Depth and Efficiency of Large Double Auctions, Econometrica
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.
Jeroen Swinkels, Martin Cripps
Swinkels, Jeroen, and Martin Cripps. 2006. Depth and Efficiency of Large Double Auctions. Econometrica. 74(1): 47-92.