Internet auctions with many traders
We study a multi-unit auction environment similar to eBay. Sellers, each with a single unit of a homogenous good, set reserve prices at their own independent second-price auctions. Each buyer has a private value for the good and wishes to acquire a single unit. Buyers can bid as often as they like and move between the sellers' auctions in a dynamic environment. We characterize a perfect Bayesian equilibrium for this decentralized trading mechanism in which, conditional on reserve prices, an efficient set of trades occurs at a uniform trading price. When the number of buyers and sellers is large but finite, the sellers set reserve prices equal to their true costs under a very mild distributional assumption, so ex-post efficiency is achieved. The buyers' strategies in this equilibrium are very simple and do not depend on their beliefs about the other buyers' valuations, or the number of buyers and sellers. They bid almost myopically. Their only `sophisticated' choice is where to bid when they are indifferent between several sellers.
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