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

TL;DR

This paper analyzes the equilibrium properties of obvious strategy profiles in large finite-player games, showing they form convergent sequences of approximate equilibria and are easy to implement.

Contribution

It introduces the concept that obvious strategy profiles are asymptotically optimal and form convergent approximate equilibria in large games under a continuity assumption.

Findings

Obvious strategy profiles form convergent sequences of approximate symmetric equilibria.

Realizations of obvious strategy profiles are asymptotically approximate pure equilibria.

The approach offers an easily implementable solution without coordination issues.

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.