Rev. Econ. Design (2013) 17:17–26 DOI 10.1007/s10058-012-0135-5 ORIGINAL PAPER An equity characterization of second price auctions when preferences may not be quasilinear Toyotaka Sakai Received: 28 January 2012 / Accepted: 5 September 2012 / Published online: 5 October 2012 © Springer-Verlag 2012 Abstract In a single item auction model that allows non-quasilinear preferences, we show that an auction rule satisfies weak envy-freeness for equals, strategy-proofness, and nonimposition if and only if it is a (generalized) second price auction. This char- acterization is established on a wide class of preference domains, including the quasi- linear domain, a positive income effect domain, and a negative income effect domain. Keywords Non-quasilinear preference · Second price auction · Strategy-proofness · Equal treatment of equals · Fair allocation JEL Classification D44 · D63 · C72 · C78 1 Introduction We consider the problem of designing auction rules in a model with a single item and non-quasilinear preferences. In auction models with non-quasilinear preferences, Saitoh and Serizawa (2008) and Sakai (2008) introduce generalized second price auctions that are natural extensions of (usual) second price auctions Vickrey (1961). They demonstrate that these auction rules are the only ones satisfying efficiency and I am grateful to an associate editor, Yoko Kawada, and in particular, an anonymous referee for their very insightful comments. I also thank participants of the First Symposium on Mechanism Design and Social Choice at Keio University, Waseda Conference and Lectures on Game Theory and Mechanism Design, and a seminar at Hitotsubashi University for their helpful comments. This research is financially supported by KAKENHI (22730158). T. Sakai (B ) Department of Economics, Keio University, Tokyo108-8345, Japan e-mail: tsakai@z5.keio.jp 123