Theoretical Economics, Volume 3, Number 2 (July 2008)

Theoretical Economics 3 (2008), 155–192


Monotone methods for equilibrium selection under perfect foresight dynamics

Daisuke Oyama, Satoru Takahashi, Josef Hofbauer

Abstract


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.

Keywords: Equilibrium selection, perfect foresight dynamics, supermodular game, strategic complementarity, stochastic dominance, potential, monotone potential

JEL classification: C72, C73

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