The dynamic cost of ex post incentive compatibility in repeated games of private information

In a repeated game with private information, a perfect public equilibrium (PPE) can break down if communication is not necessarily simultaneous or if players can “spy” on each others’ information. An ex post perfect public equilibrium (EPPPE) is a PPE that is ex post incentive compatible in each stage game; unlike PPE, EPPPE is robust under to any communication protocol, and to spying. However, robustness comes at a cost to the players: in many games, efficient payoffs in the corresponding static mechanism design problem cannot be supported as average payoffs in an EPPPE, even when players are patient. In two- player repeated allocation games, an optimal EPPPE never employs a (static) efficient outcome function in any stage game. Instead, the players always prefer to give up some static efficiency by sometimes allocating to the player with the lower valuation. Under independent valuations, optimal equilibria are often stationary, but when valuations are globally interdependent, optimal equilibria are never stationary. Applied to the problem of collusion with hidden costs, these results yield new insights into the phenomenon of price wars in collusive equilibria.