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Recursive structure and equilibria in games with private monitoring

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Author Info
Massimiliano Amarante () (University of California, Los Angeles - Department of Economics)
Abstract

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 interactivedecision 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.

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Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0102-48.

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Length: 26 pages
Date of creation: 2002
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Handle: RePEc:clu:wpaper:0102-48

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  1. George J. Mailath & Stephen Morris, . "Repeated Games with Imperfect Private Monitoring: Notes on a Coordination Perspective," Penn CARESS Working Papers 5d82f80bcea2483b6387c5b68, Penn Economics Department. [Downloadable!]
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  2. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  3. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine. [Downloadable!]
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  4. Paul Milgrom & Robert Weber, 1981. "Distributional Strategies for Games with Incomplete Information," Discussion Papers 428R, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  5. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January. [Downloadable!] (restricted)
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  6. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September. [Downloadable!] (restricted)
  7. V. Bhaskar & Eric van Damme, 1998. "Moral Hazard and Private Monitoring," Game Theory and Information 9809004, EconWPA. [Downloadable!]
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  8. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October. [Downloadable!] (restricted)
  9. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832 Elsevier. [Downloadable!] (restricted)
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