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

The authors characterize full implementation of social choice sets in mixed-strategy Bayesian equilibrium. The results concern both exact and virtual mixed implementation. For exact implementation, the authors identify a strengthening of Bayesian monotonicity, which they 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.