Kuhn's theorem: Difference between revisions
Themusicgod1 (talk | contribs) mNo edit summary |
Themusicgod1 (talk | contribs) m Generality |
||
| Line 1: | Line 1: | ||
Kuhn's Theorem is a theorem in game theory, which relates perfect recall, mixed and unmixed strategies, and the expected payoffs thereof. |
Kuhn's Theorem is a theorem in game theory, which relates perfect recall, mixed and unmixed strategies, and the expected payoffs thereof. |
||
The theorem states that if a [[Game Theory | Game]] is a game of perfect recall (ie a [[Von Neumann| C-game]]), for every [[mixed strategy]] there is a [https://en.wikipedia.org/wiki/Mixed_strategy#Behavior_strategy behavioral strategy] that has an equivalent payoff(ie the strategies are equivalent). The theorem does not specify what this strategy is, only that it exists. |
The theorem states that if a [[Game Theory | Game]] is a game of perfect recall (ie a [[Von Neumann| C-game]]), for every [[mixed strategy]] there is a [https://en.wikipedia.org/wiki/Mixed_strategy#Behavior_strategy behavioral strategy] that has an equivalent payoff(ie the strategies are equivalent). The theorem does not specify what this strategy is, only that it exists. It is valid both for finite games, as well as infinite games(ie games with continuous choices, or iterated infinitely){{Robert Aumann, Mixed and Behavior Strategies in Infinite Extensive Games, (Advances in Game Theory, Annals of Mathematics, Studies 52, edited by M. Dresher, L. S. Shapley, and A. W. Tucker, pp. 627–650, Princeton, University Press, Princeton, 1964)}}. |
||
{{stub}} |
{{stub}} |
||
Revision as of 18:07, 11 May 2014
Kuhn's Theorem is a theorem in game theory, which relates perfect recall, mixed and unmixed strategies, and the expected payoffs thereof.
The theorem states that if a Game is a game of perfect recall (ie a C-game), for every mixed strategy there is a behavioral strategy that has an equivalent payoff(ie the strategies are equivalent). The theorem does not specify what this strategy is, only that it exists. It is valid both for finite games, as well as infinite games(ie games with continuous choices, or iterated infinitely)Template:Robert Aumann, Mixed and Behavior Strategies in Infinite Extensive Games, (Advances in Game Theory, Annals of Mathematics, Studies 52, edited by M. Dresher, L. S. Shapley, and A. W. Tucker, pp. 627–650, Princeton, University Press, Princeton, 1964).