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Title:Reputation in continuous-time games with multiple commitment types
Author(s):Ryu, Seokjong
Director of Research:Williams, Steven R.; Cho, In-Koo
Doctoral Committee Chair(s):Williams, Steven R.
Doctoral Committee Member(s):Perry, Martin K.; Lemus, Jorge
Department / Program:Economics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Continuous-time games
Multiple commitment types
Abstract:We study a continuous-time game with imperfect monitoring in which a large player faces a continuum of infinitely-lived small players. We extend Faingold and Sannikov (2011) to a framework in which the support of the prior belief of the small players contains any finite number of commitment types. In this setting, we show the existence of a unique Markov equilibrium, we characterize a partial differential equation (PDE) for the equilibrium payoff, and we derive an optimality condition for the equilibrium actions. Also, we provide a stochastic representation of the Markov equilibrium payoffs, which is the solution to the PDE. Finally, we show that the equilibrium action of the sufficiently patient large player follows a non-stationary process that is determined by the small players’ posterior beliefs.
Issue Date:2017-04-17
Rights Information:Copyright 2017 Seokjong Ryu
Date Available in IDEALS:2017-08-10
Date Deposited:2017-05

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