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Title: Extremal structures and symmetric equilibria with countable actions
Authors: Khan, M.A.
Sun, Y. 
Keywords: Cournot-Nash equilibrium distributions
Extreme point
Issue Date: 1995
Citation: Khan, M.A.,Sun, Y. (1995). Extremal structures and symmetric equilibria with countable actions. Journal of Mathematical Economics 24 (3) : 239-248. ScholarBank@NUS Repository.
Abstract: In this paper we show that a Cournot-Nash equilibrium distribution τ of an atomless anonymous game with countable actions is a symmetric equilibrium if and only if it is an extreme point of the set of all Cournot-Nash equilibrium distributions of the game with the same marginals as τ. This characterization allows us to show, as an application of the Krein-Milman theorem, that any particular Cournot-Nash equilibrium of such a game can be reallocated such that players with the same characteristics always take the same action, which is to say that it can be symmetrized. As a consequence of the usual result on the existence of distributional equilibria, we also obtain the existence of symmetric equilibria for the games under consideration. © 1995.
Source Title: Journal of Mathematical Economics
ISSN: 03044068
Appears in Collections:Staff Publications

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