most member states, empty vehicle running
ranges between 15% and 30%, and capacity utilization by
weight ranges from 54% to 57% over a 5-year period (Euro-
stat, 2019) [3]. Considering the vehicle capacity utilization
problem, since freight transportation is a primary compo-
nent of supply chains, horizontal collaboration is considered
a crucial strategy to optimize the overall cost and the related
environmental and social impacts [4]. A lack of informa-
tion exchange and the absence of social trust deter horizontal
collaboration [5]. A logistics platform is presented to solve
the information exchange problem, as in Yunmanman, Huo-
lala et al. In present-day China, the sustainability of such
a platform is strategically important, because it can opti-
mize vehicle capacity utilization and reduce empty mileage
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[6]. That is, the sustainability issue of horizontal collab-
oration is becoming a challenge for freight transportation
in China. In this context, it is significant to understand the
interests and interactions of freight transportation stakehold-
ers. In practice, most freight transportation platforms cannot
coordinate stakeholders’ interests to ensure the sustainable
operation of horizontal collaboration. Therefore, the behav-
iors and interactions of freight transportation stakeholders
from a sustainable operation perspective represent an impor-
tant and interesting topic, which is our research’s focus.
Specifically, vehicle capacity utilization includes many
stakeholders, freight carriers, freight shippers, and logis-
tics platforms, which are considered to be the three critical
capacity utilization participants. The three participants often
face a conflict of interest when maximizing their respective
interests. For example, in the case of weak mutual trust, logis-
tics platforms can often obtain some extra benefits through
non-compliant operations. Moreover, the total return of the
logistics platform will decrease, which is not aligned with
the expected revenue of freight transportation and retards
horizontal collaboration. According to Garc´ıa-Perez et al.
[7], sustainability can be seen as the result of the coordina-
tion of interests among multiple stakeholders. It is almost
impossible to achieve the sustainable operation of logistics
platforms if the conflicts of interest among logistics platform
participants are not balanced [8]. In addition, due to the lack
of information exchange, a lack of regulatory systems for
logistics platforms, and high privacy security concerns, the
regulation of the logistics platform market is typically subject
to considerable uncertainty. Therefore, achieving sustainable
vehicle capacity utilization depends on the strategic regula-
tory game that addresses the behaviors of freight carriers,
freight shippers, and logistics platforms.
In recent years, issues related to the behavior of actors
involved in vehicle capacity utilization have received increas-
ing attention, but this research remains in its early stages.
First, most researchers are keen to elaborate on the impor-
tance of the issue through case studies [9,10]. To quantify
the economic and environmental benefits of collaboration
by companies, Palmer et al. [11] reported a 23% reduc-
tion in cost with 58% fewer road kilometers traveled and
a 46% reduction in CO2 emissions in an actual strategy
examination. Second, research on the improvement of opti-
mization algorithms remains limited in the literature [6,
12,13]. To reduce the overall cost and related environ-
mental and social impacts, Muñoz-Villamizar et al. [14]
proposed a biased randomization-based algorithm to solve
the problem with a multiobjective function to explore the
relationships between delivery and environmental costs. The
optimal selection of vehicle types depends considerably
on the time horizon under evaluation and demand varia-
tion. Third, from the perspective of sustainable operations,
research has focused on mechanisms to coordinate inter-
ests using game theory [15]. Hernández et al. [16] indicated
that a higher degree of collaboration and capacity utiliza-
tion improves the tradeoff between collaborative capacity and
holding costs. To analyze conflicts of interest, a three-player
evolutionary game model (TEGM) emphasizing bounded
rationality and dynamic decision-making processes was for-
mulated to study the interest-coordination mechanism among
freight transportation participants. On the one hand, due to
incomplete information and information asymmetry [17],
freight carriers, freight shippers, and logistics platforms fail
to acknowledge one another’s decisions (e.g., willingness
to cooperate, trust, or privacy security concerns), and they
show bounded rationality in their decision making based on
their previous interactions. On the other hand, the develop-
ment of cooperation is hindered, because the model is widely
applied in internal rather than external networks. With the
profit space continuously narrowed and the pressure from
the competitive environment of the logistics industry, it is
significant to construct an effective mechanism to facilitate
the logistics platforms and the freight transportation compa-
nies to collaborate to improve the vehicle capacity utilization,
reduce freight costs, and promote the development of freight
industry. Thus, the behavioral system among freight carriers,
freight shippers, and logistics platforms should be captured
by dynamic decision-making processes using the TEGM. It
is important to apply a TEGM to study logistics platforms
and user companies’ behavioral strategies.
According to an overview of the studies on the behavior
of freight transportation participants, the research questions
and motivations of this paper are summarized as follows.
Our study intends to answer the following questions:
(1) To coordinate logistics platform and freight transporta-
tion companies in vehicle capacity utilization problems
by analyzing the positive externalities, which aims to
build an effective mechanism to increase the logistics
platform’s social value.
(2) To promote the logistics platform to provide high-level
services according to the logistics platform’s collabora-
tion trajectory changes over time, which aims to enhance
the freight shippers and the freight carriers attending the
logistics platform, then the vehicle capacity utilization
will be increased.
To address the aforementioned issues, by adopting a
stakeholder approach, the conflicts of interest among freight
carriers, freight shippers, and logistics platforms are analyzed
in this paper. In addition, due to asymmetric information,
short-sightedness, and self-interest, freight transportation
participants may exhibit bounded rationality in multistage
games. A TEGM is developed to analyze the equilibrium
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and evolutionary stability strategies, which imply the inter-
actions and interest-coordination mechanisms among freight
transportation participants.
The purpose of our study is to increase the motivation of
freight transportation participants in the logistics platform.
Our contributions are summarized in the following
points:
(1) An efficient mechanism formulated by TEGM with
three players is developed to explore interactions among
freight carriers, freight shippers, and logistics platforms,
which overcomes the limitations of the two-player game
mechanism applied in previous studies.
(2) The interest-coordination mechanism among freight
transportation participants is designed to guide each
participant to choose the behavioral strategy, which is
beneficial to the sustainability of freight transportation.
The behavioral strategies of freight transportation par-
ticipants are theoretically and numerically analyzed, and
conclusions contributing to the sustainability of freight
transportation are obtained.
(3) We systematically investigate the factors influencing the
behaviors and interactions of freight transportation par-
ticipants and analyze the impact of rewards and penalties
imposed by positive network externality, tax incentives,
and freight shippers/carriers’ incentives on evolution-
ary stability strategies. We propose suggestions for the
sustainable development of the freight transportation
industry.
The remainder of the study is organized as follows.
“Related work” presents a literature review on dual supply
chains. Section “Model formulation” describes the TEGM
mathematical model used in this study and the assump-
tions and notations applied in this paper. Section “Model
analysis” introduces the interactions among freight carriers,
freight shippers, and logistics platforms. Section “Numerical
analysis” performs a numerical analysis to gain additional
management insights. Finally, “Conclusions and implica-
tions for future research” provides conclusions and directions
for future research.
Related work
In recent years, to solve the vehicle capacity utilization prob-
lem, there has been much-related work is reviewed in terms
of the selection of vehicles, the optimization algorithm, the
horizontal cooperation mechanism, and the logistics platform
for freight sharing.
First, the selection of vehicles is one of the main focuses
of this work. Leach et al. [18] increased the maximum length
of vehicles to 25.25 m to expand the volumetric carrying
capacity. They also contend that high-capacity vehicles will
yield valuable environmental and financial benefits but are
unlikely to have the same impact on road safety. Liimatainen
et al. [19] reported that the use of longer and heavier vehicles
(LHVs) for various commodities in road freight transport can
ensure considerable savings in traffic volume and emissions.
Isler et al. [20] designed a visualized geostrategic railway
network for freight services to solve multiple freight type
transport problems. Carrone et al. [21] found that the use of
autonomous vehicles (AVs) in regular vehicle (RV) operation
areas will reshape the transport system and greatly improve
capacity utilization. Sun et al. [22] raised a road-rail com-
bined transport form to minimize the total costs and carbon
dioxide emissions of the routes. The costs and carbon dioxide
emissions problem can be minimized through the selection
of vehicles to a certain extent; however, the high-capacity
vehicles also mean greater investment in fixed assets.
Second, some scholars have improved optimization algo-
rithms to solve the less-than-truckload (LTL) carrier problem
without the investment in fixed assets. Barcos et al. [23]
developed an ant colony optimization algorithm to solve
real-life less-than-truckload carriers serving many-to-many
distribution network problems and solve it for a real case
in Spain. To increase truck payload utilization and mitigate
externalities, Mesa-Arango and Ukkusuri [24] proposed a
branch-and-price algorithm to solve a multicommodity one-
to-one pickup-and-delivery vehicle routing problem, which
implies that nonconsolidated bids are dominated by con-
solidated bids. Maknoon et al. [13] proposed a sequential
priority-based heuristic algorithm to address the schedul-
ing truck problem in a less-than-truckload logistics network.
Estrada-Romeu and Robuste [25] proposed an improved
tabu search algorithm to identify when freight consolidation
strategies are cost-efficient in less-than-truckload carriers’
operations, which reduces the transportation costs by 20%.
Based on the historical data of a freight transport company,
Sicilia-Montalvo et al. [26] developed an intuitive application
to optimize long-distance freight transport in an improved
ant colony algorithm. Wu et al. [27] modeled a vehicle
routing problem with a time window supply chain to study
the selection between a private trucker and an outside car-
rier. They also developed a heuristic algorithm to minimize
the total cost of the selection. Wang et al. [28] presented
a fuzzy mixed-integer linear programming model to opti-
mize imprecise total costs with uncertain data in intermodal
freight transportation and took node capacity, detour, and
vehicle utilization into account to estimate its performance.
Shao et al. [29] proposed an auction-based waste collection
synchronization mechanism with a two-layered algorithm to
optimize less-than-truckload transportation service procure-
ment in the waste collection industry. Hernández and Peeta
[30] insisted that a higher degree of collaboration always
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leads to a win–win situation in a single-carrier collabora-
tion problem when a less-than-truckload carrier seeks to
acquire other carriers’ capacity to service excess demand.
Karam and Reinau [31] proposed a double combination to
improve the eco-efficiency of road freight transport in empty
tractor–semitrailer trips, but it is less effective for just-in-
time deliveries. Obviously, the algorithm optimization has
achieved great benefits for enterprises, but with the develop-
ment of the supply chain, the limitation of the enterprise’s
internal operation optimization becomes more obvious.
Third, other scholars have searched for an effective hori-
zontal cooperation mechanism. Through a case study of the
inventory routing problem (IRP) with multiple suppliers and
customers,Soysaletal.[32] found that horizontal collabo-
ration among suppliers plays a major role in decreasing total
costs and emissions. Based on an incremental perspective,
Pomponi et al. [5] found that mutual trust among partners
and the extent of cooperation are two main dimensions for
companies to achieve horizontal collaborations. Sitadewi
et al. [9], using Indonesian case study data, reported that
trust is a key enabler of horizontal collaboration in their
section on freight trucking transportation. Lotfi et al. [33]
used qualitative research methods to understand horizontal
collaboration in micro-and small companies, and the results
show that relational rents, relational capital, and relational
governance mechanisms have important effects on collab-
oration. To balance the distribution of interests among
participants, Vanovermeire et al. [34] insisted that the total
cost can be further decreased by applying a Shapley value
method, and when the partners adopt a flexible attitude, hor-
izontal logistics alliances can increase both collaborative and
individual gains with the Shapley value. Seok and Nof [35]
found that bids among manufacturers/coalitions are effective
in dealing with collaborative capacity sharing (CCS) prob-
lems among manufacturers. Chakravarty et al. [17] studied
the optimal contracting problem with a newsvendor model,
and the results show that the optimal contract may approach
the first-best capacity level and benefit both firms. Padilla
Tinoco et al. [36] reported that co-loading is the type of
horizontal collaboration that can reduce transportation costs
and CO2 emissions; they argued that a cost-sharing agree-
ment might lead to a stable situation for the partnership.
More literature on horizontal collaboration is summarized in
Serrano-Hernández et al. [37]. De Vos et al. [38] developed a
heuristic solution method to solve the cyclic inventory rout-
ing problem by considering horizontal collaboration through
a third-party logistics service provider. Padmanabhan et al.
[39] proposed a solution method based on a large neigh-
borhood search to solve a centralized collaborative planning
scheme model, which benefits collaboration among less-
than-truckload carriers. Palhazi Cuervo et al. [40] conducted
a simulation study to prove that different partner characteris-
tics perform differently in horizontal logistics collaboration.
Hacardiaux et al. [41] accounted for partners’ preferences
regarding the decrease in logistical costs versus reduced
CO2 emissions to formulate a multi-partner multiobjective
location-inventory model that ensures fair and efficient hor-
izontal cooperation in logistics.
It is known that horizontal collaboration in logistics would
reduce costs, increase fulfillment rates, and decrease CO2
emissions, but it remains rare, because it is not usually sus-
tainable [42]. Buijs et al. [43] investigated the important role
of available information technology applications for collab-
orating freight carriers in the less-than-truckload industry in
a case study. Pan et al. [2] provided a literature review on
horizontal collaborative transport and reported that the phys-
ical internet is a horizontal collaborative transport solution
that has been developed since 2010. Although enterprises
realize the importance of horizontal cooperation, the lack of
effective information exchange and weak mutual trust leads
that the horizontal cooperation only occurring in the original
close cooperation between enterprises.
To realize efficient information exchange and build mutual
trust relationships, logistics platforms for freight sharing
have attracted considerable interest. Arnäs et al. [44]devel-
oped a platform for transporters’ hybrid shipment control
of less-than-truckload (LTL) transport networks to reduce
resource requirements and carbon emissions. Royo et al. [12]
proposed a mixed delivery system for pallet and package
delivery companies to improve the use of resources, which
is preferable to a pure system. Atasoy et al. [45] proposed
a mixed-integer programming formulation for pickup and
delivery problems with time windows to trade off the inter-
ests of platform providers, shippers, and carriers and used
a dynamic pricing approach to ensure that carriers are bet-
ter off collaborating. Rodríguez Cornejo et al. [46] presented
lean thinking in the physical internet (PI), a value stream map
method to minimize waste that is resilient to change, which
can easily identify empty transport and unnecessary CO2
emissions. Based on localization data, travel time and time-
window constraints, Montecinos et al. [6] proposed a sharing
logistics platform with a matching algorithm for less-than-
truckload systems to reduce the number of trucks, operational
costs, traveling distances, and gas emissions. To maximize
the utility of logistics resources utilization, Cai et al. [47]
proposed a subsidy strategy to solve the problems in the
transaction orders of drivers and consignors on the sharing
logistics platform. Logistics platforms are established, but
there is a less effective mechanism to make them work effec-
tively.
In summary, although the aforementioned literature has
discussed either the behavior of freight transportation partic-
ipants or horizontal collaboration, there are still limitations
that need to be addressed.
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Complex & Intelligent Systems
(1) According to the aforementioned literature, a logistics
platform is introduced to provide information services
and freight sharing strategies based on the internet [2].
However, the operational effect of existing logistics plat-
forms is unsatisfactory. Thus, we propose an effective
mechanism by formulating a TEGM consisting of three
players, including freight carriers, freight shippers, and
a logistics platform, to achieve sustainability in freight
transportation.
(2) An empirical approach [9,10], or a qualitative approach
[33], to investigate the freight transportation company’s
optimal strategy is popular in the existing literature.
However, although cooperation brings many benefits,
there is still a lack of enthusiasm for it among par-
ticipants. Our work aims to study the interaction and
interest-cooperation mechanisms among freight trans-
portation participants to achieve sustainability in freight
transportation.
(3) There are conflicts of interest among the major freight
transportation participants [5]. Thus, it is necessary to
understand the interests and interactions of freight trans-
portation participants to coordinate them to achieve
sustainable development in the freight transportation
industry.
Model formulation
Problem description
The Chinese government offers numerous supports for net-
work logistics platform enterprises, including offering subsi-
dies to logistics platforms for their R&D, building supporting
facilities and infrastructures, imposing a value-added tax,
and tax incentives. In this study, we consider the three most
influential stakeholders, including freight carriers, freight
shippers, and logistics platforms, to achieve sustainability
in the freight transportation industry. As shown in Fig. 1,the
behavior of investors is significantly affected by both logis-
tics platforms and freight transportation companies. In detail,
a good reputation can attract more freight transportation com-
panies to share their demand/transportation information on
a logistics platform [46]. Moreover, the lack of regulation,
the non-compliant operation of logistics platforms and the
default behavior of freight transportation companies are the
main causes of chaos in the freight transportation industry.
Thus, research on the sustainability of freight transportation
can also simplify the discussion of the behavioral strategies
chosen by freight carriers, freight shippers, and logistics plat-
forms regarding their conflicts of interest.
Specifically, the logistics platform needs to follow the
competitive rules of the market, regulate its behavior accord-
ing to local policies and regulations, and ensure the secu-
rity of logistics platform transactions. Specifically, through
high-level services, the logistics platform can transfer tax
incentives to freight transport participants through tax plan-
ning and improve user matching between freight carriers and
shippers. Freight shippers are freight transportation compa-
nies that send freight transportation demand information to
a freight carrier through the logistics platform. The freight
carriers are companies or individuals that deliver the goods to
the agreed location following the freight shippers’ requests
on the logistics platform. These three participants often have
conflicts of interest when pursuing their respective inter-
ests, and such conflicts will prevent horizontal collaboration
among freight transportation companies from solving the
vehicle capacity utilization problem.
In addition, in the presence of information asymme-
try, it is difficult for logistics platforms to encourage more
freight transportation companies to share their capacity due to
incomplete information sharing. Furthermore, freight ship-
pers do not know whether the carrier will adopt a “share”
strategy or whether the platform will offer “high-level ser-
vice”. Similarly, freight carriers also do not know any
information about the other participants. Thus, a dynamic
game exists in the interaction among freight carriers, freight
shippers, and logistics platforms. In other words, since the
three participants exhibit bounded rationality, the behavioral
choices are closely related to their previous behaviors. There-
fore, a TEGM that determines how to balance the interests
among the three participants is developed in the presence of
information asymmetry is the focus of the following work.
Assumptions and parameter settings
Assumption 1. To simplify the problem and limit the scope
of the research, the TEGM has only three participants, where
the logistics platform enjoys government tax preference and
supplies information-sharing services for freight carriers
and shippers; freight carriers receive transportation orders
through the logistics platform, and freight shippers release
demand information through the logistics platform.
Assumption 2. Considering human beings’ ability to cal-
culate and recognize the environment is limited. The three
participants in the freight transportation system are subject
to bounded rationality which leads them to choose their strat-
egy by the duplicate dynamic equation, as this is more aligned
with reality, and we choose evolutionary game theory as the
main research method.
Assumption 3. Like other bounded rationality assumptions
[48], to model the objection of three freight transportation
participants, they are all assumed to be risk-neutral, so they
aim to maximize their interests. As a horizontal collabora-
tion intermediary, the logistics platform aims to maximize
its profit. Freight carriers, as actual carriers, maximize their
vehicle capacity utilization and attempt to maximize their
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Fig. 1 Working mechanism of the logistics platform
income. Freight shippers, as demand information support-
ers, also seek to maximize their profits.
Assumption 4. Due to the encouragement of local policies
in China, the logistics platform always obtains a certain
degree of actual value-added tax preference, which is a
main driver for the logistics platform gathering freight par-
ticipants. Based on the basic value-added tax rate for the
transport industry t1(t1denotes the basic value-added tax
rate), the logistics platform will pay taxes at preferential tax
rates t2(t2denotes the value-added tax rate after subsidiza-
tion by the government’s preferential policies).
Assumption 5. The participants’ decision preferences will
determine the evolutionary stability strategy, so based on an
incomplete information game: the set of strategies of freight
carriers is C {share transportation capacity, do not share
transportation capacity}, where x represents the probability
of freight carriers choosing the “share transportation capac-
ity” strategy, 1-x represents the probability of freight carriers
choosing the “do not share transportation capacity” strategy,
and 0 ≤x≤1. The set of strategies of freight shippers is A
{share demand information, do not share demand informa-
tion}, where y represents the probability of freight shippers
choosing the “share demand information” strategy, 1-y rep-
resents the probability of freight shippers choosing the “do
not share demand information” strategy, and 0 ≤y≤1. The
set of strategies of the logistics platform is P {high-level
service, low-level service}, where z represents the probabil-
ity of the logistics platform choosing the “high-level service”
strategy, 1-z represents the probability of the logistics plat-
form choosing the “low-level service” strategy, and 0 ≤z≤
1.
The superscript “S” is used throughout to denote the shar-
ing strategy for both freight carriers and shippers, and “N”
denotes the no-sharing strategy. The combination is denoted
M{S,N}. The subscript “H” denotes the “high-level
service” strategy and “L” denotes the “low-level service”
strategy. The combination is denoted B{H,L}; “C”isfor
freight carriers, “A” is for freight shippers and “P”isforthe
logistics platform. obviously, t1>t2. According to the afore-
mentioned assumptions, the main factors that are considered
by freight carriers, freight shippers, and the logistics platform
in the behavioral strategies are clarified, and the parameters
involved in the model are defined, as shown in Table 1.
Return matrix of a three-player evolutionary game
model
Case 1. {share transportation capacity, share demand infor-
mation, high-level service}. The revenue for carriers in the
sharing strategy when the logistics platform chooses the
“high-level service” strategy is (1−t2)rS
CH, and the incentive
payments by the logistics platform for sharing the transporta-
tion capacity of freight carriers is IC; therefore, the revenue
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Table 1 Symbols and
descriptions of the parameters Participants Parameter Description
Freight carriers xThe probability of freight carriers choosing the “share transportation
capacity” strategy, and 0 ≤x≤1
CM
CThe costs incurred by freight carriers under strategy M, M {S,N}.
Sharing strategy means more costs, so CS
C>CN
C
ICThe incentive payments of the “high-level service” logistics
platform for the carrier’s “share transportation capacity” strategy
dCThe economic loss caused by the negative strategy of freight
shippers or the logistics platform
rM
CB The revenue for carriers under strategy Mwhen the logistics
platform chooses strategy B, M {S,N}and B{H,L} Sharing
strategy means less revenue than no sharing for revenue transfer,
so rS
CH <rN
CH and rS
CL <rN
CL
Freight shippers yThe probability of freight shippers choosing the “share demand
information” strategy, and 0 ≤y≤1
CM
AThe costs incurred by freight shippers under strategy M, M {S,
N}. Sharing strategy means more costs, so CS
A>CN
A
IAThe incentive payments from a “high-level service” logistics
platform for the shipper’s “share demand information” strategy
dAThe economic loss caused by the negative strategy of freight carriers
or the logistics platform
rM
AB The revenue for shippers under strategy Mwhen the logistics
platform chooses strategy B, M {S,N}and B{H,L}. Sharing
strategy means less revenue than no sharing for cost transfer, so
rS
AH <rN
AH and rS
AL <rN
AL
Logistics
platform
zThe probability of the logistics platform choosing the “high-level
service” strategy, and 0 ≤z≤1
EC,EAThe additional revenue of the logistics platform under the freight
carriers/shippers sharing strategy
dPThe economic loss caused by the negative strategy of freight carriers
or shippers
RBThe positive network externality for the logistics platform in
strategy B, B {H,L}. RH>RL
CBThe costs of the logistics platform in strategy B, B {H,L}.
High-level service means higher costs, so CH>CL
of the freight carriers under shared transportation capacity
is (1 −t2)rS
CH +IC. Similarly, the revenue of freight shippers
is (1 −t2)rS
AH +IA. The total revenue of the logistics plat-
form under the freight carriers/shippers sharing strategy is
EC+EA, the external benefits of the logistics platform under
the “high-level service” strategy is RH, and the cost is CH;
therefore, the revenue of the logistics platform is RH—CH+
EC+EA—IC—IA.
Case 2. {share transportation capacity, share demand infor-
mation, low-level service}. Based on Case 1, when the
logistics platform chooses the “low-level service” strategy,
it will not share tax breaks or incentive payments with the
other participants. Therefore, the revenue for carriers under
the sharing strategy is (1 −t1)rS
CL. Similarly, the revenue
of freight shippers is (1 −t1)rS
AL. The total revenue of the
logistics platform under the freight carriers/shippers shar-
ing strategy is EC+EA, the external benefits of the logistics
platform under the “low-level service” strategy is RL, and
the cost is CL; therefore, the revenue of the logistics platform
is RL—CL+EC+EA.
Case 3. {share transportation capacity, do not-share demand
information, high-level service}. Based on Case 1, if freight
shippers choose the “ do not share demand information”
strategy, both freight carriers and the logistics platform will
suffer a loss; therefore, the revenue of freight carriers is (1−
t2)rS
CH +IC−dC, and the revenue of the logistics platform is
RH−CH+EC−dP−IC.Moreover, the revenue of freight
shippers is (1 −t1)rN
AH.
Case 4. {share transportation capacity, do not share demand
information, low-level service}. Based on Case 3, when the
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logistics platform chooses the “low-level service” strategy,
without tax breaks or incentive payments from the logistics
platform, the revenue of freight carriers is (1 −t1)rS
CL −dC,
and the revenue of the logistics platform is R L−CL+EC−dP.
Moreover, the revenue of freight shippers is (1 −t1)rN
AL.
Case 5. {do not share transportation capacity, share demand
information, high-level service}. Based on Case 1, if freight
carriers choose the “do not share transportation capacity”
strategy, freight carriers and logistics platform profits will
decline; therefore, the revenue of freight carriers is (1 −
t1)rN
CH,and the revenue of the logistics platform is R H−CH+
EA−dP−IA.Meanwhile, the revenue of freight shippers
is (1 −t2)rS
AH +IA−dA.
Case 6. {do not share transportation capacity, share demand
information, low-level service}. Based on Case 5, when the
logistics platform chooses the “low-level service” strategy,
without tax breaks or incentive payments from the logistics
platform, the revenue of freight carriers is (1 −t1)rN
CL, and
the revenue of the logistics platform is RL−CL+EA−dP.
Moreover, the revenue of freight shippers is (1−t1)rS
AL −dA.
Case 7. {do not share transportation capacity, do not share
demand information, high-level service}. Based on Case
5, if freight shippers choose the “do not share demand
information” strategy, the revenue of freight carriers is
(1−t1)rN
CH −dC, and the revenue of the logistics platform is
RH−CH−2dP.Moreover, the revenue of freight shippers
is (1 −t1)rN
AH −dA.
Case 8. {do not share transportation capacity, do not share
demand information, low-level service}. Based on Case
7, when the logistics platform chooses the “low-level ser-
vice” strategy, without tax breaks or incentive payments
from the logistics platform, the revenue of freight carriers
is (1 −t1)rN
CL −dC,and the revenue of the logistics platform
is RL−CL−2dP.Moreover, the revenue of freight shippers
is (1 −t1)rN
AL −dA.
In summary, the return matrix of the TEGM among freight
carriers, freight shippers, and the logistics platform can be
obtained according to the aforementioned statements. It is
shown in Table 2.
Model analysis
Freight carriers
The freight carriers’ strategy will be influenced by the prob-
ability of the logistics platforms providing the “high-level
service”, as shown in Fig. 2, when the initial state of the
behavioral strategy of the freight carriers is in different
spaces, such as V1,and V2, the freight carriers will adopt a
x
y
z
z=z
C
z
>z
C
z
<z
C
V
1
V
2
1
1
1
Fig. 2 Dynamic trend diagram for the freight carriers
different strategy. In the subsections, we are going to discuss
these two cases.
Replicator dynamic equation and evolutionary stability
analysis
Proposition 1. When the initial state of the behavioral strat-
egy of the freight carriers is in space V 1, that is z > zC, and
x1 will be the equilibrium point, the freight carriers will
adopt the strategy of “share transportation capacity”. There-
fore, as the tax incentives on the platform encourage freight
carriers to choose “share transportation capacity”, so the
cost of sharing capacity for the freight carriers is less than
the benefits obtained thereby, the freight carriers will adopt
the strategy of “share transportation capacity”.
Proposition 2. When the initial state of the behavioral strat-
egy of freight carriers is in space V2, that is z < zC, and x
0 will be the equilibrium point, the freight carriers will
adopt the strategy of “do not share transportation capac-
ity”. Therefore, when the cost of sharing capacity for the
freight carriers exceeds the benefits obtained thereby, the
freight carriers will adopt the “do not share transportation
capacity” strategy.
Assume that the freight carriers’ expected returns from
adopting the “share transportation capacity” strategy are EC1,
the expected returns from adopting the “do not share trans-
portation capacity” strategy are EC2, and the freight carriers’
average expected returns under the mixed strategies are EC.
Then, we have the following:
EC1yz[(1 −t2)rS
CH +IC]
+y(1 −z)(1 −t1)rS
CL +z(1 −y)[(1 −t2)rS
CH
+IC−dC]+(1−y)(1 −z)[(1 −t1)rS
CL −dC](1)
EC2yz(1 −t1)rN
CH +y(1 −z)(1 −t1)rN
CL
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Complex & Intelligent Systems
Table 2 Return matrix of the three freight transportation participants
Freight carriers Freight shippers Logistics platform
High-level service (z) Low-level service
(1−z)
Share transportation capacity (x) Share demand information (y)(1 −t2)rS
CH +IC
(1 −t2)rS
AH +IA
RH−CH+EC+EA−IC−IA
(1 −t1)rS
CL
(1 −t1)rS
AL
RL−CL+EC+EA
Do not share demand information
(1−y)(1 −t2)rS
CH +IC−dC
(1 −t1)rN
AH
RH−CH+EC−dP−IC
(1 −t1)rS
CL −dC
(1 −t1)rN
AL
RL−CL+EC−dP
Do not share transportation capacity
(1−x)
Share demand information (y)(1 −t1)rN
CH
(1 −t2)rS
AH +IA−dA
RH−CH+EA−dC
P−IA
(1 −t1)rN
CL
(1 −t1)rS
AL −dA
RL−CL+EA−dP
Do not share demand information
(1−y)(1 −t1)rN
CH −dC
(1 −t1)rN
AH −dA
RH−CH−2dP
(1 −t1)rN
CL −dC
(1 −t1)rN
AL −dA
RL−CL−2dP
+z(1 −y)[(1 −t1)rN
CH −dC]
+(1−y)(1 −z)[(1 −t1)rN
CL −dC](2)
ECxE
C1+(1−x)EC2(3)
The duplicate dynamic equation [48] implies the players
imitate the rate of growth dominant strategy per unit of time
t. The freight carriers select the duplicate dynamic equation
for “share transportation capacity” as
FCdx
dt x(1 −x)[z((1 −t2)rS
CH +IC−(1 −t1)rN
CH)
+(1−z)(1 −t1)(rS
CL −rN
CL)] (4)
For ease of calculation, let zC
(1−t1)(rN
CL−rS
CL)
(1−t2)rS
CH−(1−t1)rN
CH+IC+(1−t1)(rN
CL−rS
CL).
➀When zzC, then FC≡0, which shows that all levels
are stable.
➁When z zC,setFC0; then, x0 and x1aretwo
stable points.
Let F
Cbe the derivative of xand derived from FC:
F
C(1 −2x)[z((1 −t2)rS
CH +IC
−(1 −t1)rN
CH)+(1−z)(1 −t1)(rS
CL −rN
CL)] (5)
According to the requirements of the evolutionary stability
strategy (ESS)F
C<0, zCis analyzed, because 0 < x<1,
0<y<1,and0<z< 1, ESSs are obtained considering the
following two scenarios.
Scenario 1. If 0 < z<zC, when x0, F
C<0; when x1,
F
C>0; therefore, x0 is an ESS. That is, the freight carri-
ers adopt the “do not share transportation capacity” strategy.
Scenario 2. If zC<z< 1, when x0, F
C>0; when x
1, F
C<0; therefore, x1 is an ESS. That is, the freight
carriers adopt the strategy of “share transportation capacity”.
According to the analysis, the dynamic evolutionary trend
of freight carriers is shown in Fig. 2; therefore, propositions
1 and 2 are proven.
Evolutionary analysis of freight carriers
As shown in Fig. 2, when the other parameters are fixed, zC
increases as t2increases. When zCincreases, the area of V2
expands. That is, as the tax rate after subsidization through
the government’s preferential policies increases, the “share
transportation capacity” strategy will lead freight carriers to
afford higher costs. To maximize their own profits, freight
carriers will choose “do not share transportation capacity”.
Similarly, when t1increases and zCdecreases, the area of V1
contracts. In other words, an increase in the basic tax rate
will cause the freight carriers to choose “share transporta-
tion capacity”, which will reduce the real tax rate payment
through tax preference for the logistics platform. When IC
increases and zCdecreases, the area of V1expands. This
shows that the logistics platform is increasing the incen-
tive payment to enable freight carriers to choose “share
transportation capacity” under the provision of high-level
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Complex & Intelligent Systems
x
y
z
z=z
A
z>z
A
z<z
A
V
3
V
4
1
1
1
Fig. 3 Dynamic trend diagram for the freight shippers
services. when (rN
CL −rS
CL) is increased and zCincreases,
and the area of V2expands. In other words, when the plat-
form provides “low-level service”, freight carriers will tend
to choose “do not share transportation capacity” to maxi-
mize their profits. When rS
CH increases, rN
CH decreases, and
zCdecreases, the area of V1expands. This means that when
the platform provides “high-level service”, the freight carri-
ers will gain more profits by choosing “share transportation
capacity”.
Freight shippers
The freight shippers’ strategy will be influenced by the prob-
ability of the logistics platforms providing the “high-level
service”, as shown in Fig. 3, when the initial state of the
behavioral strategy of the freight shippers is in different
spaces, such as V3,and V4, the freight shippers will adopt
a different strategy. In the subsections, we are going to dis-
cuss these two cases.
Replicator dynamic equation and evolutionary stability
analysis
Proposition 3. When the initial state of the behavioral strat-
egy of the freight shippers is in space V3, that is z > zA, and
y1 is the equilibrium point, the freight shippers will adopt
the strategy of “share demand information”. Therefore, con-
sidering that the tax incentives of the platform encourage
freight shippers to choose “share demand information”,
when the cost of sharing traffic for the freight shippers is less
than the benefits obtained thereby, the freight shippers will
adopt the strategy of “do not share demand information”.
Proposition 4. When the initial state of the behavioral strat-
egy of freight shippers is in space V 4, that is z <zA, and y
0 is the equilibrium point, the freight shippers will adopt the
strategy of “do not share demand information”. Therefore,
when the cost of sharing capacity for the freight shippers
exceeds the benefits obtained thereby, the freight shippers
will adopt the strategy of “do not share demand informa-
tion”.
Assume that the freight shippers’ expected returns from
adopting the “share demand information” strategy are EA1,
the expected returns from adopting the “do not share demand
information” strategy are EA2, and the freight shippers’ aver-
age expected returns under the mixed strategies are EA. Then,
we have the following:
EA1xz[(1 −t2)rS
AH +IA]+x(1 −z)(1 −t1)rS
AL
+z(1 −x)[(1 −t2)rS
AH +IA−dA]
+(1−x)(1 −z)[(1 −t1)rS
AL −dA](6)
EA2xz(1 −t1)rN
AH +x(1 −z)(1 −t1)rN
AL
+z(1 −x)[(1 −t1)rN
AH −dA]
+(1−x)(1 −z)[(1 −t1)rN
AL −dA](7)
EAyEA1+(1−y)EA2(8)
The freight shippers select the duplicate dynamic equation
for “share demand information” as
FAdy
dt y(1 −y)[z((1 −t2)rS
AH +IA−(1 −t1)rN
AH)
+(1−z)(1 −t1)(rS
AL −rN
AL)] (9)
For ease of calculation, let zA
(1−t1)(rN
AL−rS
AL)
(1−t2)rS
AH−(1−t1)rN
AH+IA+(1−t1)(rN
AL−rS
AL).
➀When zzA, then FA≡0, which shows that all levels
are stable.
➁When z zAset FA0; then, y0 and y1aretwo
stable points.
Let F
Abe the derivative of yand derived from FA:
F
A(1 −2y)[z((1 −t2)rS
AH +IA−(1 −t1)rN
AH)
+(1−z)(1 −t1)(rS
AL −rN
AL)] (10)
According to the requirements of the evolutionary stability
strategy F
C<0, zAis analyzed, because the ESSs of 0 < x
<1,0<y< 1, and 0 < z< 1 are obtained considering the
following two scenarios.
Scenario 3. If 0 < z<zA, when y0, F
A<0; when y1,
F
A>0; therefore, y0 is an ESS. That is, freight shippers
adopt the strategy of “do not share demand information”.
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Complex & Intelligent Systems
Scenario 4. If zA<z< 1, when y0, F
A>0; when y1,
F
A<0; therefore, y1 is an ESS. That is, freight shippers
adopt the strategy of “share demand information”.
According to the analysis, the dynamic evolutionary trend
of freight shippers is shown in Fig. 3; therefore, propositions
3 and 4 are proven.
Evolutionary analysis of freight shippers
As shown in Fig. 3, when the other parameters are fixed, if
t2increases, and zAincreases. When zAincreases, the area
of V4expands. That is, when the logistics platform increases
tax incentives, freight shippers will choose to “share demand
information” to reduce costs. The tax benefits raised by the
logistics platform will not enable freight shippers to choose
“share demand information” but will lead them to choose the
“do not share demand information” strategy. Similarly, when
t1increases and zAdecreases, the space of V3becomes larger;
in other words, the increase in the basic tax rate amount of the
freight shippers will enable them to share demand informa-
tion and reduce their real tax rate by the logistics platform’s
tax preference. When IAincreases and zAdecreases, the area
of V3expands, which shows that the logistics platform has
increased the incentives for freight shippers under the provi-
sion of high-level services, and freight shippers will tend to
choose to “share demand information”; when (rN
AL −rS
AL)
is increased and zAincreases, the area of V4expands. In
other words, when the logistics platform provides a lower
of level service, freight shippers will prefer to choose the
“do not share demand information” strategy, and then rS
AH
increases, rN
AH decreases, and zAdecreases, the area of V3
contracts. This means that when the logistics platform pro-
vides a high level of service, freight shippers will prefer to
choose the “share demand information” strategy.
Logistics platform
The logistics platforms’ strategy will be influenced by the
positive network externality and freight transportation com-
panies’ sharing strategy, as shown in Fig. 4, when the initial
state of the behavioral strategy of the logistics platform is
in different spaces, such as V5,and V6, the logistics plat-
form will adopt different strategies. In the subsections, we
are going to discuss these two cases.
Replicator dynamic equation and evolutionary stability
analysis
Proposition 5. When the initial state of the behavioral strat-
egy of the logistics platform is in space V5, that is x IC+yIA<
RH−CH−RL+CL, and z 1is the equilibrium point, the
logistics platform will adopt the strategy of “high-level ser-
vice”. Therefore, considering that the freight carriers and
x
y
z
V6
V5
1
1
1
xIC+yIA=R1
−
CH
−
R2+CL
xIC+yIA<R1
−
CH
−
R2+CL
xIC+yIA>R1
−
CH
−
R2+CL
Fig. 4 Dynamic trend diagram for the logistics platform
freight shippers choose their “sharing” strategy to benefit
the logistics platform, when the benefits of providing high-
level services are greater than those of providing low-level
services, the logistics platform will choose the “high-level
service” strategy.
Proposition 6. When the initial state of the behavioral
strategy of the logistics platform is in space V6, that is,
xI
C+yIA>RH−CH−RL+CL, and z 0is the equi-
librium point, the logistics platform will adopt the strategy
of “low-level service”.
Assume that the logistics platform’s expected returns
from adopting the “high-level service” strategy are EP1,the
expected returns from adopting the “low-level service” strat-
egy are EP2, and the logistics platform’s average expected
returns under the mixed strategies are EP. Then, we have
the following:
EP1xy(RH−CH+EC+EA−IC
−IA)+x(1 −y)(RH−CH+EC−dP−IC)
+y(1 −x)(RH−CH+EA−dP−IA)
+(1−x)(1 −y)(RH−CH−2dP) (11)
EP2xy(RL−CL+EC+EA)+x(1 −y)(RL−CL
+EC−dP)+y(1 −x)( RL−CL+EA−dP)
+(1−x)(1 −y)(RL−CL−2dP)(12)
EPzEP1+(1−z)EP2(13)
The logistics platform selects the duplicate dynamic equa-
tion for “high-level service” as
FPdz
dt z(1 −z)[RH−CH−RL+CL−yIA−xI
C]
(14)
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Complex & Intelligent Systems
For ease of calculation, let wxI
C+yIA,w1RH−
CH−RL+CL,w2(RH−RL+CL−CH−yIA)/IC.
➀When ww1, then FP≡0, which shows that all levels
are stable.
➁When w w1,setFP0; then, z0 and z1aretwo
stable points.
Let F
Pbe the derivative of zand derived from FP:
F
P(1 −2z)[RH−CH−RL+CL−yIA−xI
C] (15)
According to the requirements of the evolutionary stability
strategy F
P<0, w,w1, and w2are analyzed, and because 0
<x<1,0<y< 1, and 0 < z< 1, ESSs are obtained considering
the following two scenarios.
Scenario 5. When w>w1, that is x>w2, when z0,
F
P<0; when z1, F
P>0; therefore, z0 is an ESS.
That is, the logistics platform adopts the strategy of “low-
level service”.
Scenario 6. When w<w1, that is x<w2, when z0, F
P>0;
when z1, F
P<0; therefore, z1 is an ESS. That
is, the logistics platform adopts the strategy of “high-level
service”.
According to the analysis, the dynamic evolutionary trend
of the platform is shown in Fig. 4; therefore, propositions 5
and 6 are proven.
Evolutionary analysis of logistics platform
As shown in Fig. 4, the initial state of the platform’s behavior
strategy is related to the size of xand yin spaces V5and V6,
and when yremains unchanged, ICdecreases, and xbecomes
larger. When xincreases, the area of V6expands. That is,
when the logistics platform provides “high-level services”,
the incentives for freight carriers to choose “share trans-
portation capacity” increase, so that the benefits obtained by
the platform from providing low-level services are greater
than those obtained by providing high-level services. Thus,
the platform provides “low-level service”. Similarly, when
(RH–RL) decreases and xdecreases, s the area of V5expands;
in other words, the net positive network externality of high-
level service being provided by the platform exceeds that
of low-level service, which will lead to the platform to pro-
vide “high-level service”. When (CL–CH) decreases, and x
decreases, s the area of V5expands. This means that the cost
for the platform to provide a low level of service is lower than
the cost of providing a high level of service, and the platform
benefits when the freight carriers choose to share. To obtain
more benefits, the platform will encourage the freight carriers
to choose to share to be able to provide high-level services.
In this case, the benefits gained by the platform from provid-
ing high-level services are greater than those from providing
low-level services; therefore, the logistics platform will be
more inclined to provide high-level services.
Evolutionary stability analysis of the three
participants
The purpose of the evolutionary analysis is to determine
the evolutionary stability strategy of the two sides of the
game, that is, the dynamic balance formed by the two sides
of the game with limited rationality when they pursue the
maximization of their immediate interests. The replicated
dynamic equations reflect the dynamic decision trajectories
of the three parties in the game on the time axis. It is clear
that when FC0, FA0 and FP0 are extremum nec-
essary conditions, the equilibrium points of the pure strategy
include E0(0,0,0), E1(0,0,1), E2(0,1,0), E3(0,1,1), E4(1,0,0),
E5(1,0,1), E6(1,1,0), and E7(1,1,1). In an asymmetric game,
if evolutionary game equilibrium Eis an evolutionary sta-
ble equilibrium, then Emust be a strict Nash equilibrium,
and the strict Nash equilibrium is a pure strategy equi-
librium, that is, the mixed equilibrium must not be an
evolutionarily stable equilibrium in an asymmetric game, so
it is only necessary to study the asymptotic stability of the
pure strategy equilibrium. Therefore, this paper only ana-
lyzes E0(0,0,0), E1(0,0,1), E2(0,1,0), E3(0,1,1), E4(1,0,0),
E5(1,0,1), E6(1,1,0), and E7(1,1,1).
The asymptotic stability of the equilibrium points is deter-
mined by the Lyapunov discriminant method, so the Jacobian
matrix and its eigenvalues are solved first. The Jacobian
matrix is as follows:
J⎡
⎢
⎣
∂FC/∂x∂FC/∂ y∂FC/∂z
∂FA/∂x∂FA/∂ y∂FA/∂ z
∂FP/∂x∂FP/∂ y∂FP/∂ z
⎤
⎥
⎦(16)
Thus, the following formulas are acquired.
∂FC/∂x(1 −2x)[z((1 −t2)rS
CH +IC
−(1 −t1)rN
CH)+(1−z)(1 −t1)(rS
CL −rN
CL)]
∂FC/∂y0
∂FC/∂zx(1 −x)[(1 −t2)rS
CH
−(1 −t1)(rN
CH +rS
CL −rN
CL)+IC]
∂FA/∂x0
∂FA/∂y(1 −2y)[z((1 −t2)rS
AH +IA−(1 −t1)rN
AH)
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Complex & Intelligent Systems
+(1−z)(1 −t1)(rS
AL −rN
AL)]
∂FA/∂zy(1 −y)[(1 −t2)rS
AH
−(1 −t1)(rS
AL +rN
AH −rN
AL)+IA]
∂FP/∂x−z(1 −z)IC
∂FP/∂y−z(1 −z)IA
∂FP/∂z(1 −2z)[RH−CH−RL+CL−xI
C−yIA]
According to the Lyapunov discriminant method, the eval-
uation criteria of its evolutionary stability are as follows: if
all eigenvalues λ< 0, the equilibrium point is an evolutionary
stable point (ESS), which is the confluence; if all eigenval-
ues λ> 0, the equilibrium point is an unstable point, which
is the source; if all eigenvalues λhave positive and negative
real numbers, the equilibrium point is a saddle point; and if
λis a conjugate imaginary number, the equilibrium point is
the center point. The stability of each equilibrium point is
analyzed, as shown in Table 3.
It is obvious that λ31 λ11,λ51 −λ11,λ71 −λ11,
λ32 −λ12,λ33 −λ23 ,λ52 λ12,λ72 −λ12,λ53
−λ43,λ73 −λ63,λ43 >λ63,λ23 >λ63 . According to
the Lyapunov stability theorem and the results in Table 3,the
following scenarios can be obtained.
Scenario 1: When λ11 < 0 and λ12 < 0, the evolutionary
stable equilibrium point is E1(0,0,1).
In this scenario, the freight carriers adopt the strategy of
“do not share transportation capacity”, the freight shippers
adopt the strategy of “do not share demand information”, and
the logistics platform provides “high-level service”. In this
state, even if the logistics platform is willing to provide a high
level of service and the freight carriers and freight shippers
will be rewarded by choosing a sharing strategy, since the
tax incentives are not high enough, the cost of choosing to
share is higher than that of choosing not to share, so both
freight carriers and freight shippers prefer to choose a non-
sharing strategy. That is, (1−t2)rS
CH+IC<(1−t1)rN
CH,(1−
t2)rS
AH +IA<(1−t1)rN
AH; therefore, the freight carriers will
choose “do not share transportation capacity”, and the freight
shippers will choose “do not share demand information”.
This reduces the logistics platform’s profit. However, when
the logistics platform provides high-level services and lower
tax incentives, the benefits gained by the logistics platform
exceed its losses, so the logistics platform can also benefit
more by providing high- rather than low-level services. That
is, if RH−RL>CH−CL, the logistics platform is willing
to adopt a “high-level service” strategy.
Scenario 2: When λ11 < 0 and λ12 >0,λ23 >0,E3(0,1,1)
is an asymptotically stable point.
In this scenario, the freight carriers adopt the strategy of
“do not share transportation capacity”, the freight shippers
adopt the strategy of “share demand information”, and the
logistics platform provides “high-level service”. In this case,
when the logistics platform provides a high level of service,
the freight shippers will be rewarded for choosing a sharing
strategy and a tax incentive. As the freight carriers’ strategy
is “do not share transportation capacity”, the freight ship-
pers will suffer a loss, but their gain is far greater than their
loss. Therefore, the freight shippers can obtain more benefits
by choosing the “share demand information” strategy. Since
(1−t2)rS
AH+IA>(1−t1)rN
AH, the freight shippers are willing
to choose a sharing strategy to promote the development of
sharing. For the freight carriers, even if the logistics platform
is willing to provide high-level services and they will obtain
incentive payments from the logistics platform by choosing
to share transportation capacity, the tax preference enjoyed
through the platform is still low. This is why the freight car-
riers prefer to choose “do not share transportation capacity”.
That is, (1 −t2)rS
CH +IC<(1 −t1)rN
CH; therefore, freight
carriers will not share transportation capacity. The freight
shippers’ choice of the “share demand information” strategy
will benefit the logistics platform. Even if the freight carriers’
choice of “do not share transportation capacity” will cause
some economic loss, the logistics platform will also choose
a high level of service, because its gain far exceeds its losses.
That is.RH−RL>IA+CH−CL. As a result, the platform
will provide a high level of service.
Scenario 3: When λ11 > 0 and λ12 < 0, the evolutionary
stable equilibrium point is E5(1,0,1).
In this scenario, the freight carriers adopt the strategy of
“share transportation capacity”, the freight shippers adopt
the strategy of “do not share demand information”, and
the logistics platform adopts the strategy of “high-level ser-
vice”. In this case, when the logistics platform provides a
high level of service, the freight carriers will gain a satis-
factory incentive payment from the logistics platform for
choosing the “share transportation capacity” strategy and
can also enjoy a tax incentive. Even if the freight shippers’
choice of the “do not share demand information” strategy
will cause some economic loss, their gain far exceeds their
loss. Therefore, the freight carriers can obtain more bene-
fits when choosing to share transportation capacity. That is,
(1 −t2)rS
CH +IC>(1 −t1)rN
CH. Therefore, freight carri-
ers are willing to choose the “share transportation capacity”
strategy to promote the development of sharing. For the
freight shippers, even if the logistics platform is willing to
provide high-level services and provide an incentive pay-
ment if they choose the “share demand information” strategy,
the freight shippers can obtain more benefits by choosing
the “do not share demand information” strategy. That is,
(1−t2)rS
AH+IA<(1−t1)rN
AH. Therefore, the freight shippers
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Complex & Intelligent Systems
Table 3 Equilibrium point stability analysis
Equilibrium Eigenvalue Stability
E0(0,0,0) λ01 −(1 −t1)(rN
CL −rS
CL)<0
λ02 −(1 −t1)(rN
AL −rS
AL)<0
λ03 RH−CH−RL+CL>0
Saddle point
E1(0,0,1) λ11 (1 −t2)rS
CH −(1 −t1)rN
CH +IC
λ12 (1 −t2)rS
AH −(1 −t1)rN
AH +IA
λ13 −(RH−CH−RL+CL)<0
If λ11 <0andλ12 <0,E1(0,0,1) is ESS
E2(0,1,0) λ21 −(1 −t1)(rN
CL −rS
CL)<0
λ22 (1 −t1)(rN
AL −rS
AL)>0
λ23 RH−CH−RL+CL−IA
Saddle point
E3(0,1,1) λ31 (1 −t2)rS
CH −(1 −t1)rN
CH +ICλ11
λ32 −[(1 −t2)rS
AH −(1 −t1)rN
AH +IA]−λ12
λ33 −(RH−CH−RL+CL−IA)−λ23
If λ11 <0,λ12 >0,and λ23 >0,E3(0,1,1) is ESS
E4(1,0,0) λ41 (1 −t1)(rN
CL −rS
CL)>0
λ42 −(1 −t1)(rN
AL −rS
AL)<0
λ43 RH−CH−RL+CL−IC
Saddle point
E5(1,0,1) λ51 −[(1 −t2)rS
CH −(1 −t1)rN
CH +IC]−λ11
λ52 (1 −t2)rS
AH −(1 −t1)rN
AH +IAλ12
λ53 −[RH−CH−RL+CL−IC]−λ43
If λ11 >0,λ12 <0andλ43 >0,E5(1,0,1) is ESS
E6(1,1,0) λ61 (1 −t1)(rN
CL −rS
CL)>0
λ62 (1 −t1)(rN
AL −rS
AL)>0
λ63 RH−CH−RL+CL−IC−IA
If λ63 >0,E6(1,1,0) is the unstable point. Otherwise, E6(1,1,0)
is the saddle point
E7(1,1,1) λ71 −[(1 −t2)rS
CH −(1 −t1)rN
CH +IC]−λ11
λ72 −[(1 −t2)rS
AH −(1 −t1)rN
AH +IA]−λ12
λ73 −[RH−CH−RL+CL−IC−IA]−λ63
If λ11 >0,λ12 >0andλ63 >0,E7(1,1,1) is ESS
will choose the “do not share demand information” strategy.
However, the gains of the logistics platform exceed its losses,
so the logistics platform can obtain more benefits by provid-
ing high-level services than by providing low-level services,
that is, RH−RL>IC+CH−CL. As a result, the platform
will provide a high level of service.
Scenario 4: When λ11 >0,λ12 > 0 and λ63 > 0, the evolu-
tionary stable equilibrium point is E7(1,1,1).
In this scenario, both the freight carriers and freight ship-
pers choose a sharing strategy, and the logistics platform
provides a high level of service. In this case, when the logis-
tics platform provides a high level of service, the freight
carriers and the freight shippers choose to share to obtain
the rewards given by the platform and can also enjoy rela-
tively high tax preferences. The freight carriers and freight
shippers can obtain more profits by choosing a sharing
strategy. That is, (1 −t2)rS
CH +IC>(1 −t1)rN
CH and
(1 −t2)rS
AH +IA>(1 −t1)rN
AH; therefore, the freight carri-
ers and freight shippers are willing to choose to share. This
will benefit the logistics platform. Even if the logistics plat-
form provides rewards to the freight carriers and shippers, it
can also gain excess profits. Thus, the logistics platform will
benefit more from a high-level service than a low one, that
is to say RH−RL>IC+IA+CH−CL, and the logistics
platform is willing to provide a high level of service.
Scenario 5: When λ11 >0,λ12 > 0 and λ63 < 0, there is
no stable equilibrium point. Based on Scenario 4,ifλ63 <0,
all the aforementioned equilibrium points will not be satis-
fied, and a complex scenario with no stable equilibrium point
will be discussed in the next section containing the numerical
analysis.
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Complex & Intelligent Systems
Numerical analysis
To further validate the proposed model, MATLAB R2020b
is used to simulate and calculate Scenario 5, which is
more complex than the others. To simplify the analysis of
the influence of the initial state of the system and related
parameters on the development of the final dynamic game,
The following conditions need to be imposed on the vari-
ables: λ11 (1 −t2)rS
CH −(1 −t1)rN
CH +IC>0,λ12
(1 −t2)rS
AH −(1 −t1)rN
AH +IA>0, and λ63 RH−CH−
RL+CL−IC−IA<0.
This sub-section explores the effectiveness of models by
considering the data of the Yunmanman Company’s real
case. Yunmanman Company is a typical representative of the
logistics platform in the field of freight transportation. The
website address of Yunmanman Company is https://www.
ymm56.com/. The values of parameters are gathered based
on the data of both the local government department (http://
hunan.chinatax.gov.cn/) and experts’ opinions. Specifically,
the values of the basic value-added tax rate t10.11 and
the value-added tax rate after subsidization by the govern-
ment’s preferential policies t20.05 are available in the
statistics information of the local government department.
Nevertheless, other parameters, i.e., the revenue for carriers
and shippers under strategy M, the incentive payments of the
“high-level service” logistics platform for the carriers and
shippers’ “share transportation capacity” strategy are diffi-
cult to be determined in practice. Accordingly, the values of
such parameters are estimated based on the model assump-
tions and experts’ opinions of Yunmanman Company, which
is similar to Scenario 5. The values of parameters are IC
3, IA2, rS
CH 6.8, rN
CH 10,rS
CL 0.5,rN
CL 1,rS
AH
7.5,rN
AH 10,rS
AL 0.5, and rN
AL 1. When x1, y1, and
z1, that is, the freight carriers choose “share transporta-
tion capacity”, the freight shippers choose “share demand
information”, and the logistics platform chooses “high-level
service”, which is also the development goal of the freight
transportation industry in China. To study the influence of
key system parameters on the equilibrium strategies, sensi-
tivity analysis on the equilibrium strategies with respect to
(x(0), y(0), z(0)), t2,RH,IA, and ICis conducted. In this
study, only one parameter varies, and the others are fixed,
and the numerical results are shown in Figs. 5,6,7,8,9.
Sensitivity analysis of the initial proportion
(x(0),y(0), z(0))
As shown in Fig. 5, the evolution result of the three-player
game varies according to the initial proportions of the three
participants. When the initial proportions are the same, (x(0),
y(0), z(0)) (0.5, 0.5, 0.5), as time passes in Fig. 5a,
the freight carriers change their probability: xgradually
increases, then slowly decreases and finally converges to 1.
The freight shippers change their probability: ygradually
increases, then declines substantially, and finally converges to
0. The logistics platform changes its probability: zincreases
and then decreases and finally converges to a certain value
between 0.4 and 0.6. When the initial proportions are dif-
ferent, (x(0), y(0), z(0)) (0.1, 0.3, 0.2), as time passes
in Fig. 5b, the freight carriers change their probability: x
increases sharply and then decreases slowly and finally con-
verges to 1. the freight shippers change their probability: y
gradually increases, then gradually decreases and the fluc-
tuation amplitude decreases and finally converges to 0. The
logistics platform changes its probability: zincreases to the
threshold 1, then decreases to the threshold 0, and then
reaches a certain value between 0.4 and 0.6. This implies
that the initial proportion value only affects the process of the
evolutionary game, but the final convergence result remains
unchanged.
Sensitivity analysis of tax incentives t2
As shown in Fig. 6, when the tax rate after subsidization
by the government’s preferential policies t2varies among
0.01, 0.08 and 0.1, over time, the probability of the platform
actively selecting the “high-level service” strategy increases.
However, the final strategy of the freight carriers and the
freight shippers remain unchanged. The freight carriers have
been very likely to choose the “share transportation capac-
ity” strategy, while the freight shippers choose the “do not
share demand information” strategy. This is because freight
carriers will gain the tax incentives provided by the logistics
platform and obtain more rewards, which will benefit carriers
that adopt the “share transportation capacity” strategy. How-
ever, the freight shippers will prefer the “do not share demand
information” strategy, because despite the worse benefits,
the tax incentives and rewards are increased. For the logis-
tics platform, with the improvement of tax incentives and
the freight carriers’ and shippers’ strategies being definite,
the probability of choosing the “high-level service” strat-
egy continues to increase. This implies that the tax incentive
value affects the process of the evolutionary game through
the logistics platform’s strategy and has less influence on
freight carriers and shippers.
Sensitivity analysis of positive network externality
RH
As shown in Fig. 4, the evolutionary result of the three-player
game varies according to the positive network externality.
When the positive network externality value is low, as time
passes in Fig. 7a, the freight carriers, freight shippers and
logistics platform’s probabilities (x,y,z) will all converge
to 0. That is, the freight carriers choose the “do not share
transportation capacity” strategy, freight shippers choose the
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Complex & Intelligent Systems
Fig. 5 (a)x(0) 0.5, y(0) 0.5, and z(0) 0.5, (b)x(0) 0.1, y(0) 0.3, and z(0) 0.2
“do not share demand information” strategy and the logistics
platform chooses the “low-level service” strategy. However,
when the positive network externality value is high, as time
passes in Fig. 7b, the freight carriers, freight shippers and
logistics platform’s probabilities (x,y,z) will all converge to
1. That is, the freight carriers choose the “share transporta-
tion capacity” strategy, freight shippers choose the “share
demand information” strategy and logistics platform choose
the “high-level service” strategy. This implies that when Sce-
nario 5 is in the ascendancy, the positive network externality
is the key factor in the evolutionary result of the three-player
game, and a high-level RHultimately leads to a cooperative
relationship.
Sensitivity analysis of freight carriers’ incentive IC
AsshowninFig.8, the evolutionary result of the three-player
game varies according to the value of the parameter rep-
resenting freight carriers’ incentives IC. When the freight
carriers’ incentive value is low, as time passes in Fig. 8aIC
1, the freight carriers’ probability xwill converge to 0, while
the freight shippers and logistics platform’s probabilities (y,
z) will converge to 1. This indicates that the freight carriers
choose the “do not share transportation capacity” strategy,
the freight shippers choose a “share demand information”
strategy and logistics platforms choose the “high-level ser-
vice” strategy. However, when the freight carriers’ incentive
value is high, as time passes in Fig. 8bIC5, the freight
shippers’ probability yconverges to 0, while the freight car-
riers’ and logistics platform’s probabilities (x,z) will both
change trend. That is, the logistics platform has greater incen-
tives to provide share rewards to the freight carriers, but its
revenue cannot cover the cost. Therefore, the probability of
the logistics platform choosing a high level of service will
decrease, while the probability of the freight carriers choos-
ing the “share transportation capacity” strategy increases.
Thus, freight carriers’ positive attitude will encourage the
logistics platform to choose the “high-level service” strategy.
Therefore, both the freight carriers and logistics platform
are in a state of fluctuation. In this case, for the freight
shippers, the benefit of choosing the “do not share demand
information” strategy is greater than that of “share demand
information”, so the freight shippers tend to choose the “do
not share demand information” strategy.
Sensitivity analysis of freight shippers’ incentive IA
AsshowninFig.9, other parameters remain unchanged, and
the final evolutionary results of the three participants can be
changed by the value of the freight shippers’ incentive IA.
When the freight shippers’ incentive value is low, as time
passes in Fig. 9aIA1, the freight carriers and logistics
platform’s probabilities (x,z) will converge to 1, while the
freight shipper’s probability ywill converge to 0. This indi-
cates that the freight carriers choose the “share transportation
capacity” strategy, freight shippers choose the “do not share
demand information” strategy and logistics platform chooses
the “high-level service” strategy. However, when the freight
shippers’ incentive value is high, as time passes in Fig. 9b
IA3, the freight shippers’ probability yconverges to 1,
while the freight carriers’ probability xconverges to 0, and
the logistics platform’s probability zwill decline and then
increase and finally converge to a threshold value (this value
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Complex & Intelligent Systems
Fig. 6 (a)t20.01, (b)t20.08, (c)t20.1
∈(0.2, 0.4)). Therefore, when the logistics platform pro-
vides high-level services, the incentive for freight shippers
to share increases, and they have a strong incentive to choose
the strategy of “do not share demand information”. However,
the platform needs to share more revenue, which will reduce
its benefits, so it is less motivated to choose the “high-level
service” strategy. The result also enables the freight carriers
to choose the “do not share transportation capacity” strategy.
From Figs. 8and 9, we can see that both the freight
carriers and shippers will not be attracted to the logistics
platform by a low incentive, such as IA1 and IC1.
This implies that a sense that the incentive is fair guarantees
that freight transportation participants will choose a sharing
strategy. Perceptions of unfairness can lead to resistance and
rejection behavior [49]. In addition, tax incentives and pos-
itive external network externalities are the key factors for
logistics platforms to choose a high level of service. To per-
fectly coordinate the supply chain while considering vehicle
capacity utilization, a fairness incentive, tax incentives and
positive network externality are considered. This implies that
the authorities should provide an appropriate tax incentive to
the logistics platform to invest in a “high-level service” strat-
egy, which will give the freight carriers and shippers more
initiatives to choose a sharing strategy. Consequently, the
logistics platform can develop positive network externalities
and provide a fair incentive payment to freight carriers and
shippers; hence, both freight carriers and shippers are willing
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Complex & Intelligent Systems
Fig. 7 (a)RH16, (b)RH25
Fig. 8 (a)IC1, (b)IC5
to support a sharing strategy, which leads to a win–win situ-
ation.
Discussion and managerial insights
1. Considering the freight transportation companies’ hor-
izontal collaboration, it is critical to construct an exci-
tation mechanism to coordinate the logistics platform
and freight transportation companies to increase the rate
of vehicle utilization. The logistics platforms prefer to
obtain a higher positive network externality to facilitate
horizontal collaboration, they must provide a “high-level
service”. From Fig. 7, we can conclude that when RH
16, namely, the positive network externality is lower, the
horizontal collaboration is not working. However, when
RHincreases to 25, the positive network externality is
located at a higher level, and the logistics platform and
freight transportation companies will be coordinated.
2. The logistics platforms that prefer to promote horizon-
tal collaboration should consider four cases: (1) when
the positive network externality and tax incentive are
both higher, the logistics platforms should provide a
“high-level service” to attract the freight transportation
companies. (2) When the positive network externality
and tax incentive are both lower, the logistics platforms
will provide a “low-level service” to protect their own
profits. (3) When the positive network externality is
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Complex & Intelligent Systems
Fig. 9 (a)IA1, (b)IA3
higher and the tax incentive is lower, the logistics plat-
forms should provide a “high-level service” at a low level
to attract the freight transportation companies (in Figs. 8a
and 9a, IC1 and IA1). (4) When the positive net-
work externality is lower and the tax incentive is higher,
the logistics platforms should provide a “low-level ser-
vice”, because the tax incentive may not cover its costs
(in Fig. 7a, RH16).
3. Our result indicates the significance of fair incentive
quantity between the freight shippers and the freight car-
riers. From Figs. 8,9, we can see that both the freight
carriers and shippers will not be attracted to the logistics
platform by a low incentive, such as IA1 and IC1.
This implies that a sense that the incentive is fair guaran-
tees that freight transportation participants will choose a
sharing strategy. As a result, the logistics platform should
take both the fairness between members and a moderate
incentive quantity into account when making incentive
decisions.
Conclusions and implications for future
research
This paper discussed the interaction and cooperation among
freight transportation participants from a sustainability per-
spective. Conflicts of interest among freight carriers, freight
shippers and logistics platforms are analyzed. Thereafter,
the evolutionary trends of the three participants’ behavioral
strategies are analyzed using a three-player evolutionary
game model. Finally, the impacts of relevant factors on the
evolutionary results of the behavioral strategies of the partic-
ipants are investigated. The conclusions are as follows:
(1) Strict fairness of the logistics platform is necessary for
the sustainable operation of the platform in the long
term. According to the numerical analysis, there are no
differences in the results of the three-player game with
different initial states.
(2) Given the conflict of interest among freight carriers,
freight shippers and logistics platforms, the interests of
the three participants can be transformed into revenues
and costs to formulate a TEGM. The replicator dynam-
ics equation is used to solve for the equilibrium solution
of the TEGM. The behavioral strategies of the three
participants can be changed to “share transportation
capacity”, “share demand information” and “high-level
service” to balance the interests of the participants by
adjusting the parameters (e.g., t2,RH,IC,IA).
(3) By reducing the tax on freight transportation on the
logistics platform and increasing the positive network
externality, the logistics platform will eventually choose
the “high-level service” strategy. By increasing the pay-
ment incentives and tax incentives for freight carriers
and shippers, they will eventually choose the “share
transportation capacity” and “share demand informa-
tion” strategies. Moreover, a fair payment incentive can
balance freight carriers’ and shippers’ enthusiasm to
participate in horizontal collaboration on a logistics plat-
form.
This study provides several insights into the behav-
ioral theory of freight transportation participants regard-
ing sustainable operation. First, a theoretical link between
sustainable principles and the behavior of freight trans-
portation participants is proposed to balance the interests
of the participants. Second, this paper aims to design an
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Complex & Intelligent Systems
interest-coordination mechanism among freight transporta-
tion participants to guide each participant to choose the
behavioral strategy that benefits the sustainability of freight
transportation. Third, meaningful suggestions are provided
for authorities’ development of freight transportation. In
the era of logistics distribution, vehicle capacity utilization
has become very common in many areas, such as freight
transportation. Therefore, it will be helpful to consider vehi-
cle capacity utilization to study horizontal collaboration on
logistics platforms. Furthermore, this study can be extended
by introducing the Bayesian network inference mechanism,
because the freight demand distribution can be explored over
time in a Bayesian manner when it is unavailable. We hope
to study these problems in the future.
Funding This work was funded by National Natural Science Foun-
dation of China (Grant no. 62073341), National Aerospace Science
Foundation of China (Grant no. 71801105), Scientific Research Start-
up Foundation for Introduction of Advanced Talents in Hunan Institute
of Technology (Grant no. HQ19004), 2021 Teaching reform research
project of Hunan Institute of Technology (Grant no. hgjg-202106) and
Scientific research project of Hunan Institute of Technology (Grant no.
2022hy003).
Open Access This article is licensed under a Creative Commons
Attribution 4.0 International License, which permits use, sharing, adap-
tation, distribution and reproduction in any medium or format, as
long as you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons licence, and indi-
cate if changes were made. The images or other third party material
in this article are included in the article’s Creative Commons licence,
unless indicated otherwise in a credit line to the material. If material
is not included in the article’s Creative Commons licence and your
intended use is not permitted by statutory regulation or exceeds the
permitted use, you will need to obtain permission directly from the copy-
right holder. To view a copy of this licence, visit http://creativecomm
ons.org/licenses/by/4.0/.
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