We construct an uncoupled randomized strategy of repeated play such that, if every player follows such a strategy, then the joint mixed strategy profiles converge, almost surely, to a Nash equilibrium of the one-shot game. The procedure requires very little in terms of players' information about...

We extend Kohlberg and Mertens' (1986) structure theorem on the Nash correspondence to show that its graph is not only homeomorphic to the underlying space of games, but that the homeomorphism extends to the ambient space of games times strategies, thus implying the graph is unknotted. This has...

This paper derives sufficient conditions for a class of games of incomplete information, such as first price auctions, to have pure strategy Nash equilibria (PSNE). The paper treats games between two or more heterogeneous agents, each with private information about his own type (for example, a...

We consider an infinitely-repeated Bertrand game, in which prices are perfectly observed and each firm receives a privately-observed, i.i.d. cost shock in each period. We focus on symmetric perfect public equilibria (SPPE), wherein any "punishments" are borne equally by all firms. We identify a...

We consider an infinitely-repeated Bertrand game, in which prices are perfectly observed and each firm receives a privately-observed, i.i.d. cost shock in each period. We focus on symmetric perfect public equilibria (SPPE), wherein any "punishments" are borne equally by all firms. We identify a...

We analyze collusion in an infinitely repeated Bertrand game, where prices are publicly observed and each firm receives a privately observed, i.i.d. cost shock in each period. Productive efficiency is possible only if high-cost firms relinquish market share. In the most profitable collusive...

We consider an infinitely-repeated Bertrand game, in which prices are perfectly observed and each firm receives a privately-observed, i.i.d. cost shock in each period. Productive efficiency is possible only if high-cost firms are willing to relinquish market share. In the most profitable...

This paper shows a fundamental property of vector fields representing dynamics on spaces of mixed strategies of normal form games whose zeros coincide with the Nash equilibria of the underlying games. The property shown is that the indices of components of zeros of any vector field in this class...

We consider two ascending auctions and show that many of the (unwanted) collusive or signaling equilibria studied in the literature in the framework of the SEAMO (simultaneous English auction for multiple objects) don't have a counterpart in the JAMO (Japanese auction for multiple objects). We...

Social media are at the center of countless debates on polarization, misinformation, and even the state of democracy in various parts of the world. An essential feature of social media is the ranking algorithm that determines how content is presented to the users. This paper studies the dynamic...