Reputation and cooperation in the repeated second-price auctions

Abstract

This paper shows that there are strong reputational effects in a general class of second price auctions, including single-unit English and Vickrey auctions with interdependent values, multiunit ascending and uniform price auctions and a War of Attrition. It is based on recent results on reputation with symmetric discounting. If a reputation is one sided and bidders are patient, the bidder with reputation must obtain most of the surplus in the sequence of auctions, the other bidder and the seller get very little. If the reputation is two-sided then the bidders engage in a game akin to War of Attrition. The resulting payoff is very low for the bidders and very high for the seller. In any case, Folk Theorem fails: collusion in the second price auctions is impossible. The predictions of the model are that the path of prices is declining, in fact prices in the early auctions should reach levels that are higher than the value of the object and there should be a set of strong bidders emerging after a few auctions. A recent series of auctions of spectrum for UMTS services in Europe seems to fit both the assumptions and predictions of the model.

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