Subgame-Perfect Implementation Under Information Perturbations

We consider the robustness of extensive form mechanisms to deviations from common knowledge about the state of nature, which we refer to as information perturbations. First, we show that even under arbitrarily small information perturbations the Moore-Repullo mechanism does not yield (even approximately) truthful revelation and that in addition the mechanism has sequential equilibria with undesirable outcomes. More generally, we prove that any extensive form mechanism is fragile in the sense that if a non-Maskin monotonic social objective can be implemented with this mechanism, then there are arbitrarily small information perturbations under which an undesirable sequential equilibrium also exists. Finally, we argue that outside options can help improve efficiency in asymmetric information environments, and that these options can be thought of as reflecting ownership of an asset.

[1]  Arunava Sen,et al.  VIRTUAL IMPLEMENTATION IN NASH EQUILIBRIUM , 1991 .

[2]  Patrick W. Schmitz,et al.  On the Interplay of Hidden Action and Hidden Information in Simple Bilateral Trading Problems , 2002, J. Econ. Theory.

[3]  S. Morris,et al.  Robust Rationalizability Under Almost Common Certainty of Payoffs , 2011 .

[4]  Hitoshi Matsushima.  A new approach to the implementation problem , 1988 .

[5]  Takashi Kunimoto.  How Robust is Undominated Nash Implementation , 2010 .

[6]  Roberto Serrano,et al.  Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms , 2011, Games Econ. Behav..

[7]  E. Maskin,et al.  The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility , 1979 .

[8]  Hitoshi Matsushima,et al.  Virtual implementation in iteratively undominated strategies: complete information , 1992 .

[9]  R. Zeckhauser,et al.  Efficiency Despite Mutually Payoff-Relevant Private Information: The Finite Case , 1990 .

[10]  D. Fudenberg,et al.  Perfect Bayesian equilibrium and sequential equilibrium , 1991 .

[11]  E. Maskin,et al.  Implementation and Renegotiation , 1998 .

[12]  Eric Maskin,et al.  Unforeseen Contingencies and Incomplete Contracts , 1999 .

[13]  Marion Oury,et al.  Continuous Implementation , 2009 .

[14]  Drew Fudenberg,et al.  Subgame Perfect Implementation with Almost Perfect Information and the Hold-Up Problem , 2009 .

[15]  D. Fudenberg,et al.  Rational Behavior with Payoff Uncertainty , 1990 .

[16]  Eitan Muller,et al.  The equivalence of strong positive association and strategy-proofness , 1977 .

[17]  Richard Holden,et al.  Subgame Perfect Implementation under Approximate Common Knowledge: Evidence from a Laboratory Experiment , 2011 .

[18]  In-Koo Cho,et al.  A Refinement of Sequential Equilibrium , 1987 .

[19]  H. J. Jacobsen,et al.  The One-Shot-Deviation Principle for Sequential Rationality , 1996 .

[20]  Matthew O. Jackson,et al.  A crash course in implementation theory , 2001, Soc. Choice Welf..

[21]  D. Monderer,et al.  Approximating common knowledge with common beliefs , 1989 .

[22]  Richard P. McLean,et al.  FULL EXTRACTION OF THE SURPLUS IN BAYESIAN AND DOMINANT STRATEGY AUCTIONS , 1988 .

[23]  Yeon-Koo Che,et al.  Cooperative Investments and the Value of Contracting , 1999 .

[24]  David M. Kreps,et al.  Signaling Games and Stable Equilibria , 1987 .

[25]  Drew Fudenberg,et al.  Subgame Perfect Implementation with Almost Perfect Information , 2008 .

[26]  Redaktionen.  THE REVIEW OF ECONOMIC STUDIES , 1960 .

[27]  David M. Kreps,et al.  On the Robustness of Equilibrium Refinements , 1988 .

[28]  Drew Fudenberg,et al.  Perfect Bayesian and Sequential Equilibrium , 1991 .

[29]  John. Moore,et al.  Subgame Perfect Implementation , 1988 .

[30]  Takashi Kunimoto,et al.  Implementation with near complete information: The case of subgame perfection , 2009 .

[31]  Jeffrey C. Ely,et al.  Implementation with Near-Complete Information , 2003 .

[32]  E. Maskin.  Nash Equilibrium and Welfare Optimality , 1999 .

[33]  John. Moore,et al.  Nash Implementation: A Full Characterization , 1990 .

[34]  Stefan Reichelstein,et al.  On the Informational Requirements for the Implementation of Social Choice Rules , 1981 .

[35]  Sanford J. Grossman,et al.  The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration , 1986 .

[36]  Daniel Krähmer,et al.  Exit options in incomplete contracts with asymmetric information , 2012, J. Econ. Theory.

[37]  Philippe Aghion,et al.  RENEGOTIATION DESIGN WITH UNVERIFIABLE INFORMATION , 1994 .

[38]  Tatsuyoshi Saijo,et al.  STRATEGY SPACE REDUCTION IN MASKIN'S THEOREM: SUFFICIENT CONDITIONS FOR NASH IMPLEMENTATION , 1988 .

[39]  P. Malliavin.  Infinite dimensional analysis , 1993 .

[40]  E.E.C. van Damme,et al.  Games with imperfectly observable commitment , 1997 .

[41]  Eric Maskin,et al.  Two Remarks on the Property-Rights Literature , 1999 .

[42]  R. Myerson.  Two-Person Bargaining Problems with Incomplete Information , 1982 .