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The Relationship Between Agent-based Simulation

and Game Theory in the Case of Parallel Trade

Ruhollah Jamali∗and Sanja Lazarova-Molnar†∗

∗The Maersk Mc-Kinney Moller Institute, University of Southern Denmark, 5230 Odense, Denmark

{ruja,slmo}@mmmi.sdu.dk

†Institute AIFB, Karlsruhe Institute of Technology, 76133 Karlsruhe, Germany

sanja.lazarova-molnar@kit.edu

Abstract—Pharmaceutical parallel trade emerged due to the

European Union’s single market for medicines. While many

players, such as manufacturers, wholesalers, parallel traders,

pharmacies, regulatory authorities, and hospitals, are involved

in this market, having a model that accurately reﬂects the

parallel trade market could be a considerable advantage for

players in this market. One way to model the parallel trade

market is by employing game theory, which is frequently used

to model and explain business interactions. However, game

theory imposes limitations on models. Agent-based modeling is

a promising framework for studying the parallel trade market,

which allows us to investigate macroscopic outcomes that emerge

from microscopic rules, decisions, and interactions. Moreover,

agent-based modeling allows for high expressiveness and com-

plexity in agents, improving agents’ efﬁciency in autonomy and

reactivity compared to current game theoretic models. In this

paper, we develop the concept of an agent-based model for the

pharmaceutical parallel trading market based on an available

game-theoretic model of the market.

Index Terms—agent-based modeling and simulation, game

theory, modeling and simulation, pharmaceutical parallel trade

I. INT ROD UC TI ON

Modeling and simulation enable us to test hypotheses or de-

cisions with the desired number of assumptions and obtain an

intuitive result that is easy to interpret, reducing the possibility

of making decisions that negatively impact predeﬁned perfor-

mance metrics and allowing decision-makers to assess various

factors’ impact. A model is an abstraction of an objective

process or system that can help us study the process/system of

interest and predict the impact of different inputs on selected

performance measures. Simulation refers to the process of

using a computational model to gain insight into a complex

system’s behavior and evaluate designs and plans without

actually bringing them into existence on a real-world level [1].

Agent-based modeling is a computational modeling

paradigm in which the dynamic actions, reactions, and in-

tercommunication protocols among agents in a shared en-

vironment are invoked. Agent-based modeling demonstrated

remarkable performance in modeling real-world business in-

teractions [2]–[4]. Game theory, on the other hand, provides

a theoretical framework to model relationships of competing

agents and their logical interactions [5]. Both frameworks,

agent-based modeling and game theory, are related, allowing

for knowledge exchange on different models [6]–[9]. In this

paper, we discuss the relationships between game theory and

agent-based modeling and utilize an existing game theory

model of the pharmaceutical parallel trade market [10], [11]

to develop the basis of agent-based models for simulating the

interactions between different players in this market. An agent-

based model of the pharmaceutical trading market enables us

to run simulations considering various assumptions to research

and predict the market.

The paper is structured as follows. Section II offers an

overview of game theory and agent-based modeling back-

ground and their relationship. We conclude Section II with an

introduction of our domain of interest, i.e., parallel trade, and

its characteristics. In Section III, we present a game-theoretic

model for the parallel trade of pharmaceuticals. Further in this

section, we discuss employing the game-theoretic model as

a basis for agent-based modeling. In Section IV, we discuss

our work and possible future routes. In the ﬁnal Section, we

summarize our contributions.

II. BACKGROU ND A ND R EL ATED W OR K

This section provides a background on game theory and

agent-based modeling. Next, we discuss the relationship be-

tween these two paradigms. Finally, we provide information

about the parallel trade of pharmaceuticals and discuss the

application of game theory and agent-based simulation for this

market.

A. Game Theory

Game theory studies strategic interactions of logical agents

(players or decision-makers) in different scenarios. There are

always payoffs and outcomes for each agent’s action, depend-

ing on other agents’ decisions [12]–[15]. The idea of game the-

ory was introduced by Neumann and Morgenstern [16] where

they argued that most economic questions should be analyzed

as games. Strafﬁn deﬁnes game theory as a method of making

a decision under speciﬁc and interactive conditions, in which

the consequences of actions are affected by the actions of other

agents [17]. Game theory models are abstract representations

of various real-life situations, including economics, computer

science, and social psychology, which provides promising

tools for investigating decision outcomes in a situation.

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In game theory, a game is deﬁned as a situation in which

a decision-maker makes strategic actions that could impact

other players’ actions and responses. The value associated with

the action in the game is called payoff, which also depends

on other agents’ decisions. A strategy is a plan of action

or decision for playing a game. Games are categorized as

cooperative and non-cooperative, where players can form an

alliance in cooperative games. On the other hand, in non-

cooperative games, they compete with each other, and they

are self-enforcing. There are various solutions and strategies

for a game. A strategy with the best payoff is called dominant

strategy, and a state of a game in which every player is doing

their best regardless of other players’ actions is called equi-

librium [12]–[15]. In other words, when a unilateral decision

change by one player would have a negative impact on his

payoff, the players are in an equilibrium.

An advertising game is a simple game example in which

two companies decide whether to advertise or not. Let us

say we have two companies, A and B. If both companies

advertise, both will gain 10 dollars; if one company advertises

and the other does not, each will get 20 and 5 dollars,

respectively. Finally, if none of them advertises, they will gain

nothing. Table I is a summarized representation of this game,

where each tuple represents the payoff of each company for a

different choice, the ﬁrst number is the payoff for company A,

and the second one is the payoff for company B. In this game,

the dominant strategy for both companies is to advertise. In

the case of advertising, their income (either 20 or 10) is higher

than not advertising (either 5 or 0) case. Therefore, equilibrium

can be achieved if these two companies choose to advertise in

the market.

The purpose of game theory is to provide a framework for

developing a model for players to determine what strategy or

combination of strategies they should follow to optimize their

proﬁt, reward, or other success indicators. Pecorino [10], and

Grossman and Lai [18] formalized parallel trade as a game

theory model, which could investigate agents’ interaction in

this market and also investigate what they are trying to achieve

through interaction.

TABLE I

ADVE RTIS IN G GAM E RE PRE SE NTATIO N

Company B

Advertise Does not advertise

Company A Advertise (10, 10) (20, 5)

Does not advertise (5, 20) (0, 0)

B. Agent-based Modeling

Agent-based modeling (ABM) is a computational frame-

work for modeling and simulating dynamic processes involv-

ing autonomous and interacting agents, with the intent to

assess agents’ effects on the whole system. In other words,

ABM is a computational replication of a conceptual model

of a system based on discrete entities (agents) with deﬁned

properties and behavior rules used to simulate the entities

on a computer to mimic the phenomena occurring in the

real world. ABM is suitable for modeling complex systems

composed of various interacting autonomous agents with many

degrees of freedom. Autonomous agents can represent individ-

uals, companies, organizations, authorities, customers, or the

like, acting independently in response to external factors and

through interactions with each other. One of the ﬁrst tutorials

for building agent-based models of real-world problems was

presented at the Winter Simulation Conference in 2005 [19].

Various complex systems have been simulated with agent-

based models, from social and economic models [20] to lo-

gistic optimization models [21], and crowd simulation models

[22].

Compared with game-theoretic frameworks, agent-based

modeling can go far beyond what is analytically feasible. One

good example of ABM application is the representation of

Hotelling’s law [23]. Hotelling’s law is an economic observa-

tion that shows that the rational decision for ﬁrms is to make

their products as similar as possible. However, with Hotelling’s

law model and using ABM, we can investigate many aspects

of a market. For example, we can investigate how different

stores can compete over market share by changing the price

of the same product. In this example, stores are the agents

with a variable attribute, the price of the product, and a ﬁxed

attribute, which is their location on the grid. The environment

is the neighborhood, represented as a grid, and each cell

represents a customer. The interaction rule in this example

is that customers add up the price and the distance from the

store and then choose the lowest sum as their preference, and

in case of a tie, they will choose randomly. In this example, we

can investigate how adjacent stores end up in competition and

observe that isolated stores have the most signiﬁcant venue.

Having such observation in simulation, we can say that the

location of a store has a signiﬁcant impact on its revenue.

Figure 1 represents this model for ﬁve stores using Netlogo

[24], in which stores compete by changing the price of the

same product to get a more signiﬁcant market share.

The pharmaceutical trading market and its activities can be

modeled as an agent-based model in which the agents are

ﬁrms, wholesalers, and shops, and the price and bargaining

power could be traits. Using such a model, we can investigate

the outcome of decisions like pricing and ordering.

C. The Relationship between Game Theory and Agent-Based

Simulation

Several studies have pointed out and established relation-

ships between game theory and agent-based simulation, al-

though in different contexts than the one we consider. Szilagyi

[9] described the difference between game theory and agent-

based modeling, speciﬁcally for two-person games and N-

person games, and then reviewed the usefulness of agent-

based modeling in the investigation of N-person games. In

another relevant study on evolutionary game theory, Adami et

al. discuss the differentiation between the game theory model

and agent-based modeling and the idea of how it could be

beneﬁcial to use a game-theoretic model to understand the

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Fig. 1. Hotelling’s law agent-based simulation representation of stores

competition to get a bigger market share of the same product by changing

price of the product

selective pressure that affects the evolution of agents with

potential conﬂicts [25]. In their paper, they investigated the

limitations of the mathematics of game theory to model evo-

lution, where the decisions are not always deterministic, and

previous experiences can also inﬂuence them. Furthermore,

Adami et al. explored how using an agent-based modeling

method in a game-theoretic framework could capture evo-

lutionary information. Following this study, we encountered

a case study of agent-based models for evolutionary game

theory [26], where the authors present a game with complex

interactions and examine how an agent-based model can be

used to ﬁnd evolutionary stable states.

D. The Case of Parallel Trade

The European single market for pharmaceuticals enabled

parallel trade of pharmaceuticals over Europe [27]. The par-

allel trade of pharmaceuticals enables companies to import

products from purchase markets where direct importers sell

their preparations at lower prices. The parallel market prevents

monopoly suppliers from engaging in international price dis-

crimination [28].

The margins in parallel trading of pharmaceutical products

are tiny; therefore, decisions concerning timing and pricing

can signiﬁcantly affect proﬁtability. Furthermore, companies

selling pharmaceuticals often pay huge penalties if they are

unable to deliver agreed products within the agreed time frame.

Hence, parallel trading is characterized by a range of complex

business decisions and factors, such as which pharmaceutical

products to buy, when to apply for marketing authorization,

what price to pay for which product, the amounts to buy, which

markets to enter with a speciﬁc product, patent expiry dates,

when to leave which markets, etc.

All pharmaceutical trading decisions are strongly affected

by a dynamic set of actions from various players (agents)

in the market. There have been many efforts for modeling

parallel trade environment, investigating various aspects of it

[28]–[30]. Since all agents in this market make decisions with

their objectives, we can model parallel trade employing non-

cooperative game-theoretic models.

III. THE R EL ATIO NS HI P BE TW EE N AGE NT-BA SE D

MO DE LI NG A ND G AM E TH EO RY IN THE CASE OF PAR AL LE L

TR AD E

A. Underlying Game Theory Models for Parallel Trade

The pharmaceutical parallel trade market has been modeled

using game theory [10], [11], where Pecorino’s goal was to

investigate a ﬁrm’s proﬁt with the presence of parallel trade

or without it. Pecorino also discussed the change in social

welfare due to the parallel trade regime. Guo et al. wanted

to investigate the impact of having parallel traders in the

pharmaceutical market and its impact on a ﬁrm’s proﬁt. Both

models represented an economic view to investigate the impact

of parallel trade. We continue to elaborate in more detail on

Pecorino’s model.

The problem deﬁnition is as follows. A simple pharma-

ceutical market consists of at least two countries; here, we

name them Eand Ias Exporter and Importer, respectively. We

consider a monopolist pharmaceutical manufacturer located in

Eto produce and sell a patented medicine in Eand sell that

medicine in Iafter negotiating its price with their government.

We refer to the price of this medicine in Eand I,PE, and

PI, respectively.

To simplify the model, we consider the production cost of

the medicine to be zero. We will refer to the demand in E

as QE, and QIrepresents the demand in I. Since we aim

to develop a general model, we have a normalized demand

function for the noted medicine in country E, so both prices

and demands are between zero and one. The demand function

in Eis QE= 1−PE. For the country I, the demand function

is QI=α−PI, where αis assumed to be less than 1such that

the monopoly price in Eis higher than I. Since both demand

functions have the same slope, αcould be interpreted as the

unambiguous market size measure.

We consider two steps for setting PEand PI. In the ﬁrst

step, the ﬁrm and the government in Inegotiate the price of

the medicine (PI), which is determined by a Nash bargaining

game [10]. According to Pecorino, the price will be the one

that maximizes this weighed geometric average, i.e.:

max

PI

[CS (PI)γ][πI](1−γ),(1)

where γand 1−γrepresent the bargaining power of the

country Iand the ﬁrm, respectively, during the negotiation.

γvaries between zero and one, demonstrating the trade-

off between each party’s bargaining power in this market.

Here CS (PI)represents the consumer surplus, which is the

payoff for the country in the bargaining, and πIis the proﬁt

of the ﬁrm. The consumer surplus is the area under the

demand curve, which in our case, will be half of the demand

function squared. Furthermore, since the production cost of the

medicine is assumed to be zero, the proﬁt can be expressed as

a product of the demand and the price. In our case, we have

the following:

CS (PI) = 1

2(α−PI)2and πI= (α−PI)PI.(2)

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By putting these into equation 1, the PIthat maximize the

equation 1 (equilibrium price (PINE )) will be:

PINE =α(1 −γ)

2.(3)

For the second step, we consider there exist nparallel

traders that purchase the medicine in Iwith the negotiated

price of PIand sell it in Ewith a transfer cost of t.

Considering exporter country E, we can estimate equilibrium

price (PE)modeling parallel traders and the ﬁrm having a

Cournot competition. Cournot competition is an economic

model describing companies’ competition in quantities for

providing a homogeneous product. In our case, a homogeneous

product is a patented medicine. In Cournot competition, ﬁrms

are rational, meaning they act strategically to maximize their

proﬁt given other ﬁrms’ decisions. All these characteristics can

be observed in the pharmaceutical trading market. Solving the

Cournot equilibrium, we have:

qt=(1−2(PI+t)

n+ 2 ,if PI≤1

2−t

0, otherwise .(4)

Where qtis the quantity sold in country Eby a parallel trader.

Then, the total quantity sold by all parallel traders (QT)is:

QT=n×qt,(5)

and the quantity sold in the country Eby the pharmaceutical

trader QMis equal to:

QM=(1−2n(PI+t)

2(n+ 2) ,if PI≤1

2−t

0, otherwise .(6)

The equilibrium price is:

PE=(1

2[1 −n(1 −2(PI+t))

n+ 2 ],if PI≤1

2−t

1

2, otherwise .(7)

In this way, we calculate the equilibrium prices in both

countries, considering nparallel traders. Having this model

and equilibrium prices, we can investigate general assumptions

like how bargaining power could impact an equilibrium. For

example, Guo et al. [11] demonstrated the impact of different

values of the bargaining power on the equilibrium price in

different market sizes. However, markets such as pharmaceuti-

cal parallel trade are dynamic and complex, and to accurately

model them; we need a more dynamic framework in which

parameters, such as bargaining power and transfer cost, could

ﬂuctuate as agents’ features as in the real world.

B. The Synthesis of Agent-based Modeling and Game theory

Although game theory can represent a mathematical formal-

ization and equilibrium for the competition in pharmaceutical

trading, we need a more ﬂexible and dynamic framework to

use data and simulate models repetitively to investigate the

impacts of different possible decisions. Agent-based modeling

can provide these features while utilizing the game theory

model. Generally, an agent-based model contains a collec-

tion of autonomous decision-making entities, which we term

agents. These agents have different attributes that can be ﬁxed

or variable, and they interact with each other based on a set of

rules. In the agent-based model that we subsequently describe,

we use the game theory model introduced in Section III-A as

a basis for deﬁning agents’ attributes and the corresponding

rules of interaction.

The whole idea is that the pharmaceutical trading mar-

ket can be modeled by deﬁning agents, environment, and a

description of agent-agent and agent-environment interaction.

The agents and the environment have attributes and rules of

interaction, and these can be deﬁned as either variable or

ﬁxed. After deﬁning attributes and rules, simulation of the

actions and interactions of autonomous agents can help us to

understand the behavior of the system and what governs its

outcome.

We use the following deﬁnitions to base our agent-based

model. First, we deﬁne the environment and agents of our

agent-based model. In the model that we propose, we consider

two countries (Eand I), a manufacturer, a government (gov-

ernment of country I), and nparallel traders. We deﬁne the

environment as a set of two countries: country Ias a part of the

environment has two attributes: the price of the medicine (PI),

which is variable, and the unambiguous market size measure

(0 < α < 1) which is ﬁxed, and we consider the market

size in Eto be also a ﬁxed variable with the value of 1as we

had in the demand function deﬁned in Section III-A. Then,

we deﬁne manufacturer, government and parallel traders as

agents. Their attributes are as follows. Government has only

one attribute, which is the bargaining power (γ), and it is ﬁxed.

Manufacturers have the following attributes: bargaining power

(which is 1minus the bargaining power of the government),

which is ﬁxed, market share in country E, which is variable,

and revenue, which is also variable. Parallel traders have the

following attributes: transfer cost (t), which is ﬁxed, market

share in country E, which is variable, and revenue (sell minus

costs), which is also variable.

Secondly, we deﬁne the rules for the model and deﬁne what

happens in each step of the agent-based model. Each step

has two chronological events happening. First, the government

of the country Iand the manufacturer start a negotiation to

set the price (PI)according to the Nash bargaining game

that we discussed in Section III-A. Subsequently, there are

two possibilities: (1) if PI>1

2−t, then there is no

revenue for the parallel traders, so they will not participate

in the market and the manufacturer will act as a proﬁt-

maximizing monopolist in the country Eand set the price as

1

2;(2) if PI≤1

2−t, then parallel traders can participate

in the market of country E. Then parallel traders and the

manufacturer compete to maximize their revenue in country

E. Since parallel traders and manufacturers are selling the

same product in the market, they will compete by adjusting

their sell quantity (market share) to maximize their proﬁt while

knowing other players’ current market share. Manufacturer

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proﬁt function (πm)is:

πm= [1 −(qm+qT)]qm+PIqT,(8)

where qmand qTare the sell quantity of the manufacturer and

total sell quantity of parallel traders in country E, respectively.

The ﬁrst term of this equation represents the proﬁt of the

company from their sales in country Eand the second term

represents proﬁt from sell in country I. Proﬁt function for a

parallel trader (πt)is:

πm= [1 −(qm+qT)−PI−t]qt,(9)

where qtis a parallel trader’s sell quantity in country E.

In every step of our model, the manufacturer calculates their

proﬁt function using current market share values and adds the

result to their revenue. Afterward, the manufacturer adjusts

their market share by considering increasing, decreasing, or

keeping the current market share in both countries, and they

will adjust it by the value that brings the highest proﬁt for

them in both countries. Parallel traders also perform the same

procedure; however, they only consider the market in the

country E. Subsequently, with new market shares, we can

calculate the medicine price in the country Efor the next

step using the demand function of country E. Figure 2 is a

visualization of the above-described agent-based model, where

all described attributes and possible interactions are illustrated.

Fig. 2. Illustration of the agent-based model of the simpliﬁed parallel trade

scenario

The basis of the agent-based model is derived from the game

theory model. However, the agent-based model gives us the

ﬂexibility to consider more factors in the market. For instance,

not all parallel traders need to have the same properties;

instead, we can consider an attribute like supply power to vary

across time and agents. With the agent-based model, we can

simulate various scenarios to investigate the impact of different

elements on the market, such as setting prices, increasing

supply power, or long-term strategies, deﬁning more realistic

scenarios. Such an agent-based model can, furthermore, be

calibrated using available data.

IV. DIS CU SS IO N

The ﬁrst step to simulating a business process is to for-

malize it and have a model that accurately reﬂects the actual

process, given the goals of the simulation study. While this

simulation can differ in goals, such as ﬁnding the best price

for a product, selecting a market that offers better revenue

and less competition, or improving the company section, it

could be tricky to ﬁnd a suitable model to represent the

target business process. In our case, since parallel trade has

economic characteristics, competition in this market could

be represented as a non-cooperative game where each player

pursues their interests. Considering this, we can utilize game

theory, which is the mathematical study of interactions and

strategies among players. With game theory, we are able to

represent economic behaviors by using models and features.

In game theory, a game is in fact, a formalized description

of a strategic situation. However, this formalization could be

rigid in some cases, so we want to consider randomness. For

example, evolutionary behavior could cause randomness in

each player’s characteristics. In parallel trade also, players

can learn from mistakes, change their behavior, and grow in

size and power. Hence, we need a ﬂexible tool to employ

game-theoretic formalization. Agent-based modeling can give

us this ability. In our agent-based model, agents will not decide

randomly, but they will consider the situation rationally, and

with the model they have, they will decide. Their decisions

could have several aspects, such as reducing the bargaining

power of the rival in the Nash bargaining situation or only

considering net proﬁt. Employing such a model allows us to

simulate different scenarios and investigate various decisions.

Following what we discussed, this model can be devel-

oped further by considering more and more features and

characteristics. For example, we can formalize a company’s

personality with a basis of different characteristics like the

idea of Oldham and Morris [31] work where they formalized

a normal person’s personality as a combination of 16 different

disorders. Having such formalization can help us develop a

more realistic model where companies are different regarding

their past and decisions rather than having a model where

all the companies are the same. We can also consider some

characteristics of the product, such as medicine quality which

deﬁnitely impacts a user’s preference.

Considering all characteristics that we discussed, data can

provide information to approximate such characteristics and

features. Also, having historical data would enable us to

validate the model. However, companies may act according

to their strategy, which is related to their characteristics and

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growth overview. Considering the fact that currently, we did

not formalize the characteristics of a company before, we

may face a lack of data, which means that in some cases,

a simpler model can give us a better replication of an actual

world situation.

In our future work, we aim to involve other players in the

pharmaceutical trading market, such as wholesalers, hospitals,

and pharmacies. Although having information and deﬁning

characteristics for each of these players would be a challenge,

we may need to involve them to get a more realistic replication

of such a market.

V. SUMMARY AND OUTLOOK

In this paper, we reviewed game theory and agent-based

modeling and simulation in an attempt to link both and

develop a basis for utilizing existing game theory models

towards building an agent-based model of the parallel trade

market of pharmaceuticals. Therefore, we presented a game

theoretic model of the pharmaceutical trading market, which

we subsequently used to develop an agent-based model for

this market, resulting improvement of agents’ efﬁciency in

autonomy and reactivity. After all, we discussed how using

an agent-based model for the pharmaceutical trading market

would be beneﬁcial for different purposes, such as inves-

tigating the economic impact of parallel trade presence in

the pharmaceutical market or developing a decision support

system for the different players in this market. Developing an

agent-based model for the pharmaceutical parallel trade market

provides the opportunity to utilize available historical data of

this market to run a data-driven simulation. This simulation

can give us the opportunity to research economic parallel trade

impacts on players and prices, all players’ decision outcomes,

and market activities.

There are a number of aspects where we can further

develop this model. The ﬁrst one is considering more than two

counties, we considered the current model as an initial model

to investigate the whole European pharmaceutical market.

Therefore, in future we will expand the model to more than

two countries. The second one is to deﬁne the personality of

each player in this market, considering different characteristics

for them. The third one is to consider more attributes and

interactions in the pharmaceutical market. Finally, we plan to

use historical data for the parameter estimation and simulation,

as well as validation of the model, leading to a software to

support the simulation of different decisions and scenarios

within the domain of parallel trade of pharmaceuticals.

ACK NOW LE DG ME NT

This work is partly funded by the Innovation Fund Denmark

(IFD) under File No. 9065-00207B.

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