UJIAN TENGAH SEMESTER (UTS)

TEORI PERMAINAN BISNIS

Sarah Aryana
2144051

PROGRAM MAGISTER MANAJEMEN

FAKULTAS EKONOMI
UNIVERSITAS INTERNASIONAL BATAM
2023
1. What is exactly Game Theory? Set up the 3 part should be in the games theory
domain.

Game Theory is an approach mathematically to formulate situations of competition and

conflict between the various interest. This theory was developed to analyze the decision-
making process of different competitive situations involving two or more parties. In the
game, the first party is called the player row while the second party is called a column
player. The assumption is that each player (individual or group) has the ability to make
decisions freely and rationally. Each player is considered to have a series of plans or a set
of strategies to choose from. Strategy shows for every situation that arises in the process
of the game used to decide what action to take.
Factors that influence the use of game theory are:
1. The number of players
 When the number of players is two, the game is referred to as a two-player game.
 In a two-player game, it can be divided into two, namely a two-person zero-sum game
and a two-person non-zero sum game

2. Total profit and loss

 If the amount of profit and loss is zero is called a game with zero sums
 The zero two-player game is a competition of two players where the win of one is the
loss of the other player, so the number of wins and losses is zero.

3. The number of strategies carried out

 If not equal to zero, the game is called a non-zero sum game.
 In a non-zero two-player game, one player's win may not necessarily be the other
player's loss.

2. Game theory gets interesting, however, only when there is tactical interaction, that
is, when everyone tries to figure out their rivals strategy before they move. Which
one of this sport determine their move by using game theory: football (American or
European); Table Tennis; Tennis; Swimming; Chess; Diving; Marathon;
Basketball. Choose and give your explanation.

I choose football (American). In football, we know that there are penalty kicks and we
even know the term "penalty shootout" when a team's victory depends on the success or
failure of a penalty kick. When a penalty kick occurs, a player must face the opposing
team's goalkeeper in a mentality battle.

Based on game theory, the most optimal action of a player and goalkeeper is to always
ensure that the direction of his kicks and jumps cannot be predicted by the opponent. One
of the results of research conducted by Ignacio Palacios-Huerta, an economist from
 Brown University, revealed that in penalty kicks, professional football players are
actually able to apply game theory optimally.

Example :

Left : 58x + 93 (1-x) Right

= 58 + 93 – 93x = 95 + 70(1-x)
= 93 – 35x = 70 + 25x

If an equation is made : level of success : 79,6%

93 – 35x = 70 + 25x
23 = 60x
X= 23/60 = 0,383

3. There has been a growing recognition that game theory is a crucial tool for
understanding the modern business world. Game theory makes it possible to move
beyond overly simple ideas of competition and cooperation to reach a vision of
coopetition more suited to the opportunities for our time. Read Brandenburger and
Nalebuff (1997 – Co-opetition) and make a short simple paper to explicate Game
Theory before move to competition or cooperation strategy. Hints: Several
component to explicate Game Theory are: Added Value, Rules, Perception,
Boundaries, Rationality and Irrationality.

Brandenburger and Nalebuff (1997) describe coopetition as part of a business game

related to value creation and empowerment. schematically the entire business game
scenario is described in a tool called the value network (Value Net). Brandenburger and
Nalebuff identify all the elements in play. there are 5 game elements, namely Player
(Player), Added Value (added value), Rules (rules), Tactics (tactics), Scope (coverage).
according to both PARTS are elements that can be used to change the business game.

Coopetition combines the advantages of competition and cooperation into a new dynamic
that can be used not only to generate more profits but also to change the nature of the
business environment as desired. To actively change the business game, a strategic
framework is needed to work from, and coopetition theory provides such a framework.
that way, not only can you change the way you play, but also to get the maximum profit.

Coopetition strategy is a part of game theory where this theory is an approach that
illustrates a business environment game involving two or more companies. Game theory
helps to model, analyze and understand the behavior of the parties involved in business.
The application of game theory is able to change the field of business strategy, one of
which is through a coopetition strategy, where companies are required to be able to
compete while working together to create and gain value (Brandenburger & Nalebuff,
1997).
 Game Theory Group Article
Mata Kuliah Theory Permainan
Pada Program Studi Magister Manajemen
Fakultas Bisnis dan Manajemen

Disusun Oleh:
Kelompok 3

Claudio E Winarno (2144049)

Mira Yunita (2144044)
Sarah Aryana (2144051)

PROGRAM STUDI MAGISTER MANAJEMEN

UNIVERSITAS INTERNASIONAL BATAM
2023
Choice, Chances & Strategic Moves

Claudio E Winarno1, Mira Yunita2, Sarah Aryana3

Abstract

This study sought to explore the interplay between choice, chance, and strategic moves. This
study utilized secondary data from previous studies to briefly explain how choice, chances and
strategic moves interplay with each other. Strategic moves can be powerful tools for achieving
desired outcomes, but they can also backfire if they are not well-designed or well-executed.
Therefore, a player should carefully consider the costs and benefits of making a strategic move,
as well as the possible reactions and responses of other players.

Keywords: game theory; choice; chance; strategic moves

Introduction
The study of logical behavior in competitive and interdependent settings is what game
theory is all about. It is an organized approach to the study of how individuals who behave
rationally and strategically interact with one another. The objective of game theorists is to create
models of games that are straightforward to understand and investigate. The outcome of any
individual's decision is contingent not only on that individual's decision but also on the decisions
made by all the other participants. The study of games focuses on the dynamic relationship
between player decisions, random events, and calculated play.
It is evident that game theory can be applied to the process of decision-making, which is
practically useful for businesses that must think strategically to remain effective and competitive
in their industries. For instance Hendalianpour (2020) developed a game-theoretic model to help
retailers make pricing and lot-sizing decisions for perishable products. The model uses DIGN
(double interval grey numbers) to better understand consumer behavior and improve analytical
results for practical decision-making. The model can help retailers optimize proper resource
allocation and provide optimal pricing strategies for perishable goods.
Wang et al (2021) sheds light on how to strategize a social media communication during
critical events, highlighting how an opportunistic approach strategy proved to be disastrous for
the United Express Flight 3411 incident by sparking negative social media consequences. They
discovered that a company's optimal choice of strategy during a social media storm is contingent
on the costs of that strategy and the likelihood of netizens publicly condemning the company on
social media. The findings indicate that the company's choice of response strategy affects the
evolution of the strategy pursued by Internet users.
Beal et al (2020) offer an additional illustration of how game theory could be utilized in
football decision-making, as winning a game requires numerous tactical decisions, including but
not limited to assigning positions to players, composing a team, and reacting to in-game events.
These decisions must be made in the face of considerable levels of uncertainty and frequently in
highly dynamic environments. The study found that away teams are more likely to select
strategies that reduce the opponent's chances of winning than those that maximize their own.
Conversely, home teams have an advantage and employ a dominant strategy to increase their
chances of winning.
The aforementioned literature provides a picture of choice, chance, and strategic moves
interplay with each other and are indeed a central feature of game theory. In these circumstances,
the outcome of a person's decision is contingent not only on their own actions but also on the
actions of others. Therefore, game theory could help to investigate how individuals and
organizations make decisions based on their knowledge of the available options, the probability
of various outcomes, and the strategies of others. Choice, one central aspect of game theory
suggests that individuals and organizations must make decisions based on the available
alternatives. The outcome of the decision-making process is influenced by probabilities and
unpredictability, which makes chance an important factor.
Strategic moves are the actions that individuals or organizations take to achieve their
desired outcome while considering the options and strategies of others. Individuals or
organizations are assumed to be rational, payoff-maximizing decision-makers in game theory.
The payoff is the benefit or cost associated with each potential outcome. By analyzing the
interplay between choice, chance, and strategic moves, game theory provides a framework for
predicting outcomes and making well-informed decisions in strategic situations. This article will
discuss how choice and chance with strategic moves could help individuals or groups to take an
effective strategic decision that could help them select appropriate strategy given the
circumstances that they are facing.
2. Literature Review
2.1 Choice
Choice is the freedom of organizational actors to choose and act according to their own
volition (Rond & Thietart, 2007). Rond & Thietart (2007) assumes that decisions are
implemented (for choice has no bit otherwise). In light of the fact that strategic choice involves
some form of individual judgment, the argument is less relevant to abstract conceptions of
agency (e.g., organizations, industries or the public). Strategic Choice alone is insufficient to
explain strategy. Choice, like chance, is a background-dependent contributory factor.
2.2 Chance
Chance refers to an event happening in the absence of any obvious design or randomly (Rond &
Thietart, 2007) One that is irrelevant to any present need or of which the cause in unknown.
Chance coincidences can open up new avenues for future choices.
2.3 Strategic Moves
2.3.1 Nash Equilibrium
In general, the optimal move for any given player in a game depends on the moves of the
other players. Therefore, when choosing an action, a player must consider the actions of the other
players. therefore, she must believe the other player's action (Osborne, 2000). The underlying
assumption of the analysis is that each player's belief is based on her past experience playing the
game and that this experience is extensive enough for her to predict how her opponents will act.
No one informs her of the actions her opponents will take, but her experience with the game
allows her to predict them.
The solution theory consists of two components. First, each player chooses her action based on
the rational choice model, taking into account her belief regarding the other player's action.
Second, each player's perception of the other's action is accurate. The definition of a Nash
equilibrium is intended to represent a steady state among skilled players. A different approach to
understanding player actions in strategic games assumes that players are aware of one another's
preferences and considers what each player can infer about the other player's actions based on
their own rationality and knowledge of the other player's rationality. It leads to a conclusion that
differs from the Nash equilibrium for many games. The approach provides an alternative
interpretation of a Nash equilibrium for games with identical outcomes, as the result of rational
calculations by players who do not necessarily have experience playing the game.
2.3.2 Pure Strategy
A pure strategy denotes a choice of an available action in games in strategic form (Grüne-
Yanoff & Lehtinen, 2012) . The formal theory defines a game as consisting of a set of players, a
set of pure strategies for each player, an information set for each player and the player’s payoff
function. A player’s pure strategy specifies her choice for each time she has to choose in the
game. If a player’s strategy requires choices at more than one time, we say that the strategy
contains a number of actions. Games which players choose between actions simultaneously and
only once are called Static games. In dynamic games players choose between actions in a
determined temporal order. All players of a game together determine a consequence. Each
choose a specific strategy, and their combination yields a specific consequences. The
consequence of a strategy profil can be a material prize for example money, but it can also be
any other relevant event, like being the winner or feeling guilt. Game theory is really only
interested in the player’s evaluation of this consequence, which are specified in each player’s
payoff or utility function.

2.3.3 Mixed Strategy

In mixed-strategy games, each player does not know which strategy the other players will
employ. Therefore, each player will attempt to devise a strategy whose payoff value does not
influence the opponent's strategy selection. First, the maximin and minimax methods are applied.
Mixed-strategy games are those in which the maximum value is not equal to the minimum value.
In these games, there is no saddle point, and pure strategy is not the optimal strategy. The
subsequent step is to implement the dominant strategy in an effort to reduce the size of the pay-
off matrix.
In a game solved with a mixed strategy, each player's strategy will have a probability
indicating the proportion of time or number of components used to execute the strategy. The
selection of a strategy will be made at random from among the available options. The
opportunity will determine the percentage of each strategy that will be selected. It is essential to
use this opportunity as a guide for executing strategic priorities. The specified odds may be based
on the decision maker's experience with decisions made by opponents or on research conducted
on the future outcomes of a decision.
2.3.4 Dominant & Dominated Strategy
A strategy is dominated if it is not the optimal response strategy regardless of the
opponent's strategy choices. In contrast, a strategy is dominant if it is the optimal strategy (i.e., it
maximizes a player's utility payoff) regardless of the opponent's strategy choices (Heap &
Varoufakis, 2003). Given that one of the two players has a dominant strategy, both the theorist
and the players are able to identify a single outcome as the only viable solution for the game.
This is referred to as an equilibrium solution because it is the only outcome that is not threatened
by ever-more-informed analysis of the situation. The more the players consider their situation,
the more likely it is that they will agree on an outcome.
2.3.5 Maximin & Minimax Strategy
A player's maximin strategy is a strategy that maximizes their objective function, which is
minimized by the opponent's strategy. A player's minimax strategy is the opponent's strategy that
minimizes their objective function, which is maximized by his strategy (Satoh & Tanaka, 2018).
The maximizer lists his minimum gains from each strategy and then chooses the strategy that
yields the greatest minimum gain. The player who seeks to minimize his loss enumerates his
maximum loss for each strategy and then chooses the strategy with the smallest loss among his
maximum losses.

3. Methodology
This study employs a qualitative approach in which the author expressed an opinion over
prior research. This study relies on secondary, with researchers utilizing scholarly journals,
books, and websites as references. This research approach is a case study, in which the
researcher investigates a study done by previous researcher and describe the topic taken as a case
study to give a clear picture of how choices and chances interplay with strategic approaches.
4. Discussion
4.1 Pure & Mixed Strategy
 Pure strategy is a decision rule that specifies a single action for a player in a game,
irrespective of the game’s state or the actions of other players. A mixed strategy is a decision rule
that assigns probabilities to various actions and then chooses an action at random based on these
probabilities. A mixed strategy can be viewed as a method for introducing uncertainty or
randomness into a game, making it more difficult for other players to predict or exploit one's
behavior. A pure strategy is a special case of a mixed strategy in which the probability of one
action is 1 and that of all other actions is 0. A mixed strategy can also be viewed as a convex
combination of pure strategies, with the coefficients representing the probabilities associated
with each pure strategy.
The decision between pure and mixed strategies is influenced by the structure and goals of
the game, as well as the preferences and beliefs of the players. Some games have pure strategy
Nash equilibria, in which each player can choose the optimal response to the strategies of the
other players without requiring randomization. Other games have mixed-strategy Nash
equilibria, in which each player can only choose the optimal response by randomly selecting
among various actions. Some games have both types of Nash equilibria, while others have none.
The benefits and drawbacks of pure and mixed strategies vary depending on the situation
and the players' objectives. Pure strategies may be more straightforward, transparent, consistent,
or credible than mixed ones. Mixed strategies may be more adaptable, resilient, unpredictable, or
effective than pure strategies. The optimal choice of strategy is determined by the trade-offs
between these factors and the expected returns from various outcomes. To provide a clear picture
of how pure & mixed strategy are employed consider a scenario in which two companies, A and
B, compete for market share. They can either advertise heavily or reduce their advertising
spending. Below is the pay-off matrix for this game, with payoffs expressed in millions of
rupiah.
  B Advertise Less B Advertise More
A Advertise Less 2, 2 0,5
A Advertise More 5, 0 1,1
Table 1. Pure Strategy

This game lets companies choose their advertising budgets. Both companies can make 2
million by spending less. The company that heavily advertises earns 5 million while the other
earns nothing. Both companies profit 1 million from heavy advertising. The pay-off matrix can
help businesses choose the best strategy. Company A should spend 5 million on advertising if it
thinks Company B will spend less. Company A should advertise heavily if it thinks Company B
will, earning 1 million. No matter Company B's strategy, Company A should heavily advertise.
Company B should spend 5 million on advertising if it thinks Company A will spend less.
If Company B thinks Company A will advertise heavily, it should spend less and make 1 million.
Thus, Company B should advertise heavily if it thinks Company A will spend less and less if it
thinks it will spend more. In this two-player game, a pay-off matrix can determine each
company's optimal strategy. Both companies benefit from extensive advertising, but their
strategies depend on their perceptions of the opponent's behavior.
In contrast, in a mixed strategy, players employ various strategies to achieve the possible
outcome. In baseball, a pitcher cannot consistently throw the same type of ball because it alerts
the batter to the type of pitch. In such a situation, the batter may score more runs. However, if the
pitcher throws the ball differently each time, the batter may become confused as to the type of
pitch. Consider the following pay-off matrix for this scenario.
  Pitcher Spin Ball Pitcher Fast Ball
Batter Spin Ball 30% 10%
Batter Fast Ball 10% 30%
Table 2. Mixed Strategy

When the batter and pitcher have identical expectations of the ball, the percentage of runs
scored by the batter is 30%. When the expectation is different, however, the odds are reduced to
10%. Should both parties employ pure strategy, either party may suffer a loss. In this instance, it
is recommended that the batter adopt a mixed strategy. For instance, the pitcher throws a 50/50
combination of spin and fastball, and the batter anticipates the 50/50 combination. In this
scenario, the average hit of runs per batter would be 20%. This 20% derived from four payouts
increased to 25%.
0.25(30%) + 0.25(10%) +0.25(30%) + 0.25(10%) = 20%
However, when the pitcher throws a 50/50 mix of spin and fastball, it is possible that the
batter will not always be able to predict the correct type of ball. This would reduce the run rate to
less than 20%. Similarly, if the bowler throws the ball with a combination of 60 percent fast and
40 percent spin balls, the batter expects either a fastball or a spin ball at random. In such a
scenario, the average number of hits per batter remains at 20%. 20% derives from expected
fastball and received fastball: 0.5 * 0.6 = 0.3 expected fastball and spin ball received; 0.5 * 0.4 =
0.2 expected spin ball and spin ball received; 0.5 * 0.6 = 0.3 expected spin ball and fastball
received; 0.5 * 0.4 = 0.2 expected spin ball and spin ball received; 0.5 * 0.4 = 0.2 when
multiplied by the payout in table 2.
0.3(30%) + 0.20(10%) + 0.20(30%) + 0.30(10%) = 20%
This demonstrates that the outcome does not depend on the combination of fastball and spin ball,
but rather on the batter's belief that he can receive any type of ball from the pitcher.
4.2 Dominant & Dominated Strategy
In game theory, dominant and dominated strategies are essential concepts that help players
analyze and optimize their decisions. A dominant strategy is one that yields better results for a
player than any other strategy, regardless of the strategies chosen by other players. A dominated
strategy is one that leads to worse outcomes for a player than any other available strategy,
regardless of the strategies chosen by the other players. Consider a game in which two
companies have the option to advertise or not advertise their products. If both companies engage
in advertising, they will each earn 5 million in profit. Without advertising, each company earns
10 million in profit. If one company advertises and the other does not, the advertising company
earns 15 million and the other company earns nothing.
Advertising is the dominant strategy for both firms in this game, as it always results in
greater profits than not advertising. Non-advertising is the dominant strategy for both companies,
as it consistently yields lower profits than advertising. Consequently, the equilibrium outcome of
this game is that both firms will advertise and earn 5 million. In this matrix, the first number in
each cell represents Firm A's profit, while the second number represents Firm B's profit. For
instance, if both companies advertise, they each earn $5 million in profit, so the return for that
cell is 10 million (5, 5). If Firm A advertises and Firm B does not, Firm A will earn 15 million in
profit while Firm B will earn nothing, so the payoff for that cell is 15 million (15, 0). Advertising
is the dominant strategy for both companies, so they will choose to advertise regardless of what
the other company does. Thus, the equilibrium result is that both firms will advertise and earn $5
million each.
  B Advertise B Don’t Advertise
A Advertise 5, 5 15,0
A Don’t Advertise 0, 15 10,10
Table 3. Dominant Strategy

However, not all games have dominant or dominated strategies. Sometimes, the best
strategy for a player depends on what strategies the other players choose. For example consider a
scenario where two companies are deciding whether to enter a new market. If both companies
enter the market, they will face intense competition and lower profits due to increased supply.
However, if only one company enters the market, they will enjoy a larger market share and
higher profits. In this scenario, the best strategy for each company depends on what the other
company does. If one company enters the market, it may be more profitable for the other
company to stay out of the market and avoid the intense competition. However, if both
companies stay out of the market, they may miss out on potential profits from the new market.

  B Enter Market B Stay Out

A Enter Market 5, 5 -2,10
A Stay Out 10, -2 0,0
Table 4. Non-Dominant Strategy

In this matrix, the first number in each cell represents Company A's profit, while the
second number represents Company B's profit. For instance, if both firms enter the market, they
would each earn 5 in profit, so the payoff for that cell would be 10. (5, 5). If Company A enters
the market and Company B does not, Company A will earn a profit of 10 while Company B will
earn a profit of 2. The payoff for that cell is 10. (10, -2). As stated previously, neither company
has a dominant nor dominated strategy in this scenario. If both firms enter the market, they will
face intense competition and reduced profitability. However, if only one company enters the
market, it will have a larger market share and generate greater profits. The optimal outcome is
contingent on the decisions made by both companies, which may be influenced by a variety of
variables including market size, demand, and the competitive landscape.
4.3 Maximin & Minimax Strategy
Maximin and minimax are two decision rules utilized in game theory to manage risk and
uncertainty. They are frequently used in zero-sum games, in which one player's gain is another's
loss. Maximin refers to the maximization of the minimal gain. A player who employs a maximin
strategy selects the move that, in the worst-case scenario, guarantees the greatest possible return.
This is also known as a pessimistic or conservative strategy, as it assumes that the other players
will act in the most unfavorable manner for the player. Minimax refers to the minimization of
maximum loss. A player who employs a minimax strategy chooses the action that, in the worst-
case scenario, minimizes the largest possible payout for the other players. This is also known as
an aggressive or optimistic strategy, as it assumes that the other players will act in a way that
benefits the player the most.
Assume that A and B are competing for a government contract to supply a specific
product. Both companies must submit bids that are lower than the maximum price that the
government is willing to pay for the product. However, the companies are unaware of one
another's bids and must decide whether to submit a high or low offer. In this scenario, both
companies could use game theory as a decision-making tool. Company A could employ a
maximin strategy, while Company B could employ a minimax strategy.
Maximin strategy entails selecting the strategy that maximizes the minimum possible
result. In this instance, Company A would want to select a bid that minimizes its potential loss in
the event that it does not win the contract. Therefore, Company A would choose a high bid in
order to minimize potential loss in the event that Company B submits a lower bid. Minimax
strategy, on the other hand, involves choosing the strategy that minimizes the maximum possible
loss. In this situation, Company B would want to choose a bid that minimizes potential losses in
the event that it does not win the contract. Therefore, Company B would select the lowest bid, as
this would minimize the potential loss should Company A submit a higher bid. Below is the
simplified version of this scenario.

  B Submits Low B Submits High

A Submits Low 10, 10 8,0
A Submits High 0, 8 5,5
Table 5. Maximin & Minimax Strategy

The first number in each cell of this matrix represents the potential profit earned by
Company A, whereas the second number represents the potential profit earned by Company B.
For instance, if Company A submits a high bid and Company B submits a low bid, Company A
earns no profit while Company B earns 8 million in profit, so the payoff for that cell is 8 million
(0, 8).
Based on this matrix, Company A would select a high bid (since this strategy maximizes the
minimum possible outcome), whereas Company B would select a low bid (since that strategy
minimizes the maximum possible loss). As a result, Company A would earn $5 million in profit
and Company B would earn 5 million in profit.
4.4 Case Study: Using Game Theory to Maximize the Chance of Victory in Two Player
Sports
To provide a clearer picture of the interplay between chance, choice, and strategic moves,
we will discuss a few case studies containing these three variables. Ravi et al (2021) developed a
tool that can assist badminton players by providing a detailed analysis of optimal decisions,
allowing the player to be well-prepared with the optimal strategy that would produce a favorable
outcome against a given opponent's strategy. Ravi et al (2021) also considered the badminton
regulations that permit coach intervention during a match. Using the proposed tool, a coach can
influence and guide a player in the middle of a game by analyzing the game up to that point. In
addition, our method has the potential to save players and coaching staff a significant amount of
time compared to sifting through hours of match videos of the player and opponents, as well as
assist them in quantitatively analyzing the performance and recommending the appropriate
preparation based on the player's historical data.
Ravi et al (2021) manually collected two top badminton athlete gameplay Lin Dan from
China and Lee Chong Wei from Malaysia spanning for 8 years (2011 – 2019), the reason why
the author collected both athlete gameplay data was for their consistency in performance and
their left-handed and right-handed variation respectively. The type of badminton shots that is
included in this study is depicted below.

Figure 1. Badminton Shots Analyzed

 Source : (Ravi et al., 2021)

Ravi et al (2021) consider this as only a two-player game, the two players here are referred
as Xp and Xo. Their recommendation tool uses Xp's history with Xo to suggest the best shot for
each shot. Xp will be match-ready with the best and safest shots to play given any shot from X o
using game theory's best response to maximize their chances of winning each point and the
match. Because they only care about Xp's strategy and how to win the match, not Xo's. Thus, a
shot-by-shot approach suffices. Ravi et al (2021) then develops model and algorithm for
simulation and for the probability and reward for each possible shot.

Figure 2. Probability & Reward Model

Source : (Ravi et al., 2021)

 Figure 3. Algorithm Model

Source : (Ravi et al., 2021)

The recommendation system recommends the best response to a X o's shot without
considering the rally's history or the player's condition. Figure 4 shows the model's
recommendations for player Xp and figure 5 for opponent Xo. The data shows that the model
identified the best shots for given shots and discarded the unplayable shots for the opponent's
shot. From the suggestions above, the shot forehand drop is repeated most. The matches showed
that both players can play forehand drop shots without error. This model allows a player to
mentally prepare for an opponent's shot that could win a point or keep Xp alive in the rally. This
information will benefit players before the match because it is modeled directly from their
abilities and behavior.
 Figure 4. Recommendations for Xp

Source : (Ravi et al., 2021)

Figure 5. Recommendations for Xo

Source : (Ravi et al., 2021)

To proceed even further Ravi et al (2021) simulate the data and demonstrate that the simulated
results are closer to the real-world match. This tool enables the players to comprehend how the
match will continue after a shot is taken, which is essential for analyzing the consequences of
taking a shot. This recommendation tool, which takes into account the history of shots played in
the current match as well as the history of the match, suggests the optimal strategy for the
players.

4.5 Case Study: Research on Franchised Store Chain Operation Based on Evolutionary
Game Theory
Franchised store chains are currently the most prevalent business model. The franchisor
and franchisees share the same brand, but the value of the brand as a whole will be diminished if
one party pursues self-interest in brand management from the standpoint of a franchised store
chain. Deng (2021), develops a franchisor-franchisee evolutionary game model based on the
assumption of constrained rationality. In this research, Deng (2021), concludes that the
franchisor and franchisees have two business strategies: cooperation and non-cooperation. The
franchised store chain's game process can be broken down into three stages. In the first phase, the
franchisor selects a cooperation or non-cooperation strategy based on its own needs. In the
second phase, the franchisee creates a strategy for their own development based on the
franchisor's strategy. In the third phase, the franchisor adjusts it self-strategy selection based on
the franchisee's strategy.
Deng (2021) develops the probability and payoff as seen below. Based on figure below,
only two points in five equilibrium points satisfy the condition of evolutionary stability strategy;
and achieve the evolutionary stability strategy, which is O (0,0) and M (1,1) , respectively the
strategy of the franchisor and the franchisee selection is (cooperation, cooperation) and (non -
cooperation, non - cooperation).
 Figure 6. Payoff & Strategy Selection

Source : (Deng, 2021)

However Deng (2021) argued that despite the optimal strategy is both cooperation for both
parties may be the best equilibrium point, but which point the system converges to depend on the
value of income matrix and specific parameters.
4.5 Case Study: Brand Switching and Strategy Selection of Bubble Tea Product Marketing
by Utilizing Markov Chain and Game Theory
Azizah & Sari (2021) analyzed two competing bubble tea stores employing a relatively
similar strategy and categorized it into five distinct categories. The first strategy focuses on the
product’s flavor, the second on its affordability, the third on offering a wide variety of products,
the fourth on attractive packaging, and the fifth on providing a satisfying customer experience.
The data was gathered by collecting respondents in accordance with the strategy, and the
resulting payoff matrix and saddle point are presented below.

Figure 7. Payoff & Matrix

Source : (Azizah & Sari, 2021)

 Figure 8. Maximin & Minimax
Source : (Azizah & Sari, 2021)

Figure 9. Saddle Point

Source : (Azizah & Sari, 2021)

The result indicates that the minimax and maximin points are equal, indicating that this is
the optimal outcome for the game, in which there is a point of equilibrium between the two
players. The results indicate that player A should employ strategy 3 (product variety) and player
B should employ strategy 2 (cheap pricing). This indicates that Player A has a wider selection of
products than Player B, while Player B offers more competitive pricing. This means that in order
to prevent the customer from switching brands, player A must expand their product selection,
while player B must adjust their pricing strategy. This example of using game theory to analyze
the situation in which the players find themselves will help them visualize how to choose their
strategy with care.
Conclusion & Recommendation
 The above example for strategy that can be chosen when there is a chance and choice for
an individuals or group shows how game theory could help them navigate all the available
choices and options for strategy. Game theory provides the players with the payoff when they
follow a certain strategy. Pure strategy is a decision rule that specifies a single action for a
player, while mixed strategy is a method for introducing uncertainty or randomness into a game
in the hopes of increasing the chance of winning the game as the other opponent may not
anticipate the coming action chosen. Dominant and dominated strategies are essential concepts to
help players analyze and optimize decisions. The best strategy for a player depends on what
strategies the other players choose, with dominant or non-dominant strategies depending on
market size, demand, and competitive landscape. Maximin and minimax are two decision rules
used in game theory to manage risk and uncertainty.
In situations involving uncertainty, conflict, or cooperation, game theory can help us
comprehend how to make optimal decisions. A key concept in game theory is the idea of a
strategic move, which is an action that influences the expectations or behavior of other players.
A strategic move can be a commitment, threat, promise, or signal that conveys information or
affects the credibility of the player. Various objectives, including deterrence, coordination,
bargaining, and signaling, can be attained through the use of strategic maneuvers. Determining
when and how to employ strategic moves effectively is one of the challenges of game theory.
Numerous factors, including timing, credibility, reversibility, and observability, influence the
success of a strategic move. A strategic move should be executed at the optimal time when it will
have the greatest effect on the beliefs or actions of the other players. A strategic move should
also be credible, meaning that the player can and will execute the action if required. A strategic
move must be irreversible, meaning the player cannot undo or alter the action once it has been
taken. A strategic move must also be observable, meaning that the other players can see or infer
the action and its results.
In the context of game theory, it is recommended to employ choice and chance with
strategic moves sparingly and with caution. Strategic moves can be potent instruments for
achieving desired outcomes, but they can also backfire if they are not well-designed or executed.
Strategic moves can also elicit responses from other players, which can escalate or complicate
the situation. A player should therefore carefully consider the costs and benefits of a strategic
move, as well as the potential reactions and responses of other players. A player should also be
prepared to adapt and revise their strategy if the situation or the availability of new information
changes.
References
Azizah, A. N., & Sari, R. P. (2021). Analisis Brand Switching dan Penentuan Strategi Pemasaran
Produk Bubble Tea Menggunakan Metode Markov Chain dan Game Theory. Jurnal
Optimalisasi, 7(1), 25. https://doi.org/10.35308/jopt.v7i1.3275
Beal, R., Chalkiadakis, G., Norman, T. J., & Ramchurn, S. D. (2020). Optimising game tactics
for football. Proceedings of the International Joint Conference on Autonomous Agents and
Multiagent Systems, 2020-May(May), 141–149.
Deng, S. (2021). Research on franchised store chain operation based on evolutionary game
theory. E3S Web of Conferences, 275. https://doi.org/10.1051/e3sconf/202127503022
Grüne-Yanoff, T., & Lehtinen, A. (2012). Philosophy of Game Theory. Philosophy of
Economics, 13, 531–576. https://doi.org/10.1016/B978-0-444-51676-3.50019-1
Heap, S. P. H., & Varoufakis, Y. (2003). Game Theory : A Critical Introduction.
Hendalianpour, A. (2020). Optimal lot-size and Price of Perishable Goods: A novel Game-
Theoretic Model using Double Interval Grey Numbers. Computers and Industrial
Engineering, 149(August), 106780. https://doi.org/10.1016/j.cie.2020.106780
Ravi, A., Gokhale, A., & Nagwekar, A. (2021). Using Game Theory to maximize the chance of
victory in two-player sports.
Rond, M. De, & Thietart, R. A. (2007). Choice, Chance, and Inevitability In Strategy. Strategic
Management, 28(February), 535–551. https://doi.org/10.1002/smj
Satoh, A., & Tanaka, Y. (2018). Maximin and Minimax Strategies in Two-Players Game with
Two Strategic Variables. International Game Theory Review, 20(1).
https://doi.org/10.1142/S021919891750030X
Wang, L., Schuetz, C. G., & Cai, D. (2021). Choosing Response Strategies in Social Media
Crisis Communication: An Evolutionary Game Theory Perspective. Information and
Management, 58(6), 103371. https://doi.org/10.1016/j.im.2020.103371

Appendix A

Contribution Statement
Claudio E Winarno - (2144049)
  Writing – original draft (Introduction, Discussion & Conclusion & Recommendation)
 Writing – proofreading & editing.
 Literature curation

Mira Yunita - (2144044)

 Literature curation
 Writing (Discussion, Literature Review, Methodology)

Sarah Aryana - (2144051)

 Literature curation
 Writing (Discussion, Literature Review, Abstract)