Game Theory
Introduction
Game theory is a branch of mathematics that studies strategic interactions, meaning situations where the outcome for each participant or "player" depends on the actions of all. In these situations, an individual's success in making choices depends on the choices of others decision theory. While initially developed to understand games of chance, it has been vastly expanded to include a wide range of situations.
History
The origins of game theory date back to the work of mathematician John von Neumann in the early 20th century. Von Neumann's 1928 article "Zur Theorie der Gesellschaftsspiele" (On the Theory of Parlor Games) established the mathematical foundations of the discipline John von Neumann. However, it was not until the publication of "Theory of Games and Economic Behavior" in 1944, co-authored with economist Oskar Morgenstern, that game theory became a distinct field of study.
Basic Concepts
Game theory is built on a few basic concepts: players, strategies, payoffs, and information.
Players
In game theory, a player is an individual or group that makes decisions. Players can be people, companies, nations, animals, or any entity that makes decisions based on the expected actions of others.
Strategies
A strategy in game theory is a complete plan of action for a player, detailing what they will do in every possible situation. A strategy must specify an action for every possible situation that might arise, based on the player's information at the time.
Payoffs
A payoff in game theory is the outcome that a player receives at the end of a game. This can be quantified in many ways, such as monetary gain, utility, or any other measure of benefit.
Information
Information in game theory refers to what each player knows at each point in the game. This includes knowledge about the rules of the game, the payoffs for all players, and the strategies chosen by each player.
Types of Games
Game theory categorizes games into several types, including cooperative games, non-cooperative games, symmetric games, asymmetric games, simultaneous games, and sequential games.
Cooperative Games
In cooperative games, binding agreements are possible. This means that players can make enforceable contracts with each other, and can form coalitions to improve their outcomes.
Non-Cooperative Games
In non-cooperative games, binding agreements are not possible. Each player makes decisions independently, and cannot enforce agreements with other players.
Symmetric Games
In symmetric games, all players are identical in terms of strategy and payoff. The classic example of a symmetric game is the prisoner's dilemma prisoner's dilemma.
Asymmetric Games
In asymmetric games, players are not identical. They may have different strategies, different payoffs, or different information.
Simultaneous Games
In simultaneous games, all players make their decisions at the same time. These games are often represented by a payoff matrix.
Sequential Games
In sequential games, players make their decisions one after the other. These games are often represented by a game tree.
Applications of Game Theory
Game theory has found applications in a wide range of fields, including economics, political science, psychology, computer science, biology, and philosophy.
Economics
In economics, game theory is used to model a wide range of situations, including auctions, bargaining, competition and cooperation among firms, and strategic behavior in voting systems economics.
Political Science
In political science, game theory is used to study voting, bargaining, wars, and international relations political science.
Psychology
In psychology, game theory is used to understand decision-making and social behavior psychology.
Computer Science
In computer science, game theory is used in the design of algorithms and networks, and in the study of artificial intelligence and machine learning computer science.
Biology
In biology, game theory is used to understand evolution and animal behavior biology.
Philosophy
In philosophy, game theory is used to explore questions about ethics, rationality, and social justice philosophy.
Conclusion
Game theory provides a powerful framework for understanding strategic interactions in a wide range of fields. Its concepts and techniques continue to be developed and refined, and its applications continue to expand.
