Robust perfect equilibrium in large games

TL;DR

This paper introduces the concept of robust perfect equilibrium for large games with many players, proving its existence and properties, and demonstrating its application to congestion and potential games.

Contribution

It defines a new equilibrium concept for large games, proves its existence, and explores its properties and applications, extending the strategic interaction literature.

Findings

Existence of symmetric robust perfect equilibrium in large games.

Unique equilibrium in congestion games with increasing costs.

Properties like admissibility and robustness are satisfied.

Abstract

This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed strategies and in pure strategies) and satisfy the important properties of admissibility, aggregate robustness, and ex post robust perfection. These properties strengthen relevant equilibrium results in an extensive literature on strategic interactions among a large number of agents. Illustrative applications to congestion games and potential games are presented. In the particular case of a congestion game with strictly increasing cost functions, we show that there is a unique symmetric robust perfect equilibrium.