Working Papers
By Year:
Paper #  Author  Title  

16018 
George J. Mailath Stephen Morris Andrew Postlewaite 
Laws and Authority  
A law prohibiting a particular behavior does not directly change the payoff to an individual should he engage in the prohibited behavior. Rather, any change in the individual’s payoff, should he engage in the prohibited behavior, is a consequence of changes in other peoples’ behavior. If laws do not directly change payoffs, they are “cheap talk,” and can only affect behavior because people have coordinated beliefs about the effects of the law. Beginning from this point of view, we provide definitions of authority in a variety of problems, and investigate how and when individuals can have, gain, and lose authority. Download Paper


12043 
V. Bhaskar George J. Mailath Stephen Morris 
"A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games"  
We study perfect information games with an infinite horizon played by an arbitrary number of players. This class of games includes infinitely repeated perfect information games, repeated games with asynchronous moves, games with long and short run players, games with overlapping generations of players, and canonical noncooperative models of bargaining. We consider two restrictions on equilibria. An equilibrium is purifiable if close by behavior is consistent with equilibrium when agents' payoffs at each node are perturbed additively and independently. An equilibrium has bounded recall if there exists K such that at most one player's strategy depends on what happened more than K periods earlier. We show that only Markov equilibria have bounded memory and are purifiable. Thus if a game has at most one longrun player, all purifiable equilibria are Markov. Download Paper


12003 
V. Bhaskar George J. Mailath Stephen Morris 
“A Foundation for Markov Equilibria with Finite Social Memory”  
We study stochastic games with an infinite horizon and sequential moves played by an arbitrary number of players. We assume that social memory is finiteevery player, except possibly one, is finitely lived and cannot observe events that are sufficiently far back in the past. This class of games includes games between a longrun player and a sequence of shortrun players and games with overlapping generations of players. Indeed, any stochastic game with infinitely lived players can be reinterpreted as one with finitely lived players: Each finitelylived player is replaced by a successor, and receives the value of the successor's payoff. This value may arise from altruism, but the player also receives such a value if he can “sell” his position in a competitive market. In both cases, his objective will be to maximize infinite horizon payoffs, though his information on past events will be limited. An equilibrium is purifiable if closeby behavior is consistent with equilibrium when agents' payoffs in each period are perturbed additively and independently. We show that only Markov equilibria are purifiable when social memory is finite. Thus if a game has at most one longrun player, all purifiable equilibria are Markov. Download Paper


09029 
V. Bhaskar George J. Mailath Stephen Morris 
"A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games"  
We study perfect information games with an infinite horizon played by an arbitrary number of players. This class of games includes infinitely repeated perfect information games, repeated games with asynchronous moves, games with long and short run players, games with overlapping generations of players, and canonical noncooperative models of bargaining. We consider two restrictions on equilibria. An equilibrium is purifiable if close by behavior is consistent with equilibrium when agents' payoffs at each node are perturbed additively and independently. An equilibrium has bounded recall if there exists K such that at most one player's strategy depends on what happened more than K periods earlier. We show that only Markov equilibria have bounded memory and are purifiable. Thus if a game has at most one longrun player, all purifiable equilibria are Markov. Download Paper


07024 
V. Bhaskar George J. Mailath Stephen Morris 
"Purification in the InfinitelyRepeated Prisoners' Dilemma", Second Version  
This paper investigates the Harsanyi (1973)purifiability of mixed strategies in the repeated prisoners’ dilemma with perfect monitoring. We perturb the game so that in each period, a player receives a private payoff shock which is independently and identically distributed across players and periods. We focus on the purifiability of oneperiod memory mixed strategy equilibria used by Ely and Välimäki (2002) in their study of the repeated prisoners’ dilemma with private monitoring. We find that any such strategy profile is not the limit of oneperiod memory quilibrium strategy profiles of the perturbed game, for almost all noise distributions. However, if we allow infinite memory strategies in the perturbed game, then any completelymixed equilibrium is purifiable. Download Paper


05014 
George J. Mailath Stephen Morris 
"Coordination Failure in Repeated Games with AlmostPublic Monitoring", Second Version  
Some privatemonitoring games, that is, games with no public histories, can have histories that are almost public. These games are the natural result of perturbing public monitoring games towards private monitoring. We explore the extent to which it is possible to coordinate continuation play in such games. It is always possible to coordinate continuation play by requiring behavior to have bounded recall (i.e., there is a bound L such that in any period, the last L signals are sufficient to determine behavior). We show that, in games with general almostpublic private monitoring, this is essentially the only behavior that can coordinate continuation play. Download Paper


04033 
George J. Mailath Stephen Morris 
"Coordination Failure in Repeated Games with AlmostPublic Monitoring"  
Some privatemonitoring games, that is, games with no public histories, can have histories that are almost public. These games are the natural result of perturbing publicmonitoring games towards private monitoring. We explore the extent to which it is possible to coordinate continuation play in such games. It is always possible to coordinate continuation play by requiring behavior to have bounded recall (i.e., there is a bound L such that in any period, the last L signals are sufficent to determine behavior). We show that, in games with general almostpublic private monitoring, this is essentially the only behavior that can coordinate continuation play. Download Paper


04004 
V. Bhaskar George J. Mailath Stephen Morris 
"Purification in the InfinitelyRepeated Prisoners' Dilemma"  
This paper investigates the Harsanyi (1973)purifiability of mixed strategies in the repeated prisoners' dilemma with perfect monitoring. We perturb the game so that in each period, a player receives a private payoff shock which is independently and identically distributed across players and periods. We focus on the purifiability of a class of oneperiod memory mixed strategy equilibria used by Ely and Välimäki (2002) in their study of the repeated prisoners' dilemma with private monitoring. We find that the strategy profile is purifiable by perturbedgame finitememory strategies if and only if it is strongly symmetric, in the sense that after every history, both players play the same mixed action. Thus "most" strategy profiles are not purifiable by finite memory strategies. However, if we allow infinite memory strategies in the perturbed game, then any completelymixed equilibrium is purifiable. Download Paper


98004 
George J. Mailath Stephen Morris 
"Repeated Games with Imperfect Private Monitoring: Notes on a Coordination Perspective"  
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 signalling technologies that allow nonstatic Nash behavior in pure strategy equilibria. Our characterization uses the language of common pbelief due to Monderer and Samet (GEE, 1989). Second, we show that in the continuum action convention game of Shin and Williamson (GEE, 1996), for any full support private monitoring technology, equilibria of the finitely repeated convention game must involve only static Nash equilibria. Ey 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


97013 
Stephen Coate Stephen Morris 
"Policy Conditionality"  
If policy makers in developing countries pursue "bad" economic policies, policy conditionality may provide financial leverage which induces them not to choose these policies. When is such policy conditionality beneficial? We point out that whether conditionality has a beneficial short run impact depends critically on the political economy explanations of the particular "bad" economic policy in question. We also argue that conditionality can only have a longrun impact if there is a tendency for reforms to "persist" and discuss alternative explanations for policy persistence. Download Paper


97012 
Stephen Morris Hyun Song Shin 
"Unique Equilibrium in a Model of SelfFulfilling Currency Attacks"  
Even though selffulfilling currency attacks lead to multiple equilibria when fundamentals are common knowledge, we demonstrate the uniqueness of equilibrium when speculators face a small amount of noise in their signals about the fundamentals. This unique equilibrium depends not only on the fundamentals, but also on financial variables, such as the quantity of hot money in circulation and the costs of speculative trading. In contrast to multiple equilibrium models, our model allows analysis of policy proposals directed at curtailing currency attacks. Download Paper


97008 
Stephen Morris Hyun Song Shin 
"Approximate Common Knowledge and Coordination: Recent Lessons from Game Theory"  