The Game Theory by J. von Neumann

Game theory is a branch of mathematics that studies strategic interactions among rational agents. It can be applied to various fields, such as economics, politics, biology, and psychology, to analyze situations where the outcomes depend on the choices of multiple players. Game theory was developed by John von Neumann, a Hungarian-American mathematician, and Oskar Morgenstern, a German-American economist, in their seminal book Theory of Games and Economic Behavior, published in 1944.

Von Neumann and Morgenstern’s Contribution

Von Neumann and Morgenstern were the first to provide a rigorous mathematical foundation for game theory. They introduced the concept of expected utility, which measures how much an agent prefers one outcome over another based on the probabilities and payoffs of each outcome. They also defined the notion of a game in extensive form, which describes the sequence of moves and information available to each player at each stage of the game, and in normal form, which summarizes the strategies and payoffs of each player in a matrix. They proved the existence of a solution concept called the minimax theorem, which states that in any zero-sum game (a game where one player’s gain is another player’s loss), there exists a strategy for each player that guarantees the best possible outcome against any strategy of the opponent. They also developed the idea of cooperative games, where players can form coalitions and share the benefits according to some rules.

Von Neumann and Morgenstern’s book had a profound impact on the development of game theory and its applications to economics and other disciplines. Their work inspired many subsequent researchers, such as John Nash, John Harsanyi, Reinhard Selten, Robert Aumann, Thomas Schelling, and John Maynard Smith, to extend and refine game theory in various directions. Game theory has become a powerful tool for understanding human behavior, social phenomena, and strategic decision making.

Works Cited

– Von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behavior. Princeton University Press.
– Stanford University. (n.d.). Von Neumann and the development of game theory. Retrieved November 21, 2023 from https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/neumann.html
– Britannica. (n.d.). Game theory – The von Neumann–Morgenstern theory. Retrieved November 21, 2023 from https://www.britannica.com/science/game-theory/The-von-Neumann-Morgenstern-theory