We study the adoption of a new technology to illustrate the effects of preemption in games of timing. We show that the threat of preemption equalizes rents in a duopoly, but that this result does not extend to the general oligopoly game. If the gain to preemption is sufficiently small, then the optimal symmetric outcome, which involves “late” adoption, is an equilibrium. This contrasts with Reinganum's result that in precommitment equilibria there must be “diffusion”. We develop a new and richer formalism for modeling games of timing, which permits a continuous-time representation of the limit of discrete-time mixed-strategy equilibria.

This paper describes a simple two-person, two-period bargaining game, and solves it using the concept of perfect Bayesian equilibrium, in which the actions of each player convey information which is used by his opponent. The paper examines the effects of changes in bargaining costs, the size of the “contract zone” and the length of the bargaining process on such aspects of the solution as the probability of impasse and the likelihood of concessions. The combination of information transfer and the lack of pre-commitment embodied in perfectness yields many surprising results. Common perceptions about the effects of parameter changes on bargaining processes are suspect, and should be checked in the particular game being discussed.

This paper studies reputation effects in games with a single long-run player whose choice of stage-game strategy is imperfectly observed by his opponents. We obtain lower and upper bounds on the long-run player's payoff in any Nash equilibrium of the game. If the long-run player's stage-game strategy is statistically identified by the observed outcomes, then for generic payoffs the upper and lower bounds both converge, as the discount factor tends to 1, to the long-run player's Stackelberg payoff, which is the most he could obtain by publicly committing himself to any strategy.

Imagine that one player, the “incumbent” competes with several “entrants”. Each entrant competes only with the incumbent, but observes play in all contests. Previous work shows that, as more and more entrants are added, the incumbent's reputation may dominate play of the game, if the entrants are faced in sequence. We identify conditions under which similar results obtain when the entrants are faced simultaneously, and we find specifications in which adding more simultaneous entrants has a dramatically different effect. We also show that, with either sequential or simultaneous play, incumbents need not prefer the situation in which their reputations can and do dominate play to the “informationally isolated” case in which each entrant observes only play in its own contest.

We introduce a new model of repeated games in large populations with random matching, overlapping generations, and limited records of past play. We prove that steady-state equilibria exist under general conditions on records. When the updating of a player’s record can depend on the actions of both players in a match, any strictly individually rational action can be supported in a steady-state equilibrium. When record updates can depend only on a player’s own actions, fewer actions can be supported. Here, we focus on the prisoner’s dilemma and restrict attention to strict equilibria that are coordination-proof, meaning that matched partners never play a Pareto-dominated Nash equilibrium in the one-shot game induced by their records and expected continuation payoffs. Such equilibria can support full cooperation if the stage game is either “strictly supermodular and mild” or “strongly supermodular,” and otherwise permit no cooperation at all. The presence of “supercooperator” records, where a player cooperates against any opponent, is crucial for supporting any cooperation when the stage game is “severe.”

This paper studies the set of equilibrium payoffs in repeated games with long- and short-run players and little discounting. Because the short-run players are unconcerned about the future, each equilibrium outcome is constrained to lie on their static reaction (best-response) curves. The natural extension of the folk theorem to games of this sort would simply include this constraint in the definitions of the feasible payoffs and minmax values. In fact, this extension does obtain under the assumption that each player's choice of a mixed strategy for the stage game is publicly observable but, in contrast to standard repeated games, the set of equilibrium payoffs is different if players can observe only their opponents' realized actions.