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This variant of backward induction has been used to solve formal games from the beginning of game theory. John von Neumann and Oskar Morgenstern suggested solving zero-sum, two-person formal games through this method in their Theory of Games and Economic Behaviour (1944), the book which established game theory as a field of study. [6] [7]
A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of a particular economic situation. One or more solution concepts are chosen, and the author demonstrates which strategy sets in the presented game are equilibria of the appropriate type.
A classic example of a dynamic game with types is a war game where the player is unsure whether their opponent is a risk-taking "hawk" type or a pacifistic "dove" type. Perfect Bayesian Equilibria are a refinement of Bayesian Nash equilibrium (BNE), which is a solution concept with Bayesian probability for non-turn-based games.
Conditions on G (the stage game) – whether there are any technical conditions that should hold in the one-shot game in order for the theorem to work. Conditions on x (the target payoff vector of the repeated game) – whether the theorem works for any individually rational and feasible payoff vector, or only on a subset of these vectors.
In game theory, a repeated game (or iterated game) is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a player will have to take into account the impact of their current action on the ...
Lloyd Stowell Shapley (/ ˈ ʃ æ p l i /; June 2, 1923 – March 12, 2016) was an American mathematician and Nobel Memorial Prize-winning economist.He contributed to the fields of mathematical economics and especially game theory.
In 1994, he received the Nobel Memorial Prize in Economic Sciences (along with John Harsanyi and Reinhard Selten) for his game theory work as a Princeton graduate student. [65] In the late 1980s, Nash had begun to use email to gradually link with working mathematicians who realized that he was the John Nash and that his new work had value.
Game theory was originally conceived as a mathematical analysis of economic processes and indeed this is why it has proven so useful in explaining so many biological behaviours. One important further refinement of the evolutionary game theory model that has economic overtones rests on the analysis of costs.