Reputation and cooperation in the repeated second-price auctions

This paper shows that there are strong reputational effects in a general class of second price auctions. If reputation is one-sided and bidders are patient, then the bidder without reputation does not challenge the other bidder often. Consequently, the bidder with reputation obtains most of the surplus, the other bidder and the seller get very little. If 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, the Folk Theorem fails: collusion in the second price auctions is impossible. The predictions of the model are that prices in early auctions should reach levels that are higher than the value of the object, then declining towards the reserve price; a set of strong bidders emerges. A recent series of auctions of spectrum for UMTS services in Europe seems to be consistent with the predictions of the model