纳什均衡的普适性

摘要：

每个实代数簇同构于某个三人博弈的完全混合纳什均衡集，也同构于每个局中人有两个纯策略的$N$ -人博弈的完全混合纳什均衡集.根据纳什-托格诺利定理，每个紧致微分流形都可以被编码为某个博弈的完全混合纳什均衡的集合。此外，还存在任意拓扑度的孤立纳什均衡。

英文摘要：

Every real algebraic variety is isomorphic to the set of totally mixed Nash equilibria of some three-person game, and also to the set of totally mixed Nash equilibria of an $N$-person game in which each player has two pure strategies. From the Nash-Tognoli Theorem it follows that every compact differentiable manifold can be encoded as the set of totally mixed Nash equilibria of some game. Moreover, there exist isolated Nash equilibria of arbitrary topological degree.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。