Virtual Implementation by Bounded Mechanisms: Complete Information

A social choice rule (SCR) F maps preference profiles to lotteries over some finite set of outcomes. F is virtually implementable in (pure and mixed) Nash equilibria provided that for all E > 0, there exists a mechanism such that for each preference profile t, its set of Nash equilibrium outcomes at θ is E-closed to the socially desirable set F(θ). Under a domain restriction, we obtain the following result: When there are at least three agents, any F is virtually implementable in Nash equilibrium, as well as in rationalizable strategies, by a bounded mechanism. No "tail-chasing" construction, common in the constructive proofs of the literature, is used to assure that undesired strategy combinations do not form a Nash equilibrium.

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