Extremal structures and symmetric equilibria with countable actions
研究了可数行动的无原子匿名博弈中，库诺-纳什均衡分布是对称均衡当且仅当它是具有相同边际分布的所有均衡分布集合的极值点，并由此证明任何均衡都可重新分配为对称均衡。
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.