Essays On Repeated Games

Much of the recent interest in the economic applications of game theory has been drawn to time-inconsistency. The most tractable time-inconsistent preferences are those exhibiting a bias for the present. In Chapter 1, repeated games with observable actions and present-biased preferences of the so-called beta-delta (or quasi-geometric) form are investigated. First, the Strotz-Pollak equilibrium solution concept is extended to infinitely repeated games with several players. By appeal to Abreu's optimal simple penal codes, we show that every pure-strategy Strotz-Pollak equilibrium path is subgame perfect and, therefore, there is ultimately no intertemporal conflict between different selves. The recursive technique of Abreu, Pearce, and Stacchetti is adapted to characterize the set of continuation payoffs. Then equilibrium payoffs are computed. Strikingly, with a public randomization device added, the set of equilibrium payoffs need not be monotonic in the long-term discount factor. At the same time, monotonicity in it implies monotonicity in the myopia-related discount factor. Upper and lower bounds on the set of equilibrium payoffs are studied. In Chapter 2, the Nash-threat and pure-strategy minimax versions of the perfect folk theorem are stated and proved for infinitely repeated games with several players having different degrees of myopia. In Chapter 3, we study infinitely repeated games with observable actions and extensive form correlation. To secure a recursive structure, we first assume that the players condition their play on the prior history of action profiles and the latest private message they have received from the device. The set of perfect correlated equilibrium payoffs is not necessarily convex and may strictly include the set of subgame perfect public randomization equilibrium payoffs, though the reverse containment is also possible since, in the case with public randomization, public histories include previous public messages. An augmented correlation device is constructed, with the corresponding set of equilibrium payoffs containing both the set of perfect correlated equilibrium payoffs and the set of subgame perfect public randomization equilibrium payoffs.