Monotone Methods for Equilibrium Selection under
Perfect Foresight Dynamics

Daisuke Oyama
Graduate School of Economics, Hitotsubashi University

Satoru Takahashi
Department of Economics, Princeton University


Josef Hofbauer
Department of Mathematics, University of Vienna

This paper studies a dynamic adjustment process in a large society of forward-looking agents where payoffs are given by a normal form supermodular game. The stationary states of the dynamics correspond to the Nash equilibria of the stage game. It is shown that if the stage game has a monotone potential maximizer, then the corresponding stationary state is uniquely linearly absorbing and globally accessible for any small degree of friction. A simple example of a unanimity game with three players is provided where there are multiple globally accessible states for a small friction. Journal of Economic Literature Classification Numbers: C72, C73.
Key Words: equilibrium selection; perfect foresight dynamics; supermodular game; strategic complementarity; stochastic dominance; potential; monotone potential.

Theoretical Economics 3 (2008), 155-192. PDF file
First draft: May 2, 2003; this version: April 2, 2008. PDF file
Working paper version: January 27, 2006. PDF file