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arXiv · 2410.22144

The equilibrium properties of obvious strategy profiles in games with many players

Enxian Chen Bin Wu Hanping Xu
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Abstract

This paper studies the equilibrium properties of the ``obvious strategy profile'' in large finite-player games. Each player in such a strategy profile simply adopts a randomized strategy as she would have used in a symmetric equilibrium of an idealized large game. We show that, under a continuity assumption, (i) obvious strategy profiles constitute a convergent sequence of approximate symmetric equilibria as the number of players tends to infinity, and (ii) realizations of such strategy profiles also form a convergent sequence of (pure strategy) approximate equilibria with probability approaching one. Our findings offer a solution that is easily implemented without coordination issues and is asymptotically optimal for players in large finite games. Additionally, we present a convergence result for approximate symmetric equilibria.

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Enxian Chen Bin Wu Hanping Xu. 2024-10-29. The equilibrium properties of obvious strategy profiles in games with many players. https://arxiv.org/abs/2410.22144

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