Game Theory
Game theory is a mathematical framework for analyzing strategic interactions between rational decision-makers, known as players, who each seek to optimize their own outcomes. Developed formally in the mid-20th century by mathematicians including John von Neumann and Oskar Morgenstern, game theory models situations where the result for any participant depends not only on their own choices but also on the choices of others. The framework applies to both competitive scenarios where players have opposing interests and cooperative situations where players can benefit from coordinated action.
Core Concepts
A game is formally defined by its players, the strategies available to each player, and the payoffs resulting from different combinations of strategy choices. The payoff structure determines what each player stands to gain or lose from various outcomes. A central concept in game theory is the Nash equilibrium, named after mathematician John Nash, which represents a state where no player can improve their outcome by unilaterally changing their strategy, given the strategies chosen by others.
Applications
Game theory has applications across economics, political science, biology, and computer science. In economics, it analyzes market competition, pricing strategies, and auction design. In biology, evolutionary game theory explains animal behavior and natural selection. Political scientists use game theory to study voting systems, international negotiations, and conflict. The framework has also become relevant to artificial intelligence and cybersecurity for modeling agent interactions and strategic decision-making in complex systems.