文章基本信息

标题：Multiplicity of Mixed Equilibria in Mechanisms: a Unified Approach to Exact and Approximate Implementation
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作者：Roberto Serrano ; Rajiv Vohra
期刊名称：Economics Working Papers / Brown University
出版年度：2009
卷号：2009
出版社：Brown University
摘要：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 implemen- tation 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 permis- sive than virtual implementation in iteratively undominated strategies, and (2) non-regular mechanisms are essential for the implementation of rules in that gap.
关键词：Exact implementation, approximate implementation, incomplete infor- mation, incentive compatibility, monotonicity.