Hedonic price equilibria , stable matching , and optimal transport : equivalence , topology , and uniqueness

Hedonic pricing with quasilinear preferences is shown to be equivalent to stable matching with transferable utilities and a participation constraint, and to an optimal transportation (Monge-Kantorovich) linear programming problem. Optimal assignments in the latter correspond to stable matchings, and to hedonic equilibria. These assignments are shown to exist in great generality; their marginal indirect payoffs with respect to agent type are shown to be unique whenever direct payoffs vary smoothly with type. Under a generalized Spence-Mirrlees condition (also known as a twist condition) the assignments are shown to be unique and to be pure, meaning the matching is one-to-one outside a negligible set. For smooth problems set on compact, It is a pleasure to thank Ivar Ekeland, whose conferences at the Banff International Research Station (BIRS) in 2004 and 2005 brought us together, and whose work on hedonic pricing [9], [10] inspired our investigation. RJM also wishes to thank Najma Ahmad, Wilfrid Gangbo, and Hwa Kil Kim, for fruitful conversations related to the subtwist criterion for uniqueness, and Nassif Ghoussoub for insightful remarks. The authors are pleased to acknowledge the support of Natural Sciences and Engineering Research Council of Canada Grant 21700603 and United States National Science Foundation Grants 0241858, 0433990, 0532398 and DMS-0354729. They also acknowledge support through CEMMAP from the Leverhulme Trust and the UK Economic and Social Research Council grant RES-589-28-0001. c ©2008 by the authors. Pierre-André Chiappori Department of Economics, Columbia University E-mail: [email protected] Robert J. McCann Department of Mathematics, University of Toronto E-mail: [email protected] Lars P. Nesheim Centre for Microdata Methods and Practice (CEMMAP), University College London, and the Institute for Fiscal Studies E-mail: [email protected]