Sections 4, 5.1, and 6.2 of this paper synthesize the first two chapters of my dissertation at MIT. I would like to thank Bengt Holmström, Glenn Ellison, Haluk Ergin, Robert Gibbons, Anna Myjak-Pycia, Michael Piore, and Jean Tirole for their advice and support. Sections 3, 4, and 7 were developed while I was at Penn State. For their generous comments, I am grateful to various seminar audiences, Andrew Atkeson, Abhijit Banerjee, Simon Board, Peter Chen, Dora Costa, Federico Echenique, Michael Egesdal, Alfred Galichon, Edward Green, Christian Hellwig, Hugo Hopenhayn, Sergei Izmalkov, George Mailath, Moritz Meyer-ter-Vehn, Kenneth Mirkin, Benny Moldovanu, Hervé Moulin, Ichiro Obara, Marco Ottaviani, Alvin Roth, Mordechai Schwarz, Alex Teytelboym, William Thomson, Hannu Vartiainen, Rakesh Vohra, Birger Wernerfelt, and, especially, Jingyi Xue and William Zame. The constructive comments of the editor and four referees greatly improved the paper. Financial support from the Hausdorff Institute in Bonn, MIT Industrial Performance Center, and Koźmiński University in Warsaw is gratefully acknowledged.
Stability and Preference Alignment in Matching and Coalition Formation
Article first published online: 10 JAN 2012
© 2012 The Econometric Society
Volume 80, Issue 1, pages 323–362, January 2012
How to Cite
Pycia, M. (2012), Stability and Preference Alignment in Matching and Coalition Formation. Econometrica, 80: 323–362. doi: 10.3982/ECTA7143
- Issue published online: 10 JAN 2012
- Article first published online: 10 JAN 2012
- Manuscript received May, 2007; final revision received June, 2011.
- Many-to-one matching;
- assortative matching;
- coalition formation;
- peer effects;
- sharing rules;
- Nash bargaining
We study matching and coalition formation environments allowing complementarities and peer effects. Agents have preferences over coalitions, and these preferences vary with an underlying, and commonly known, state of nature. Assuming that there is substantial variability of preferences across states of nature, we show that there exists a core stable coalition structure in every state if and only if agents' preferences are pairwise-aligned in every state. This implies that there is a stable coalition structure if agents' preferences are generated by Nash bargaining over coalitional outputs. We further show that all stability-inducing rules for sharing outputs can be represented by a profile of agents' bargaining functions and that agents match assortatively with respect to these bargaining functions. This framework allows us to show how complementarities and peer effects overturn well known comparative statics of many-to-one matching.