Kuhn's theorem: Difference between revisions
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In [[game theory]], '''Kuhn's theorem''' relates perfect recall, mixed and unmixed strategies and their expected payoffs. |
In [[game theory]], '''Kuhn's theorem''' relates perfect recall, mixed and unmixed strategies and their expected payoffs. |
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The theorem states that in a game where players may remember all of their previous moves/states of the game available to them, for every [[mixed strategy]] there is a [[Mixed strategy#Behavior strategy|behavioral strategy]] that has an equivalent payoff (i.e. 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).<ref>{{citation|first=Robert|last=Aumann|contribution=Mixed and behavior strategies in infinite extensive games|title=Advances in Game Theory|series=Annals of Mathematics Studies|volume=52|editor1-first=M.|editor1-last=Dresher|editor2-first=L. S.|editor2-last=Shapley|editor2-link=Lloyd Shapley|editor3-first=A. W.|editor3-last=Tucker|editor3-link=Albert W. Tucker|pages=627–650|publisher=Princeton University Press|location=Princeton, NJ, USA|year=1964|isbn= 9780691079028}}.</ref> |
The theorem states that in a game where players may remember all of their previous moves/states of the game available to them, for every [[mixed strategy]] there is a [[Mixed strategy#Behavior strategy|behavioral strategy]] that has an equivalent payoff (i.e. 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).<ref>{{citation|first=Robert|last=Aumann|authorlink=Robert Aumann|contribution=Mixed and behavior strategies in infinite extensive games|title=Advances in Game Theory|series=Annals of Mathematics Studies|volume=52|editor1-first=M.|editor1-last=Dresher|editor1-link=Melvin Dresher|editor2-first=L. S.|editor2-last=Shapley|editor2-link=Lloyd Shapley|editor3-first=A. W.|editor3-last=Tucker|editor3-link=Albert W. Tucker|pages=627–650|publisher=Princeton University Press|location=Princeton, NJ, USA|year=1964|isbn= 9780691079028}}.</ref> |
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==References== |
==References== |
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Revision as of 01:54, 15 May 2014
In game theory, Kuhn's theorem relates perfect recall, mixed and unmixed strategies and their expected payoffs.
The theorem states that in a game where players may remember all of their previous moves/states of the game available to them, for every mixed strategy there is a behavioral strategy that has an equivalent payoff (i.e. 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).[1]
References
- ^ Aumann, Robert (1964), "Mixed and behavior strategies in infinite extensive games", in Dresher, M.; Shapley, L. S.; Tucker, A. W. (eds.), Advances in Game Theory, Annals of Mathematics Studies, vol. 52, Princeton, NJ, USA: Princeton University Press, pp. 627–650, ISBN 9780691079028.
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