Fudenberg and Levine (1993a) introduced the notion of self-confirming equilibrium, which is generally less restrictive than Nash equilibrium. Fudenberg and Levine also defined a concept of consistency, and claimed in their Theorem 4 that with consistency and other conditions on beliefs, a self-confirming equilibrium has a Nash equilibrium outcome. We provide a counterexample that disproves Theorem 4 and prove an alternative by replacing consistency with a more restrictive concept, which we call strong consistency. In games with observed deviators, self-confirming equilibria are strongly consistent self-confirming equilibria. Hence, our alternative theorem ensures that despite the counterexample, the corollary of Theorem 4 is still valid.

This paper proposes a class of games called revision games . In a revision game, players start with initially prepared actions, followed by a sequence of random revision opportunities until a predetermined deadline. In the course of revisions, players monitor each other's behavior. It is shown that players can cooperate and that their behavior under the optimal equilibrium is described by a simple differential equation. We present the necessary and sufficient conditions for cooperation to be sustained in revision games. We also present applications to the preopening activities in the stock exchange and to an electoral campaign.

This paper studies a general model of matching with constraints. Observing that a stable matching typically does not exist, we focus on feasible, individually rational, and fair matchings. We characterize such matchings by fixed points of a certain function. Building on this result, we characterize the class of constraints on individual schools under which there exists a student-optimal fair matching, the matching that is the most preferred by every student among those satisfying the three desirable properties. We study the numerical relevance of our theory using data on government-organized daycare allocation.

We construct a dynamic model of election campaigns. In the model, opportunities for candidates to refine/clarify their policy positions are limited and arrive stochastically along the course of the campaign until the predetermined election date. We show that this simple friction leads to rich and subtle campaign dynamics. We first demonstrate these effects in a series of canonical static models of elections that we extend to dynamic settings, including models with valence and a multidimensional policy space. We then present general principles that underlie the results from those models. In particular, we establish that candidates spend a long time using ambiguous language during the election campaign in equilibrium.

In an earlier work (Kamada and Kojima 2015), we introduced “matching with constraints,” a two-sided matching problem in which the market is subject to feasibility constraints. That paper proposed and analyzed a possible solution to this problem and discussed various real-market applications of our results. The present paper reorganizes some of the findings from our more recent effort, based on Kamada and Kojima (2016a, b).

Many real matching markets are subject to distributional constraints. These constraints often take the form of restrictions on the numbers of agents on one side of the market matched to certain subsets on the other side. Real-life examples include restrictions on regions in medical matching, academic master's programs in graduate admission, and state-financed seats for college admission. Motivated by these markets, we study design of matching mechanisms under distributional constraints. We show that existing matching mechanisms suffer from inefficiency and instability, and propose a mechanism that is better in terms of efficiency, stability, and incentives while respecting the distributional constraints.

Real matching markets are subject to constraints. For example, the Japanese government introduced a new medical matching system in 2009 that imposes a “regional cap” in each of its 47 prefectures, which regulates the total number of medical residents who can be employed in each region. Based on Kamada and Kojima (2011), this paper studies matching markets with such constraints by examining in great detail the Japanese medical matching market. Specifically, we show that the new system introduced in 2009 has problems in terms of stability and strategy-proofness, and provide an alternative mechanism that does better.