SYMMETRIC AUCTIONS

Real-world auctions are often restricted to being symmetric (anonymous and nondiscriminatory) due to practical or legal constraints. We examine when this restriction prevents a seller from achieving his objectives. In an independent private value setting with heterogenous buyers, we characterize the set of incentive compatible and individually rational outcomes that can be implemented via a symmetric auction. Our characterization shows that symmetric auctions can yield a large variety of discriminatory outcomes such as revenue maximization and affirmative action. We also characterize the set of implementable outcomes when individual rationality holds in an ex-post rather than an interim sense. This additional requirement may prevent the seller from maximizing revenue. †DEPARTMENT OF ECONOMICS, UNIVERSITY OF TORONTO ‡DEPARTMENT OF ECONOMICS, UNIVERSITY OF PENNSYLVANIA E-mail addresses: rahul.deb@utoronto.ca, mallesh@econ.upenn.edu. Date: August 24, 2013. We would like to thank Dirk Bergemann, Heski Bar-Isaac, Amos Fiat, Johannes Hörner, René Kirkegaard, Kevin Lleyton-Brown, Steve Matthews, Maher Said, Xianwen Shi, Andrzej Skrzypacz, Jeroen Swinkels, Juuso Toikka, Gabor Virag and seminar audiences at Arizona State University, the Canadian Economic Theory Conference, the Indian Statistical Institute, NTU Singapore, the University of Western Ontario and Washington University at St. Louis for their insightful comments. We also thank Yunan Li for providing excellent research assistance. Mallesh Pai gratefully acknowledges the support of NSF Grant CCF-1101389. 1 2 RAHUL DEB AND MALLESH M. PAI An optimal auction extends the asymmetry of the buyer roles to the allocation rule itself. The assignment of the good and the appropriate buyer payment will depend not only on the list of offers, but also on the identities of the buyers who submit the bids. In short, an optimal auction under asymmetric conditions violates the principle of buyer anonymity. J. Riley and W. Samuelson (1981). “Optimal Auctions,” American Economic Review.

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