On equilibrium in pure strategies in games with many players |
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Authors: | Edward Cartwright Myrna Wooders |
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Institution: | (1) Department of Economics, Keynes College, University of Kent, Canterbury, Kent, CT2 7NP, UK;(2) Department of Economics, Vanderbilt University Nashville, Nashville, TN 37235, USA |
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Abstract: | We demonstrate that, if there are sufficiently many players, any Bayesian equilibrium of an incomplete information game can
be “ε-purified” . That is, close to any Bayesian equilibrium there is an approximate Bayesian equilibrium in pure strategies. Our
main contribution is obtaining this result for games with a countable set of pure strategies. In order to do so we derive
a mathematical result, in the spirit of the Shapley–Folkman Theorem, permitting countable strategy sets. Our main assumption
is a “large game property,” dictating that the actions of relatively small subsets of players cannot have large affects on
the payoffs of other players.
E. Cartwright and M. Wooders are indebted to Phillip Reny, Frank Page and two anonymous referees for helpful comments. |
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Keywords: | Bayesian equilibrium Purification Large games Semi-anonymity Ex-post stability Shapley– Folkman Theorem Countable strategy space |
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