Perfect Foresight Dynamics

Daisuke Oyama

*Graduate School of Economics, University of Tokyo*

This paper studies equilibrium selection based on a class of perfect foresight dynamics and relates it to the notion of p-dominance. A continuum of rational players randomly matched to play a symmetric n x n game. There are frictions: opportunities to revise actions follow independent Poisson processes. The dynamics has stationary states, each of which corresponds to a Nash equilibrium of the static game. A strict Nash equilibrium islinearly stableunder the perfect foresight dynamics if, independently of the current action distribution, there exists a consistent belief such that any player necessarily switches to the Nash equilibrium action at the first opportunity. It is shown that a strict Nash equilibrium is linearly stable under the perfect foresight dynamics with a small degree of friction if and only if it is the p-dominant equilibrium with p < 1/2. It is also shown that if a strict Nash equilibrium is the p-dominant equilibrium with p < 1/2, then it is uniquely absorbing (and globally accessible) for a small friction (but not vice versa). Set-valued stability concepts are introduced and their existence is shown.Journal of Economic LiteratureClassification Numbers: C72, C73.

Key Words:equilibrium selection; perfect foresight dynamics; linear stability; p-dominance.

Journal of Economic Theory107(2002), 288-310.

First draft: January 12, 2000; this version October 5, 2001. PDF file