Spilleteori

Spilleteori (game theory) is a mathematical framework for analyzing strategic interactions among rational decision-makers when the outcome depends on the choices of all participants. It formalizes players, their possible actions (strategies), the payoffs each participant receives, and the information available when decisions are made.

Historically, early questions about strategic behavior appeared in Zermelo's 1913 analysis of chess. The modern theory was developed by von Neumann and Morgenstern in 1944, who provided axioms for expected utility in competitive situations. John Nash introduced the concept of equilibrium in non-cooperative games in 1950, which became central. Evolutionary game theory followed, extending ideas to populations and adaptation processes.

Core concepts include players, strategies, and payoffs. Games can be represented in normal form (a matrix) or extensive form (a game tree). An equilibrium is a strategy profile where no player benefits from unilateral deviation; Nash equilibrium is the best known. Other ideas include dominant strategies, mixed strategies, and different information structures. Games can be simultaneous or sequential, finite or infinite, and cooperative or non-cooperative; mechanism design studies how institutions can be crafted to achieve desired results.

Prominent models include Prisoner's Dilemma, Battle of the Sexes, Rock-Paper-Scissors, and Cournot competition. These illustrate how rational choices can yield counterintuitive outcomes or coordination problems. Mechanism design studies how institutions can be crafted to achieve desired results.

Applications span economics, political science, biology (evolutionarily stable strategies), computer science (algorithmic game theory), and operations research. Behavioral game theory and experiments examine deviations from pure rationality.

Critiques address assumptions of rationality and common knowledge, and some models face computational complexity. Despite limitations, game theory remains a versatile tool for understanding strategic behavior and informing policy, negotiation, and design.