“Unobserved Mechanisms” by Hao Li
University of British Columbia
Vancouver School of Economics
This paper considers the possibility that some buyers who participate in a selling mechanism do not know the trading rules that the seller is using to allocate goods. We consider the simplest model in which all bidders have identically and independently distributed private values, and model the mechanism design process as a game of imperfect information in which some players cannot observe the commitments of the seller. We show that independent of how likely it is that players are uninformed, standard auction formats cannot survive as equilibria unless they are augmented with messages that allow informed players to identify themselves. If there is a strictly positive probability that there is an uninformed buyer, there is an equilibrium in which the seller holds an auction among the informed bidders with a reserve price that varies with the actual number of uninformed bidders. The lowest of these reserve prices is strictly less than the optimal reserve price with full commitment. If no informed bidder meets the reserve price, the seller makes a take it or leave it offer to one of the uninformed bidders. This offer is at least as high as the optimal reserve price with full commitment.