Arbeitspapier

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

We characterize full implementation of social choice sets in mixedstrategy 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.

Language
Englisch

Bibliographic citation
Series: Working Paper ; No. 2009-11

Classification
Wirtschaft
Noncooperative Games
Positive Analysis of Policy Formulation and Implementation
Asymmetric and Private Information; Mechanism Design
Subject
exact implementation
approximate implementation
incomplete information
incentive compatibility
monotonicity
Public Choice
Unvollkommene Information
Gleichgewichtstheorie

Event
Geistige Schöpfung
(who)
Serrano, Roberto
Vohra, Rajiv
Event
Veröffentlichung
(who)
Brown University, Department of Economics
(where)
Providence, RI
(when)
2009

Handle
Last update
10.03.2025, 11:41 AM CET

Data provider

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Object type

  • Arbeitspapier

Associated

  • Serrano, Roberto
  • Vohra, Rajiv
  • Brown University, Department of Economics

Time of origin

  • 2009

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