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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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