Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation

Roberto Serrano and Rajiv Vohra

No 2009-08, Working Papers from Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales

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, there by 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.

Keywords: exact implementation; approximate implementation; incomplete information; incentive compatibility; monotonicity (search for similar items in EconPapers)
JEL-codes: C72 D78 D82 (search for similar items in EconPapers)
Date: 2009-09-21
New Economics Papers: this item is included in nep-cta and nep-gth
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Citations: View citations in EconPapers (4)

Published in Journal of Mathematical Economics 46(5), September 2010: 775-785

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Related works:
Journal Article: Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation (2010)
Working Paper: Multiplicity of Mixed Equilibria in Mechanisms: a Unified Approach ot Exact and Approximate Implementation (2009)
Working Paper: Multiplicity of Mixed Equilibria in Mechanisms: A Unified Approach to Exact and Approximate Implementation (2009)
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