Game theory is a branch of mathematics that studies decision-making in strategic situations where two or more individuals, called players, are involved. The theory analyzes the behavior of players, the rules of the game, and the possible outcomes of the game. It also studies the strategies that the players use to achieve their goals.
The roots of game theory can be traced back to ancient times. Many games that we play today, such as chess and checkers, have been around for centuries. However, it was not until the 20th century that game theory became a formal field of study.
The formalization of game theory began in the 1940s with the work of John von Neumann and Oskar Morgenstern. In their book “Theory of Games and Economic Behavior,” they introduced the concept of a “game,” defined the rules of the game, and established the basic concepts of game theory. Since then, game theory has become an important tool in economics, political science, psychology, and other social sciences.
Game theory is particularly useful in situations where individuals are interdependent and their decisions affect each other’s outcomes. In these situations, it is essential to understand how individuals make decisions and how their actions affect the outcomes of the game. Game theory provides a framework for analyzing these interactions and predicting their outcomes.
The key concepts of game theory include players, strategies, payoffs, and equilibrium. Players are the individuals or groups involved in the game. Strategies are the actions that players take in the game. Payoffs are the rewards or costs associated with each possible outcome of the game. Equilibrium is a state in which no player can improve their outcome by changing their strategy, given the strategies of the other players.
There are two main types of games: non-cooperative and cooperative. In non-cooperative games, players act independently and do not communicate with each other. Examples of non-cooperative games include the prisoner’s dilemma and the battle of the sexes. In cooperative games, players work together to achieve a common goal. Examples of cooperative games include bargaining and the formation of coalitions.
Game theory has many applications in economics. It is used to analyze markets, auctions, and bargaining situations. In financial economics, game theory is used to analyze the behavior of firms and investors in financial markets. Game theory is also used in political science to analyze voting behavior, the behavior of political parties, and the behavior of international organizations.
Game theory is an important tool for understanding decision-making in strategic situations. It provides a framework for analyzing the behavior of individuals and predicting the outcomes of their interactions. The theory has many applications in economics, political science, psychology, and other social sciences.
Game theory has become an important tool for analyzing various social, political, and economic situations that involve strategic decision-making. It allows us to understand the incentives, behaviors, and outcomes of players in complex interactive situations. Some of the key areas where game theory has found significant applications are:
Economics: Game theory has been extensively used in economics to study various strategic situations such as oligopoly markets, bargaining, auctions, and incentives. It helps economists to model and predict the behavior of firms, consumers, and other agents in the economy.
Political Science: Game theory has also been applied to political science to analyze voting behavior, electoral competition, and international relations. It helps to understand the strategies of political parties and leaders, as well as the outcomes of political negotiations and conflicts.
Biology: Game theory has been used in biology to study the behavior of animals and evolution. It helps to model and predict the outcomes of various interactions such as predator-prey, cooperation, and conflict.
Computer Science: Game theory has found significant applications in computer science to study various algorithms and protocols in networking, distributed systems, and artificial intelligence. It helps to design efficient and robust systems that can handle strategic behavior of agents.
Psychology: Game theory has also been used in psychology to study human behavior and decision-making in social and economic situations. It helps to understand the factors that influence the choices and preferences of individuals.
Overall, game theory has provided a powerful framework for understanding strategic interactions and decision-making in various fields. Its applications have led to new insights and solutions to complex problems, as well as to the development of new theories and models.
Game theory has been extensively applied in economics to analyze strategic interactions between economic agents. Some of the key examples of its applications in economics are:
Oligopoly: Game theory has been used to study strategic behavior in oligopoly markets where a few large firms dominate the industry. It helps to predict the outcomes of various strategies such as price competition, collusion, and entry deterrence. For example, the famous prisoner’s dilemma game is often used to model the strategic behavior of firms in an oligopoly market.
Bargaining: Game theory has been applied to analyze bargaining situations between buyers and sellers, labor and management, and other economic agents. It helps to model and predict the outcomes of various bargaining strategies such as ultimatums, concessions, and threats.
Auctions: Game theory has been used to analyze different types of auctions such as first-price, second-price, and sealed-bid auctions. It helps to predict the optimal bidding strategies of bidders and the expected outcomes of the auction.
Incentives: Game theory has been used to analyze incentive mechanisms in organizations such as performance-based pay, stock options, and promotions. It helps to design optimal incentive schemes that motivate employees to perform better and achieve the goals of the organization.
International Trade: Game theory has been applied to analyze strategic interactions between countries in international trade negotiations. It helps to predict the outcomes of various strategies such as tariff reductions, quotas, and trade agreements.
Game theory has provided economists with a powerful tool for analyzing strategic interactions in various economic situations. Its applications have led to new insights and solutions to complex economic problems.
Example of game theory applied to oligopoly
Suppose there are two firms, A and B, that produce a homogenous product and compete on price. They both have the option to set a high price (H) or a low price (L). The payoff for each firm is the profit it earns from the chosen price level. The table below shows the profits earned by each firm based on the price choices made by both firms:
In this game, there are two possible equilibria: the Nash equilibrium and the cooperative equilibrium.
The Nash equilibrium occurs when both firms choose the dominant strategy, which is to set a low price. This results in a payoff of (5 0,50) for both firms.
However, there is a cooperative equilibrium where both firms can earn higher profits by agreeing to set a high price. This would result in a payoff of (100,100) for both firms. However, in the absence of an external mechanism to enforce cooperation, it is difficult for the firms to coordinate on this strategy, and they are likely to end up with the Nash equilibrium outcome.
This example shows how game theory can be used to analyze the behavior of firms in an oligopoly market and predict the outcomes of different strategies. It also highlights the importance of external mechanisms such as regulation or coordination to achieve outcomes that are more beneficial for all parties involved.
Economics without game theory would be a vastly different field of study. Game theory has become a central tool in modern economics, allowing economists to model and analyze complex interactions between individuals, firms, and other economic agents.
Before the advent of game theory, economists relied heavily on models of perfect competition and market equilibrium, which assumed that all market participants were rational, had complete information, and acted independently. These models provided useful insights into how markets function, but they often failed to capture the complexities of real-world economic interactions.
Game theory, on the other hand, allows economists to model situations in which individuals or firms must make strategic decisions based on the actions of others. It provides a framework for analyzing how different incentives and strategies can lead to different outcomes, and it has been used to study a wide range of economic phenomena, from pricing decisions by firms to international trade negotiations.
Game theory has also been used to study issues such as public goods provision, auctions, and bargaining, among others. By providing a rigorous framework for analyzing strategic interactions, game theory has allowed economists to develop more nuanced and accurate models of economic behavior.
In short, game theory has become an essential tool for economists seeking to understand the complex interactions that drive economic activity. Without it, our understanding of many economic phenomena would be greatly limited, and our ability to predict and influence economic outcomes would be significantly diminished.
Consider a scenario where two competing firms, A and B, must decide whether to set high or low prices for their products. The payoffs for each firm are shown in the following matrix:
In this matrix, the first number in each cell represents the payoff to firm A, and the second number represents the payoff to firm B.
Suppose both firms simultaneously choose their pricing strategy. If both firms set high prices, they each receive a payoff of 2. If both firms set low prices, they each receive a payoff of 1. If one firm sets a high price and the other sets a low price, the firm that sets the low price receives a higher payoff (3) than the firm that sets the high price (0).
This scenario can be analyzed using game theory. One way to approach the problem is to use the concept of Nash equilibrium, which is a solution concept that predicts the outcome of a game in which each player chooses their strategy simultaneously and neither has an incentive to change their strategy.
In this case, the Nash equilibrium is for both firms to set a low price. If firm A sets a high price, firm B has an incentive to set a low price, since this will result in a higher payoff for firm B. Similarly, if firm B sets a high price, firm A has an incentive to set a low price. Therefore, both firms have an incentive to set a low price, which is the Nash equilibrium.
This example illustrates how game theory can be used to analyze strategic interactions between economic agents, and how the concept of Nash equilibrium can be used to predict the outcomes of such interactions.
Game theory is the study of how individuals and organizations make decisions in situations where the outcome depends not only on their own actions, but also on the actions of others. It provides a framework for analyzing the behavior of agents in strategic interactions, where the choices of one agent affect the payoffs of the other agents. The following are some basic concepts of game theory:
Players: Game theory involves multiple players, who can be individuals, firms, countries, or any other entities that interact with each other.
Strategies: A strategy is a plan of action that a player chooses in order to achieve a certain outcome. In a game, each player has a set of possible strategies from which to choose.
Payoffs: Payoffs represent the outcome that a player receives as a result of his or her chosen strategy. In most games, players seek to maximize their payoffs.
Nash equilibrium: A Nash equilibrium is a set of strategies in which no player has an incentive to unilaterally change his or her strategy, given the strategies of the other players. [A Nash equilibrium is a situation in a game where each player is choosing the best strategy given the strategies chosen by the other players. In other words, no player can improve their outcome by changing their strategy if the other players’ strategies remain unchanged. Nash equilibrium is an important concept in game theory as it helps to predict how a game is likely to be played.]
Dominant strategy: A dominant strategy is a strategy that is the best choice for a player, regardless of the strategies chosen by the other players.[The prisoner’s dilemma is a classic game theory scenario that illustrates how two rational individuals might not cooperate even if it is in their best interest to do so. The scenario involves two suspects who are arrested and held in separate cells. The suspects are given the opportunity to confess or remain silent. If both suspects remain silent, they both receive a light sentence. If both confess, they both receive a harsh sentence. However, if one confesses and the other remains silent, the one who confesses receives a lighter sentence and the one who remains silent receives a harsher sentence. In this scenario, each player’s best option is to confess, even though cooperation would have resulted in a better outcome for both players.]
Prisoner’s dilemma: The prisoner’s dilemma is a classic game that illustrates the conflict between individual rationality and collective rationality. In this game, two individuals are arrested for a crime and are interrogated separately. If both individuals remain silent, they both receive a light sentence. If one individual confesses and the other remains silent, the one who confesses receives a reduced sentence, while the one who remains silent receives a heavy sentence. If both individuals confess, they both receive a moderate sentence.
Coordination game: In a coordination game, there are multiple Nash equilibria, and the players need to coordinate their actions in order to achieve the best outcome for all of them.
Iterated Prisoner’s Dilemma: The iterated prisoner’s dilemma is a variation of the prisoner’s dilemma where the game is played multiple times. In this scenario, players have the opportunity to punish each other for not cooperating in previous rounds. The iterated prisoner’s dilemma is a useful model for understanding how cooperation can be sustained over time in situations where immediate self-interest might suggest otherwise.
These concepts form the foundation of game theory and are used to analyze a wide range of economic and social phenomena.
Despite its numerous benefits, game theory has certain drawbacks when applied to economic analysis. Some of these drawbacks are:
Limited applicability: Game theory models are often based on assumptions about the behavior of players, which may not be realistic or applicable in all situations. This can limit the scope of application of game theory to certain types of problems.
Computational complexity: Game theory models can become computationally complex and difficult to solve as the number of players and strategies increase. This can limit the feasibility of using game theory in practice.
Lack of empirical validation: Game theory models are often built on theoretical assumptions and may not be empirically validated, leading to potential errors in prediction.
Assumptions about rationality: Game theory models assume that players act rationally, meaning that they make decisions that maximize their own utility. However, in reality, people may not always act rationally, leading to potential inaccuracies in game theory predictions.
Limited scope for cooperation: Game theory models often assume that players act independently and competitively, which can limit the scope for cooperation and coordination between players. This can be a major drawback in situations where cooperation is essential for achieving a desirable outcome.
Despite these drawbacks, game theory remains a valuable tool for understanding strategic decision-making in economics and other fields. With continued development of the theory and more sophisticated models, it is likely to continue playing an important role in economic analysis.
Consider a scenario where two firms, A and B, are considering whether to enter a new market. If both firms enter the market, they will each earn a profit of $10 million. If neither firm enters the market, they will each earn a profit of $5 million. However, if one firm enters the market and the other does not, the firm that enters will earn a profit of $20 million, while the firm that does not enter will earn nothing. Using game theory, we can model this scenario as a simultaneous game, where each firm chooses whether to enter the market or not. The payoffs for each firm are given in the following matrix:
Here, the first number in each cell represents the payoff for firm A, while the second number represents the payoff for firm B.
By analyzing this game, we can see that the dominant strategy for each firm is to enter the market. However, if both firms enter the market, they will each earn a lower profit than if neither firm enters. This is an example of the prisoner’s dilemma, where each firm’s dominant strategy leads to a suboptimal outcome for both firms.
In this scenario, game theory provides a useful framework for analyzing the strategic interactions between firms. However, it also highlights the limitations of rational decision-making, as the pursuit of individual self-interest can lead to a suboptimal outcome for all parties involved.
Nash equilibrium is a fundamental concept in game theory that describes a stable state of a strategic interaction between two or more individuals or groups, in which each participant is choosing their optimal strategy, given the strategies of the other participants.
In simple terms, Nash equilibrium occurs when each player’s strategy is the best response to the strategies of the other players, and no player has an incentive to change their strategy unilaterally. In other words, at Nash equilibrium, no player can increase their payoff by changing their strategy while the other players’ strategies remain unchanged.
The concept of Nash equilibrium was introduced by John Nash in his seminal paper “Non-Cooperative Games” in 1950, for which he was awarded the Nobel Prize in Economics in 1994. Nash equilibrium has since become a cornerstone of game theory, and has numerous applications in economics, political science, sociology, and other fields.
A common way to illustrate Nash equilibrium is through a game matrix, also known as a payoff matrix. Consider the following example of a simple two-player game:
In this game, each player can choose to play either Up (U) or Down (D) for Player 1, and Left (L) or Right (R) for Player 2. The numbers in the cells of the matrix represent the payoffs to each player, with the first number being the payoff to Player 1 and the second number being the payoff to Player 2.
To find the Nash equilibrium of this game, we need to look for a strategy profile in which each player’s strategy is the best response to the other player’s strategy. In this case, there are two Nash equilibria: (D,R) and (U,L).
To find the Nash equilibrium of this game, we need to look for a strategy profile in which each player’s strategy is the best response to the other player’s strategy. In this case, there are two Nash equilibria: (D,R) and (U,L).
If both players choose (D,R), then Player 1’s payoff is 5 and Player 2’s payoff is 1, which means that neither player has an incentive to change their strategy unilaterally. Similarly, if both players choose (U,L), then Player 1’s payoff is 3 and Player 2’s payoff is 3, which again satisfies the conditions of Nash equilibrium.
Nash equilibrium is a concept in game theory that refers to a stable state of a game where no player has any incentive to change their strategy unilaterally. In other words, given the strategies of all other players, no player can increase their own payoff by changing their strategy. This makes the Nash equilibrium a very important concept in game theory, as it represents a state where all players are playing optimally and there is no scope for any player to improve their position.
To understand the concept of Nash equilibrium, consider a game with two players, A and B, and two possible strategies for each player: cooperate (C) or defect (D). The payoff for each player depends on the strategies chosen by both players, as shown in the table below:
In this game, both players can either choose to cooperate or defect. The numbers in the table represent the payoffs for each player in each possible outcome. For example, if both players cooperate, they each receive a payoff of 2. If player A cooperates and player B defects, player A receives a payoff of 0 and player B receives a payoff of 3.
To find the Nash equilibrium of this game, we need to consider the strategies of both players and determine if there is any strategy that neither player has an incentive to deviate from. One possible Nash equilibrium for this game is when both players defect, as neither player can improve their payoff by switching to cooperation. If player A cooperates and player B defects, player A’s payoff would decrease from 2 to 0, and if player A defects and player B cooperates, player A’s payoff would increase from 1 to 3. Therefore, both players defecting is a stable outcome, and it represents a Nash equilibrium.
Nash equilibrium can also be extended to games with more than two players and more than two strategies. In these cases, finding the Nash equilibrium becomes more complicated, but the underlying concept remains the same: a Nash equilibrium is a stable state of the game where no player can improve their payoff by changing their strategy unilaterally.
Nash equilibrium is an important concept in game theory and has significant importance in economics. Here are some of its main importance:
Predicting outcomes: Nash equilibrium helps in predicting the outcome of a game. It can be used to analyze various economic situations, such as oligopolies, where a small number of firms dominate the market. Nash equilibrium can help predict the strategies that each firm will take and the resulting market outcomes.
Strategic decision making: Nash equilibrium provides a framework for strategic decision-making. It helps in determining the best course of action for each player in a game, given the actions of the other players. This is useful in various economic situations, such as pricing strategies, where firms must consider the actions of their competitors before making a pricing decision.
Policy implications: Nash equilibrium has policy implications in economics. For example, it can be used to analyze the impact of various policies on market outcomes. This includes policies such as taxes, subsidies, and regulations, which can impact the strategies of players in a game and the resulting market outcomes.
Auction theory: Nash equilibrium is used in auction theory to analyze various types of auctions, such as first-price and second-price auctions. It can help determine the optimal bidding strategy for each bidder, given the actions of the other bidders.
Experimental economics: Nash equilibrium is used in experimental economics to test various economic theories and to understand how people make decisions in strategic situations. This is done by conducting experiments with real people, where they are asked to play various games and make decisions based on the actions of other players.
Nash equilibrium is a powerful concept in game theory and has significant importance in economics. It provides a framework for analyzing various economic situations, predicting outcomes, and making strategic decisions.
Despite its significant contributions, game theory also has some limitations and drawbacks. Some of them are:
Simplified Assumptions: Game theory relies on a number of simplified assumptions, such as rationality and perfect information, which may not always hold true in real-world situations. This can result in models that do not accurately reflect the complexities of economic decision-making.
Limited Predictive Power: While game theory can provide valuable insights into strategic behavior, it is not always able to predict outcomes with precision. This is because many economic situations involve multiple variables and unknown factors that can make it difficult to accurately model decision-making.
Difficulty in Applying Empirically: Game theory often relies on complex mathematical models that can be difficult to apply empirically. This can make it challenging to test hypotheses and validate predictions in real-world situations.
Assumption of Static Strategies: Many game theory models assume that players will use the same strategy over time, without considering the possibility of strategic adaptation or learning. In reality, players may adjust their strategies based on the outcomes of previous interactions, which can affect the outcome of the game.
Limited Scope: Game theory is best suited for analyzing situations where there are a limited number of players and clear rules of interaction. It may not be as useful for analyzing more complex economic situations, such as those involving large numbers of players or decentralized decision-making.
Despite these limitations, game theory remains a powerful tool for analyzing strategic behavior in economics and other fields. By providing insights into how individuals and organizations make decisions in a competitive environment, game theory can help policymakers and businesses make more informed decisions and achieve better outcomes.
Consider a game between two companies, A and B, in which they have to decide whether to enter a new market or not. If both companies enter the market, they will face a strong competition and end up with a profit of $1 million each. If neither of the companies enters the market, they both remain in their current positions and make a profit of $0.5 million each. However, if one company enters the market and the other does not, the entering company will make a profit of $2 million and the non-entering company will make a profit of $0.
This game can be represented in a matrix form as follows:
The first number in each pair of parentheses represents the profit of company A, and the second number represents the profit of company B.
In this game, there are two Nash equilibria: (Enter market, Enter market) and (Don’t enter market, Don’t enter market). In the first equilibrium, neither company has an incentive to deviate from its strategy because both are earning the highest possible profit given the other’s strategy. Similarly, in the second equilibrium, neither company has an incentive to deviate because both are earning the highest possible profit given the other’s strategy.
Extensive form games are a type of game in game theory where the players’ decisions are represented in a tree-like structure. The extensive form provides a way to analyze games with sequential decision making, as opposed to simultaneous decision making in normal form games.
In an extensive form game, players take turns making decisions, with each decision leading to a new node in the tree. The game starts at the root node, where all players make their initial decisions. Each branch of the tree represents a different sequence of decisions that the players might take, and the endpoints of the branches represent the possible outcomes of the game.
The extensive form also includes information sets, which represent situations where a player cannot distinguish between different possible states of the game. For example, if a player cannot tell whether they are in the first or second round of a game, those two rounds would be part of the same information set.
One important concept in extensive form games is the notion of backward induction, where players reason backwards from the end of the game to determine the best strategy at each decision point. This allows them to identify Nash equilibria, are strategies that are optimal given the strategies of all other players.
For example, consider the game of chess. Each move a player makes represents a decision point in an extensive form game. The possible moves at each decision point are represented by the branches of the tree, and the endpoints of the tree represent the possible outcomes of the game, such as checkmate or a draw. In chess, information sets are represented by situations where a player cannot distinguish between different positions on the board, such as when both players have the same pieces on the board. Backward induction can be used to determine the best moves at each decision point, leading to a Nash equilibrium where both players play optimally given their opponent’s strategies.
In game theory, extensive form games represent the structure of sequential decision-making situations in a graphical format, which are also known as game trees. They are used to analyze games where players make decisions in a sequence, and the outcomes of earlier decisions affect the set of available actions for later decisions. Extensive form games are particularly useful for modeling games with imperfect information, such as poker or contract negotiations, where players do not have complete information about the actions of other players.
In an extensive form game, each player is represented by a node in the game tree, and each node represents a point in time at which a decision is made. The edges between nodes represent the available choices that can be made at each point in time. Each player has a set of possible actions, and their decision at each node determines which branch of the game tree is followed.
At the end of each branch, there is a terminal node that represents the outcome of the game. The outcome may be a payoff for each player, or a description of the resulting situation. These payoffs are typically represented as a set of numbers, one for each player, that describe the utility they receive from each possible outcome.
Extensive form games can be solved by finding the Nash equilibrium, which is a set of strategies, one for each player, such that no player can improve their payoff by unilaterally changing their strategy. The Nash equilibrium can be found by backward induction, which involves starting at the terminal nodes of the game tree and working backwards to the initial node, determining the optimal strategies for each player at each point in time.
Extensive form games provide a useful tool for analyzing complex decision-making situations in economics and other fields. They allow for the modeling of sequential decision-making, imperfect information, and the interdependence of player actions, making them applicable to a wide range of real-world situations.
An example of an extensive-form game is the classic game of poker. In this game, each player has a set of cards that are dealt to them, and they make bets based on the strength of their hand. The game tree for poker would start with the deal of the cards and branch out into all the possible bets that each player could make.
Another example of an extensive-form game is the game of chess. In chess, each player has a set of pieces that they can move around the board. The game tree for chess would start with the opening move of the first player and branch out into all the possible moves that each player could make.
Yet another example of an extensive-form game is the game of tic-tac-toe. In tic-tac-toe, each player has a set of Xs or Os that they can place on a 3x3 grid. The game tree for tic-tac-toe would start with the first move of the first player and branch out into all the possible moves that each player could make.
Consider a game of two players, player 1 and player 2. Player 1 can either choose strategy A or B. Player 2 can either choose strategy X or Y. The payoffs are given in the following table:
The game can be represented as a tree diagram as shown below
Player 1
/ \
A B
/ \ / \
X 5,2 1,4 3,3 Y
/ \
3,3 2,1
Player 1 chooses A or B, and then Player 2 chooses X or Y. The payoffs for the respective strategies are shown in the tree.
To find the solution of this game, we first consider Player 2’s decision. If Player 1 chooses A, Player 2 will choose X since 5 is greater than 1. If Player 1 chooses B, Player 2 will choose Y since 3 is greater than 2. Therefore, the solution of this game is (A, X) with payoffs (5, 2). This is an example of a subgame perfect Nash equilibrium.
Extensive form games play a significant role in economics as they allow for the analysis of strategic interactions between multiple agents. They provide a framework to model and analyze complex decision-making processes in various economic contexts, such as industrial organization, game theory, and mechanism design.
In industrial organization, extensive form games can be used to study oligopoly markets where firms have to make decisions regarding their production and pricing strategies. The firms’ decisions and their outcomes are interdependent and strategic, leading to outcomes that depend on the firms’ strategies. In game theory, extensive form games are used to study strategic interactions between agents with incomplete information. The extensive form framework allows for the representation of sequential decision-making, where each player’s decision can depend on the choices of the other players, as well as their beliefs about the game’s structure and the other players’ preferences.
In mechanism design, extensive form games provide a way to study the design of mechanisms that can encourage agents to behave in a certain way. For example, the auction of goods is a mechanism that aims to allocate resources efficiently by providing incentives for bidders to reveal their true valuation of the good being auctioned.
The extensive form game theory provides a powerful analytical tool that enables economists to study the strategic decision-making processes in various economic contexts, providing insights into how strategic interactions between agents shape the outcomes of economic processes.
I discuss some applications of Game theory in economics below
Industrial Organization: Game theory is used to analyze the behavior of firms in different markets, such as oligopolistic and monopolistic markets, to predict the likely outcome of the market and the effect on consumer welfare.
Auctions: Game theory is used to analyze different types of auctions, such as English, Dutch, and sealed-bid auctions, to determine the optimal bidding strategy for participants.[Game theory is often used to analyze various auction formats and to determine the optimal bidding strategies for bidders. For instance, in a second-price sealed-bid auction (also known as a Vickrey auction), bidders have an incentive to bid their true value, as this strategy maximizes their expected profit.]
Behavioral Economics: Game theory is used to understand the factors that influence human decision-making and behavior in different economic situations.
International Trade: Game theory is used to analyze international trade and negotiations, to predict the outcome of trade agreements and determine the optimal trade policies for different countries. [Game theory is used to analyze various issues in international trade, such as the optimal tariff policies for a country or the incentives for countries to form trade agreements.]
Public Economics: Game theory is used to analyze public goods and public choice theory, to determine the optimal level of public goods provision and the role of government intervention in the economy.
Finance: Game theory is used in finance to analyze financial markets and investor behavior, to determine the optimal investment strategy and the likely outcomes of different market scenarios.
Oligopoly: Game theory is used to analyze the behavior of firms in an oligopoly market, where a few large firms dominate the market. Game theory models can be used to predict the likely outcomes of various strategic decisions made by firms, such as pricing decisions or decisions to enter or exit the market.
Environmental economics: Game theory is used to analyze various environmental problems, such as pollution and overfishing. Game theory models can be used to identify the optimal strategies for regulating these activities and to design mechanisms such as cap-and-trade systems.
Social interactions: Game theory is used to analyze social interactions, such as the behavior of individuals in public goods games or the emergence of cooperation in repeated prisoner’s dilemma games.
Voting: Game theory is used to analyze various voting systems and to determine the optimal strategies for voters and candidates in elections.
Financial markets: Game theory is used to analyze the behavior of investors and traders in financial markets and to design optimal trading strategies.
Contract Theory: Game theory is also used in the study of contract theory, where it is used to analyze the incentives of parties to a contract. In this context, game theory is used to model the strategic behavior of the parties as they try to negotiate the terms of the contract. The principal-agent problem is a classic example of a contract theory problem, where the interests of the principal and agent may not be aligned.
Bargaining: Game theory is also used in the study of bargaining, where it is used to analyze the negotiation process between two parties. In this context, game theory is used to model the strategic behavior of the parties as they try to reach an agreement. The Nash bargaining solution is a well-known concept in the study of bargaining that is used to analyze the outcome of a negotiation.
Suppose there are two competing firms, Firm A and Firm B, in the market for a particular product. Each firm can choose to either lower or maintain their prices. The payoffs (profits) for each firm are given in the following matrix:
In this matrix, the first number in each cell represents the payoff for Firm A, while the second number represents the payoff for Firm B. For example, if both firms choose to maintain their prices, Firm A earns a profit of 5, while Firm B earns a profit of 5 as well.
/ \
Lower Maintain
/ \
Firm B Firm B
/ \ / \
Lower Maintain Lower Maintain
To find the Nash equilibrium of this game, we need to identify a strategy profile where neither firm has an incentive to deviate from their strategy given the other firm’s strategy. In this case, the Nash equilibrium is (Lower, Lower) since neither firm has an incentive to change their strategy.
This means that both firms will choose to lower their prices, resulting in each firm earning a profit of 10. If either firm were to deviate from this strategy, they would earn a lower profit.
Tweets
Mathematical Modeling in Economics
Twitter
Facebook
WhatsApp
LinkedIn
