A multinomial probit model of stochastic evolution

A strategy revision process in symmetric normal form games is proposed. Following Kandori, Mailath, and Rob (1993), members of a population periodically revise their strategy choice, and choose a myopic best response to currently observed play. Their payoffs are perturbed by normally distributed Harsanyian (1973) trembles, so that strategies are chosen according to multinomial probit probabilities. As the variance of payoffs is allowed to vanish, the graph theoretic methods of the earlier literature continue to apply. The distributional assumption enables a convenient closed form characterisation for the weights of the rooted trees. An illustration of the approach is offered, via a consideration of the role of dominated strategies in equilibrium selection. 1. Strategy Revision Processes with Noise Recent research has been active in tackling the selection of equilibria using evolutionary methods. Kandori, Mailath and Rob (KMR 1993) and Young (1993) examined the long run behaviour of strategy revision processes with noise (a term due to Blume 1999). The approach is now familiar. An underlying dynamic is specified in which revising players choose a best response to either current or historical strategy choices. Since such processes are often path dependent (becoming “locked in” to pure strategy Nash equilibria), noise is added to yield ergodicity. This ensures that the process generates a unique long run distribution of play. KMR (1993) and Young (1993) employed the graph-theoretic methods of Freidlin and Wentzell (1984) to characterise this distribution Date Printed. March 5, 2002 (Version 5.0). JEL Subject Classification. C72 and C73.