🤖 AI Summary
This paper investigates the equilibrium properties of *obvious strategy profiles* in large-scale finite games. Addressing the existence and implementability of approximate symmetric equilibria as the number of players tends to infinity, we propose a fully decentralized, coordination-free constructive method. Under continuity and asymptotic regularity assumptions, we prove that the empirical strategy distributions induced by obvious strategy profiles converge weakly to symmetric approximate Nash equilibria. Moreover, their random pure-strategy realizations constitute pure-strategy approximate Nash equilibria with probability approaching one. This work establishes, for the first time, *dual convergence*: (i) weak convergence of strategy distributions and (ii) high-probability convergence of pure-strategy realizations. The resulting framework yields scalable, robust, and asymptotically optimal equilibrium solutions for large games—circumventing both explicit coordination mechanisms and prohibitive computational complexity inherent in traditional approaches.
📝 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.