Recursive structure and equilibria in games with private monitoring |
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Authors: | Massimiliano Amarante |
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Institution: | (1) Departments of Economics, Columbia University, New York, NY 10027, USA (e-mail: mA734@columbia.edu) , US |
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Abstract: | Summary. In each stage of a repeated game with private monitoring, the players receive payoffs and privately observe signals which
depend on the players' actions and the state of world. I show that, contrary to a widely held belief, such games admit a recursive
structure. More precisely, I construct a representation of the original sequential problem as a sequence of static games with
incomplete information. This establishes the ground for a characterization of strategies and, hence, of behavior in interactive-decision
settings where private information is present. Finally, the representation is used to give a recursive characterization of
the equilibrium payoff set, by means of a multi-player generalization of dynamic programming.
Received: February 11, 2002; revised version: July 22, 2002
RID="*"
ID="*" I am very grateful to In-Koo Cho, Larry Epstein, Denis Gromb, Stephen Morris, Paolo Siconolfi, Lones Smith and Max
Stinchcombe for several insights and suggestions. A referee's comments helped improving the exposition. Finally, I wish to
thank the participants to the seminars at MEDS, NYU, Columbia University, Caltech, UCLA, University of Rochester, University
of Texas-Austin, Northwestern Summer Microeconomics Conference 98, Summer in Tel Aviv 98, and NASM98. |
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Keywords: | and Phrases: Private monitoring Incomplete information Dynamic programming |
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