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In repeated games with imperfect public monitoring, players can use public signals to coordinate their behavior perfectly, and thus support cooperative outcomes with the threat of punishments. But with even a small amount of private monitoring, players’ private histories may lead them to have sufficiently different views of the world that such coordination on punishments is no longer possible (we describe a simple strategy profile that is a perfect public equilibrium of a repeated prisoner’s dilemma with imperfect public monitoring and yet is not an equilibrium for arbitrarily close games with private monitoring). If a perfect public equilibrium has players’ behavior conditioned only on finite histories, then it induces an equilibrium in all close-by games with private monitoring. This implies a folk theorem for repeated games with almost-public almost-perfect monitoring. Download Paper
In repeated games with imperfect public monitoring, players can use public signals to perfectly coordinate their behavior. Our study of repeated games with imperfect private monitoring focuses on the coordination problem that arises without public signals. We present three new observations. First, in a simple twice repeated game, we characterize the private signaling technologies that allow non-static Nash behavior in pure strategy equilibria. Our characterization uses the language of common p-belief due to Monderer and Samet (GDB, 1989). Second, we show that in the continuum action convention game of Shin and Williamson (GEB, 1996), for any full support private monitoring technology, equilibria of the finitely repeated convention game must involve only static Nash equilibria. By contrast, with sufficiently informative public monitoring, the multiplicity of Nash equilibria allows a finite folk theorem. Finally, for finite action games, we prove that there are full support private monitoring technologies for which a Nash reversion infinite horizon folk theorem holds. Download Paper
Incomplete information, local interaction and random matching games all share a common mathematical structure. A type or player interacts with various subsets of the set of all types/players. A type/player's total payoff is additive in the payoffs from these various interactions. This paper describes a general class of interaction games and shows how each of these three classes of games can be understood as special cases. Techniques and results from the incomplete information literature are translated into this more general framework. A companion paper, Morris [1997], uses these techniques to derive new results concerning contagion in local interaction games. Download Paper
Each player in an infinite population interacts strategically with an infinite subset of that population. Suppose each player's binary choice in each period is a best response to the population choices of the previous period. When can behaviour that is initially played by only a finite set of players spread to the whole population? This paper characterizes when such contagion is possible for arbitrary local interaction systems (represented by general undirected graphs). Maximal contagion occurs when local interaction is sufficiently uniform and there is low neighbour growth, i.e., the number of players who can be reached in k steps does not grow exponentially in k. Download Paper
Suppose we replace "knowledge" by "belief with probability p" in standard definitions of common knowledge. Very different notions arise depending the exact definition of common knowledge used in the substitution. This paper demonstrates those differences and identifies which notion is relevant in each of three contexts: equilibrium analysis in incomplete information games, best response dynamics in incomplete information games, and agreeing to disagree/no trade results. Download Paper
Policy persistence refers to the tendency of the political process to maintain policies once they have been introduced. This paper develops a theory of policy persistence based on the idea that policies create incentives for beneficiaries to take actions which increase their willingness to pay for these policies in the future. The theory is used to show that policy persistence may lead to "political failure", in the sense that policy sequences arising in political equilibrium can be Pareto dominated. In addition, the theory is used to provide an explanation as to why \policy conditionality" may have permanent effects. Download Paper
A number of papers have shown that a strict Nash equilibrium action profile of a game may never be played if there is a small amount of incomplete information (see, for example, Carlsson and van Damme (1993a)). We present a general approach to analyzing the robustness of equilibria to a small amount of incomplete information. A Nash equilibrium of a complete information game is said to be robust to incomplete information if every incomplete information game with payoffs almost always given by the complete information game has an equilibrium which generates behavior close to the Nash equilibrium. We show that an open set of games has no robust equilibrium and examine why we get such different results from the refinements literature. We show that if a game has a unique correlated equilibrium, it is robust. Finally, a natural many-player many-action generalization of risk dominance is shown to be a sufficient condition for robustness. Download Paper
As traders learn about the true distribution of some asset's dividends, a speculative premium occurs as each trader anticipates the possibility of re-selling the asset to another trader before complete learning has occurred. Reasonable ignorance priors lead to large bubbles during the learning process. This phenomenon explains a paradox concerning the pricing of initial public offerings. The result casts light on the significance of the common prior assumption in economic models. Download Paper
If players cannot perfectly synchronize their actions in co-ordination games, the efficient equilibrium is never achieved. Download Paper
In a static economy with symmetric information, the informational requirements for competitive equilibrium are very weak: markets clear and each agent is rational. With asymmetric information, the solution concept of competitive equilibrium has been generalized to rational expectations equilibrium. But now common knowledge of market clearing and rationality is required. This paper proves versions of these results in a formal model of knowledge. Download Paper
At a rational expectations equilibrium (REE), individuals are assumed to know the map from states to prices. This hypothesis has two compo- nents, that agents agree (consensus), and that they have point expectations (degeneracy). We consider economies where agents' beliefs are described by a joint distribution on states and prices, and these beliefs are ful ̄lled at equilibrium. Beliefs are self-ful ̄lling if every price in the support of the distribution is an equilibrium price. The corresponding equilibria are Beliefs Equilibria (BE). The further restriction that agents have the same beliefs results in Common Beliefs Equilibria (CBE). We study the relation- ship between BE, CBE, and REE, thus isolating the role of consensus and of degeneracy in achieving rational expectations. Download Paper