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Multiplicity Of Mixed Equilibria In Mechanisms: A Unified Approach To Exact And Approximate Implementation

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  • Roberto Serrano

    ()
    (Brown University)

  • Rajiv Vohra

    ()
    (Brown University)

Abstract

We characterize full implementation of social choice sets in mixed strategy Bayesian equilibrium. Our results concern both exact and virtual mixed implementation. For exact implementation, we identify a strengthening of Bayesian monotonicity, which we refer to as mixed Bayesian monotonicity. It is shown that, in economic environments with at least three agents, mixed Bayesian implementation is equivalent to mixed Bayesian monotonicity, incentive compatibility and closure. For implementing a social choice function, the case of two-agents is also covered by these conditions and mixed Bayesian monotonicity reduces to Bayesian monotonicity. Following parallel steps, mixed virtual implementation is shown to be equivalent to mixed virtual monotonicity, incentive compatibility and closure. The key condition, mixed virtual monotonicity, is argued to be very weak. In particular, it is weaker than Abreu-Matsushima’s measurability, thereby implying that: (1) virtual implementation in mixed Bayesian equilibrium is more permissive than virtual implementation in iteratively undominated strategies, and (2) non-regular mechanisms are essential for the implementation of rules in that gap.

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Bibliographic Info

Paper provided by CEMFI in its series Working Papers with number wp2009_0908.

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Date of creation: Sep 2009
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Handle: RePEc:cmf:wpaper:wp2009_0908

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Keywords: Exact implementation; approximate implementation; incomplete information; incentive compatibility; monotonicity.;

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Cited by:
  1. Tomala, Tristan & Renou, Ludovic, 2010. "Mechanism design and communication networks," Les Cahiers de Recherche 926, HEC Paris.
  2. Claudio Mezzetti & Ludovic Renou, 2012. "Implementation in Mixed Nash Equilibrium," Department of Economics - Working Papers Series 1146, The University of Melbourne.
  3. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2010. "Rationalizable Implementation," Cowles Foundation Discussion Papers 1697R, Cowles Foundation for Research in Economics, Yale University.
  4. Ashraf-Ball, Hezlin & Oswald, Andrew J. & Oswald, James I., 2009. "Hydrogen Transport and the Spatial Requirements of Renewable Energy," The Warwick Economics Research Paper Series (TWERPS) 903, University of Warwick, Department of Economics.

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