Monotone methods for equilibrium selection under perfect foresight dynamics

Abstract

This paper studies equilibrium selection in supermodular games based on perfect foresight dynamics. A normal form game is played repeatedly in a large society of rational agents. There are frictions: opportunities to revise actions follow independent Poisson processes. Each agent forms his belief about the future evolution of action distribution in the society to take an action that maximizes his expected discounted payo�. A perfect foresight path is de�ned to be a feasible path of the action distribution along which every agent with a revision opportunity takes a best response to this path itself. A Nash equilibrium is said to be absorbing if there exists no perfect foresight path escaping from a neighborhood of this equilibrium; a Nash equilibrium is said to be globally accessible if for each initial distribution, there exists a perfect foresight path converging to this equilibrium. By exploiting the monotone structure of the dynamics, a unique Nash equilibrium that is absorbing and globally accessible for any small degree of friction is identi�ed for certain classes of supermodular games. For games with monotone potentials, the selection of the monotone potential maximizer is obtained. Complete characterizations of absorbing equilibrium and globally accessible equilibrium are given for binary supermodular games. An example demonstrates that unanimity games may have multiple globally accessible equilibria for a small friction