Private Strategy and Efficiency: Repeated Partnership Games Revisited

This paper studies repeated partnership games with only two public signals. It is well known that the public perfect equilibrium payoff set is bounded away from the efficient frontier of the stage game in this class of game. In this paper, I construct a strongly symmetric sequential equilibrium whose equilibrium payoff dominates the best symmetric payoff by PPE. The strategy used to construct the equilibrium depends not only on the public signal but also on the realization of one’s own past action. I call this class of strategy private strategy. I also provide an example where this private strategy sequential equilibrium approximates the efficient outcome, but the PPE payoff set is contained in an arbitrary small neighborhood of the stage game Nash equilibrium payoff. This example suggests that the difference between a PPE payoff set and a sequential equilibriujm payoff set can be potentially significant. I am grateful to George Mailath and Andrew Postlewaite for their encouragement and valuable suggestions.