The standard model of repeated games assumes perfect synchronization in the timing of decisions between the players. In many natural settings, however, choices are made synchronously so that only one player can move at a given time. This paper studies a family of repeated settings in which choices are asynchronous. Initially, we examine, as a canonical model, a simple two person alternating move game of pure coordination. There, it is shown that for sufficient patient players, there is a unique perfect equilibrium payoff which Pareto dominates all other payoffs. The result generalizes to any finite number of players and any game in a class of asynchronously repeated games which includes both stochastic and deterministic repetition. The result complement a recent Folk Theorem by Dutta (1995) for stochastic games which can be applied to asynchronously repeated games if a full dimensionality condition holds. A critical feature of the model is the inertia in decisions. We show how the inertia in asynchronous decisions determines the set of equilibrium payoffs.

We use the framework of random matching games and develop a two-country model of the world economy, in which two national currencies compete and may be circulated as media of exchange. There are multiple equilibria, which differ in the areas of circulation of the two currencies. In one equilibrium, the two national currencies are circulated only locally. In another, one currency is circulated as an international currency. There is also an equilibrium in which both currencies are accepted internationally. We also find an equilibrium in which the two currencies are directly exchanged. We first characterize the existence conditions of these equilibria in terms of the relative country size and the degree of economic integration and then use an evolutionary approach to equilibrium selection to explain the evolution of the international currency as the two economies become more integrated. Some welfare implications are also discussed. For example, a country can improve its national welfare by letting its own currency circulate internationally, provided the domestic circulation is controlled for. When the total supply is fixed, however, a resulting currency shortage may reduce the national welfare.

IN THE FIELD OF NONCOOPERATIVE GAME THEORY, Nash equilibrium (Nash (1951)) has played a central role as a solution concept. In bold strokes, one may discern two major interpretations of Nash equilibrium in the context of rational players. The first, which is close to the eductive interpretation of Binmore (1987, 1988) and the complete information interpretation of Kaneko (1987), assumes that the game is played exactly once (if it is a repeated game, the repetition occurs once), and the players have sufficient knowledge and ability to analyze the game in a rational manner. Sometimes it is assumed that all players have consistent hierarchies of beliefs, where the game and their priors are common knowledge. Bayesian interpretation such as proposed by Aumann (1987) advanced this idea to the level that the players have a common prior. From this point of view, however, Nash equilibrium seems far from being satisfactory