Game theory is a branch of mathematics and economics that deals with the study of strategic decision-making. It provides a framework for understanding and analyzing the interactions of rational individuals or players in competitive situations called games. These “games” can represent a wide range of scenarios, from simple board games to complex real-world situations like business competitions, political negotiations, and military conflicts.
The central concept in game theory is the “game,” which consists of the following components:
- Players: The individuals or entities making decisions within the game. Each player has their own set of strategies to choose from.
- Strategies: The available choices or actions that each player can take in the game.
- Payoffs: The outcomes or rewards associated with the different combinations of strategies that players choose. Payoffs can be represented as numerical values, reflecting the preferences or utilities of the players.
- Information: The knowledge that each player has about the game, including the actions taken by others and their respective payoffs. Games can be classified into categories based on whether players have complete (all information) or incomplete (partial or hidden information) knowledge.
Game theory analyzes different types of games, such as:
- Cooperative Games: In these games, players can form coalitions and work together to achieve common goals. Cooperative game theory focuses on how to distribute the gains or payoffs among the players in a fair and stable manner.
- Non-Cooperative Games: These games do not allow for formal agreements or cooperation between players. Instead, players make decisions independently, trying to maximize their own payoffs. The most famous non-cooperative game is the “Nash equilibrium,” which represents a stable state in which no player has an incentive to unilaterally change their strategy.
- Zero-Sum Games: In a zero-sum game, the total payoff remains constant, meaning any gain by one player is offset by an equal loss for another player. This type of game is purely competitive, and one player’s gain comes at the expense of others.
- Sequential Games: In these games, players take turns making decisions based on the actions of previous players. They must anticipate the moves of other players and consider the consequences of their choices in a dynamic fashion.
Game theory has found applications in various fields, including economics, political science, biology, computer science, and more. It helps in understanding strategic behavior, predicting outcomes, designing optimal strategies, and identifying stable solutions in complex decision-making scenarios. The works of John Nash, John von Neumann, and Oskar Morgenstern significantly contributed to the development of game theory and its widespread use in modern academic research and real-world applications.