Anonymous repeated games with a large number of players and random outcomes

Abstract

Green ( J. Econ. Theory 22 (1980), 155–182) demonstrates that in anonymous repeated games with random outcomes, any play which can be sustained as an equilibrium by a trigger strategy is approximately a Nash equilibrium of the stage game if there is a large, but finite, number of players and if the stage game satisfies a certain continuity assumption. This paper shows that Green's result holds when no restrictions are imposed on the strategies of the players, thus demonstrating the continuity of Nash correspondence at the nonatomic limit for these games. Moreover, the result shows that, in general, to obtain convergence, Green's continuity assumption cannot be relaxed.