Essays in Revision Games

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Essays in Revision Games

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Title: Essays in Revision Games
Author: Kamada, Yuichiro
Citation: Kamada, Yuichiro. 2012. Essays in Revision Games. Doctoral dissertation, Harvard University.
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Abstract: This dissertation consists of three essays related to revision games. The first essay proposes and analyzes a new model that we call “revision games,” which captures a situation where players in advance prepare their actions in a game. After the initial preparation, they have some opportunities to revise their actions, which arrive stochastically. Prepared actions are assumed to be mutually observable. We show that players can achieve a certain level of cooperation. The optimal behavior of players can be described by a simple differential equation. The second essay studies a version of revision games in which revision opportunities are asynchronous across players. In 2-player “common interest” games where there exists a best action profile for all players, this best action profile is the only equilibrium outcome of the revision game. In “opposing interest” games which are 2 x 2 games with Pareto-unranked strict Nash equilibria, the equilibrium outcome of the revision game is generically unique and corresponds to one of the stage-game Nash equilibria. Which equilibrium prevails depends on the payoff structure and on the relative frequency of the arrivals of revision opportunities for each of the players. The third essay studies a multi-agent search problem with a deadline: for instance, the situation that arises when a husband and a wife need to find an apartment by September 1. We provide an understanding of the factors that determine the positive search duration in reality. Specifically, we show that the expected search duration does not shrink to zero even in the limit as the search friction vanishes. Additionally, we find that the limit duration increases as more agents are involved, for two reasons: the ascending acceptability effect and the preference heterogeneity effect. The convergence speed is high, suggesting that the mere existence of some search friction is the main driving force of the positive duration in reality. Welfare implications and a number of discussions are provided. Results and proof techniques developed in the first two essays are useful in proving and understanding the results in the third essay.
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