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We consider large double auctions with private values. Values need be neither symmetric nor independent. Multiple units may be owned or desired. Participation may be stochastic. We introduce a very mild notion of “a little independence.” We prove that all nontrivial equilibria of auctions that satisfy this notion are asymptotically efficient. For any α>0, inefficiency disappears at rate 1/n2-α.
Cripps et al. (Tue,) studied this question.