Simultaneous Auctions of Imperfect Substitute Goods by Sellers of Different Reputations

Abstract

This paper studies settings where a number of sellers of different reputations for honesty simultaneously offer sealed-bid, second-price, single-unit auctions for imperfect substitute goods to unit-demand buyers. Among other applications, these settings can serve as an abstraction of large scale decentralized Internet auction marketplaces, such as eBay. I characterize the form of the bidding equilibria and derive expressions for the corresponding allocative efficiency and expected seller revenue. When bidders are restricted to submit at most one bid there exists a unique Bayes-Nash equilibrium that has the following form: Auctions are ranked according to their expected valuation, taking into account both the quality of the good and the seller's reputation. Buyers self-separate into a finite number of zones, according to their types. Buyers whose types fall in the k-th zone randomize between the top k auctions, assigning increasingly higher probability to selecting lower auctions. In such equilibria auction revenue is an increasing convex function of seller reputation. Allowing unit-demand bidders to place an arbitrary number of bids induces complex mixed strategy profiles where bidders place positive bids in all available auctions. The probabilistic nature of the bidding equilibria introduces allocative inefficiencies that are most severe when the number of bidders is roughly equal to the number of sellers.