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Gradual accumulation of contributions under incomplete information

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Gradual accumulation of contributions under incomplete information 著者 Yusuke Samejima 雑誌名 経済論集 巻 38 号 2 ページ 109-128 発行年 2013-03 URL Creative Commons : 表示 - 非営利 - 改変禁止 東洋大学 「経済論集」38 巻2 号 2013年3 月 Gradual accumulation of contributions under incomplete information Yusuke Samejima Abstract We investigate two-player contribution games that are similar to the ones studied by Compte and Jehiel [2003]but different in that our games are played in incomplete information environments. We show that, under certainconditions, there exists a perfect Bayesian equilibrium in which step-by-step contributions are realized along the equilibrium path. This gradual accumulation of contributions is not observed in Compte and Jehiel's equilibrium in complete information environments. Our result indicates that uncertainties about valuations of the opponentplayers can be a source of such gradualism. 1. Introduction Bargaining and contribution games have been studied in various aspects in the literature. The seminal work by Rubinstein [1982]shows that subgame-perfect equilibrium outcomes in bargaining problems converge to Nash bargaining solutions [Nash, 1950]as players become more patient. In Rubinstein'sbargaining models, payments are assumed to occur after players reach an agreement. So, payments arenot sunk in the bargaining process 。 Admati and Perry [1991]have investigated what if payments for a joint project are sunk in voluntary contribution games. They show that there e χists a subgame-perfect equilibrium in which payments aremade in small steps along the equilibrium path. Such gradual accumulation of payments is referred toas gradualism. Their result of gradualism is obtained under the assumptions that a cost function forthe project is arbitrarily convex and valuations for the project are the same between two players. Theyhave suggested that the sunk character of contributi

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