Journal article

Full substitutability

John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, Alexander Westkamp

Theoretical Economics | Econometric Society | Published : 2019

Abstract

Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models' definitions of substitutability to settings in which each agent can be both a buyer in some transactions and a seller in others, and show that all these definitions are equivalent. We then introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We also prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability.

University of Melbourne Researchers

Grants

Awarded by National Science Foundation


Awarded by People Programme (Marie Curie Outgoing International Fellowship) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA Grant


Awarded by Australian Research Council


Awarded by People Programme (Marie Curie Intra-European Fellowship) of the EuropeanUnion's Seventh Framework Programme (FP7/2007-2013) under REA Grant


Funding Acknowledgements

An earlier version of this paper was circulated under the title "Full Substitutability in Trading Networks." An extended abstract of this work appeared in the Proceedings of the Sixteenth ACM Conference on Economics and Computation. We thank several referees, Susan Athey, Elizabeth Baldwin, Peter Cramton, Vincent Crawford, David Delacretaz, Drew Fudenberg, Albert Gallegos, Ravi Jagadeesan, Cagatay Kayi, Paul Klemperer, Simon Loertscher, Paul Milgrom, Benny Moldovanu, Philip Reny, Alvin Roth, Larry Samuelson, Michael Schwarz, Alex Teytelboym, William Thomson, Utku Unver, Glen Weyl, and Zaifu Yang for helpful comments and suggestions. Part of this work was conducted while Hatfield was affiliated with Stanford University; Kominers was affiliated with the Becker Friedman Institute for Research in Economics at the University of Chicago and, later, the Harvard Society of Fellows; andWestkamp was affiliated with the University of Bonn and, later, Maastricht University. Hatfield appreciates the hospitality of Harvard Business School; Kominers appreciates the hospitality of Microsoft Research New England and the University of Melbourne; and Nichifor and Westkamp appreciate the hospitality of Stanford University during extended visits. Kominers thanks the National Science Foundation (Grants CCF-1216095 and SES-1459912, as well as a Graduate Research Fellowship), the University of Melbourne (the Centre for Market Design and an Eminent Research Scholar Award), the HarvardMilton Fund, the Yahoo! Key Scientific Challenges Program, the John M. Olin Center atHarvard Law School (a TerenceM. Considine Fellowship), the AmericanMathematical Society, and the Simons Foundation for support. Nichifor received funding from the People Programme (Marie Curie Outgoing International Fellowship) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA Grant 625718, and from the Australian Research Council under the Discovery Early Career Research Award DE170101183. Ostrovsky thanks the Alfred P. Sloan Foundation for financial support. Westkamp received funding from the German Science Foundation and from the People Programme (Marie Curie Intra-European Fellowship) of the EuropeanUnion's Seventh Framework Programme (FP7/2007-2013) under REA Grant 628276.