Working Paper 99-03
Department of Economics
University of North Carolina, Chapel Hill
http://www.unc.edu/depts/econ

Abstract

Random Belief and Ultraperfect Equilibria

We examine noncooperative games in which players have random beliefs about the strategy choices that other players will make. Each player chooses a best response relative to her beliefs and, at equilibrium, the probability measure that represents her beliefs has some dependence on the other players' actual choices. These beliefs and the associated equilibrium are a generalization of the beliefs and equilibrium conditions underlying Nash equilibrium in games of complete information.

We study the limiting behavior of equilibrium as beliefs converge to certainty, finding that the limiting equilibrium is trembling hand perfect. We call such a limiting equilibrium \emph{ultraperfect} and find the following: 1) not all perfect equilibria are ultraperfect, 2) being ultraperfect is neither necessary nor sufficient for being weakly proper.

 

James Friedman
Department of Economics, CB# 3305
University of North Carolina
Chapel Hill, NC 27599-3305
Jim_Friedman@unc.edu
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