Note on Unique Nash Equilibrium in Continuous Games

نویسنده

  • John Rehbeck
چکیده

This note studies the following question: If a researcher is given a finitely supported mixed strategy for each player over a continuous strategy space, does there exist a game whose unique Nash equilibrium is given by these mixed strategies? This note finds that any set of finitely supported mixed strategies on metric spaces can be represented as the unique Nash equilibrium to a separable game. If the strategy spaces are subsets of Euclidean space, then the mixed strategies can be represented as the unique Nash equilibrium to a polynomial game. ∗I thank Christopher P. Chambers and Joel Sobel for useful advice and comments. Any remaining errors are my own. 1

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تاریخ انتشار 2017