The use of public randomization in discounted repeated games

This paper presents an example where the set of subgame-perfect equilibrium payoffs of the infinitely repeated game without public randomization is not convex, no matter how large the discount factor is. Also, the set of pure-strategy equilibrium payoffs is not monotonic with respect to the discount factor in this example. These results are in sharp contrast to the fact that the equilibrium payoff set is convex and monotonic if public randomization is available.