Reputation Effects and Equilibrium Degeneracy in Continuous-Time Games

We study a class of continuous-time reputation games between a large player and a population of small players in which the actions of the large player are imperfectly observable. The large player is either a normal type, who behaves strategically, or a behavioral type, who is committed to playing a certain strategy. We provide a complete characterization of the set of sequential equilibrium payoffs of the large player using an ordinary differential equation. In addition, we identify a sufficient condition for the sequential equilibrium to be unique and Markovian in the small players’ posterior belief. An implication of our characterization is that when the small players are certain that they are facing the normal type, intertemporal incentives are trivial: the set of equilibrium payoffs of the large player coincides with the convex hull of the set of static Nash equilibrium payoffs

Uniform topologies on types

We study the robustness of interim correlated rationalizability to perturbations of higher-order beliefs. We introduce a new metric topology on the universal type space, called uniform weak topology, under which two types are close if they have similar first-order beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity is uniform over the levels of the belief hierarchy. This topology generalizes the now classic notion of proximity to common knowledge based on common p-beliefs (Monderer and Samet 1989). We show that convergence in the uniform weak topology implies convergence in the uniform strategic topology (Dekel, Fudenberg, and Morris 2006). Moreover, when the limit is a finite type, uniform-weak convergence is also a necessary condition for convergence in the strategic topology. Finally, we show that the set of finite types is nowhere dense under the uniform strategic topology. Thus, our results shed light on the connection between similarity of beliefs and similarity of behaviors in games.Rationalizability, incomplete information, higher-order beliefs, strategic topology, electronic mail game

Uniform Topologies on Types

We study the robustness of interim correlated rationalizability to perturbations of higher-order beliefs. We introduce a new metric topology on the universal type space, called uniform weak topology, under which two types are close if they have similar first-order beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity is uniform over the levels of the belief hierarchy. This topology generalizes the now classic notion of proximity to common knowledge based on common p-beliefs (Monderer and Samet (1989)). We show that convergence in the uniform weak topology implies convergence in the uniform strategic topology (Dekel, Fudenberg, and Morris (2006)). Moreover, when the limit is a finite type, uniform-weak convergence is also a necessary condition for convergence in the strategic topology. Finally, we show that the set of finite types is nowhere dense under the uniform strategic topology. Thus, our results shed light on the connection between similarity of beliefs and similarity of behaviors in games.Rationalizability, Incomplete information, Higher-order beliefs, Strategic topology, Electronic mail game

Problemas estructurales y de la crisis económica en el desarrollo social del Uruguay y respuestas en las estrategias de las políticas del gobierno democrático

Incluye BibliografíaRevisa la actuacion del gobierno democratico en el area de las politicas para enfrentar los efectos de la crisis economica en el desarrollo social del Uruguay, y enfoca la caracterizacion de las nuevas modalidades que adquieren las politicas sociales en una estrategia mas de ajuste estructural que se comienzan a implementar desde 1986, en una orientacion integral de atencion de las demandas sociales insatisfechas, luego del proceso de saneamiento y ajuste interno que se instrumento en 1985

Characterizing the Strategic Impact of Misspecified Beliefs

Previous research has established that the predictions of game theory are quite sensitive to the assumptions made about the players’ beliefs. We evaluate the severity of this robustness problem by characterizing conditions on the primitives of the model—the players’ beliefs and higher-order beliefs about the payoff-relevant parameters—for the behavior of a given Harsanyi type to be approximated by the behavior of (a sequence of) perturbed types. This amounts to providing belief-based characterizations of the strategic topologies of Dekel, Fudenberg, and Morris (2006). We apply our characterizations to a variety of questions concerning robustness to perturbations of higher-order beliefs, including genericity of types that are consistent with a common prior, and we investigate the connections between our notions of robustness and the notion of common p-belief of Monderer and Samet (1989)

Reputation phenomena in continuous -time games

A common interpretation of patience in discounted games is that the interaction takes place in continuous time and the length of the period is short, i.e., players are capable of adjusting their actions frequently. However, in imperfect monitoring games, as the period length shrinks to zero, the number of signals observed in any given interval of real time increases without bound. If signals are statistically informative, then, as the period length tends to zero, the degree of monitoring imperfection becomes asymptotically negligible. The comparative statics, thus, is in tension with the very spirit of the theory of repeated games with imperfect monitoring. In Chapter 1, I study reputation phenomena in games with frequent decisions and persistently imperfect monitoring. In these games, as the period length tends to zero, the monitoring structure approaches a continuous-time limit, and, further, the limit monitoring is non-trivially imperfect (i.e. has full support). Unlike standard imperfect monitoring games, repeated games with persistently imperfect monitoring allow a meaningful comparative statics with the period length, accommodating the continuous-time interpretation of discounting with the requirement that the overall informativeness of the monitoring be bounded. I consider games with persistently imperfect monitoring in which a long-run player faces a sequence of short-run players. The long-run player can be one of many types and the short-run players are uncertain as to which type of long-run player they face. In contrast to Chapter 1, where the focus is on payoff bounds for patient players, in Chapter 2 (joint work with Yuliy Sannikov) the interest is in a characterization of equilibrium behavior for a fixed discount rate. We study a continuous-time dynamic game between a large player and a population of small anonymous players in which the actions of the large player are imperfectly observable. We explore two versions of the game. In the complete information game, in which it is common knowledge that the large player is a strategic normal type, we show that intertemporal incentives collapse. In the incomplete information game, the small players assign positive probability to the large player being either a commitment type, who plays the same action at all times, irrespective of the past history of play, or a normal type (with payoffs from the complete information game). (Abstract shortened by UMI.

Reputation phenomena in continuous -time games

A common interpretation of patience in discounted games is that the interaction takes place in continuous time and the length of the period is short, i.e., players are capable of adjusting their actions frequently. However, in imperfect monitoring games, as the period length shrinks to zero, the number of signals observed in any given interval of real time increases without bound. If signals are statistically informative, then, as the period length tends to zero, the degree of monitoring imperfection becomes asymptotically negligible. The comparative statics, thus, is in tension with the very spirit of the theory of repeated games with imperfect monitoring. In Chapter 1, I study reputation phenomena in games with frequent decisions and persistently imperfect monitoring. In these games, as the period length tends to zero, the monitoring structure approaches a continuous-time limit, and, further, the limit monitoring is non-trivially imperfect (i.e. has full support). Unlike standard imperfect monitoring games, repeated games with persistently imperfect monitoring allow a meaningful comparative statics with the period length, accommodating the continuous-time interpretation of discounting with the requirement that the overall informativeness of the monitoring be bounded. I consider games with persistently imperfect monitoring in which a long-run player faces a sequence of short-run players. The long-run player can be one of many types and the short-run players are uncertain as to which type of long-run player they face. In contrast to Chapter 1, where the focus is on payoff bounds for patient players, in Chapter 2 (joint work with Yuliy Sannikov) the interest is in a characterization of equilibrium behavior for a fixed discount rate. We study a continuous-time dynamic game between a large player and a population of small anonymous players in which the actions of the large player are imperfectly observable. We explore two versions of the game. In the complete information game, in which it is common knowledge that the large player is a strategic normal type, we show that intertemporal incentives collapse. In the incomplete information game, the small players assign positive probability to the large player being either a commitment type, who plays the same action at all times, irrespective of the past history of play, or a normal type (with payoffs from the complete information game). (Abstract shortened by UMI.