Kuhn's theorem: Difference between revisions
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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 (i.e. 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> |
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 (i.e. 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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==External links== |
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*{{Cite journal|url=http://gki.informatik.uni-freiburg.de/teaching/ss13/gametheory/gametheory15.pdf |
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|title=Game Theory Kuhn’s Theorem|journal=UNI Freiburg|date=June 2013}} |
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==References== |
==References== |
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Latest revision as of 20:10, 20 June 2019
In game theory, Kuhn's theorem relates perfect recall, mixed and unmixed strategies and their expected payoffs. It is named after Harold W. Kuhn.
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 (i.e. games with continuous choices, or iterated infinitely).[1]
References
[edit]- ^ 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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