Játékelméleti

Játékelméleti, also known as game theory, is a branch of mathematics and economics that studies strategic decision-making. It analyzes situations where the outcome for a participant depends not only on their own actions but also on the actions of other participants. These situations are often referred to as "games."

The core idea of game theory is to model interactions between rational agents who are making choices. A game is typically defined by a set of players, a set of strategies available to each player, and a payoff function that determines the outcome for each player based on the combination of strategies chosen by all players.

Key concepts in game theory include equilibrium, where no player can improve their outcome by unilaterally changing their strategy, and optimal strategies, which are the best choices for a player given the expected actions of others. Different types of games exist, such as cooperative games where players can form binding agreements, and non-cooperative games where they cannot. Games can also be classified as zero-sum, where one player's gain is another's loss, or non-zero-sum, where joint outcomes can be beneficial or detrimental to all players.

Game theory has applications in a wide range of fields beyond economics and mathematics, including political science, psychology, computer science, biology, and even philosophy. It provides a framework for understanding and predicting behavior in competitive and cooperative scenarios.