Paths to Stability in the Assignment Problem
We study a labor market with finitely many heterogeneous workers and firms to illustrate the decentralized (myopic) blocking dynamics in two-sided one-to-one matching markets with continuous side payments (assignment problems, Shapley and Shubik, 1971). A labor market is unstable if there is at least one blocking pair, that is, a worker and a firm who would prefer to be matched to each other in order to obtain higher payoffs than the payoffs they obtain by being matched to their current partners. A blocking path is a sequence of outcomes (specifying matchings and payoffs) such that each outcome is obtained from the previous one by satisfying a blocking pair (i.e., by matching the two blocking agents and assigning new payoffs to them that are higher than the ones they received before). We are interested in the question if starting from any (unstable) outcome, there always exists a blocking path that will lead to a stable outcome. In contrast to discrete versions of the model (i.e., for marriage markets, one-to-one matching, or discretized assignment problems), the existence of blocking paths to stability cannot always be guaranteed. We identify a necessary and sufficient condition for an assignment problem (the existence of a stable outcome such that all matched agents receive positive payoffs) to guarantee the existence of paths to stability and show how to construct such a path whenever this is possible.
|Date of creation:||Sep 2013|
|Date of revision:|
|Publication status:||Forthcoming in The Journal of Dynamics and Games, 2015|
|Contact details of provider:|| Postal: Université de Lausanne, Faculté des HEC, DEEP, Internef, CH-1015 Lausanne|
Phone: ++41 21 692.33.20
Web page: http://www.hec.unil.ch/deep/publications/cahiers/series
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ning Sun & Zaifu Yang, 2009. "A Double-Track Adjustment Process for Discrete Markets With Substitutes and Complements," Econometrica, Econometric Society, vol. 77(3), pages 933-952, 05.
- Bo Chen & Satoru Fujishige & Zaifu Yang, 2011.
"Decentralized Market Processes to Stable Job Matchings with Competitive Salaries,"
11/03, Department of Economics, University of York.
- Bo Chen & Satoru Fujishige & Zaifu Yang, 2010. "Decentralized Market Processes to Stable Job Matchings with Competitive Salaries," KIER Working Papers 749, Kyoto University, Institute of Economic Research.
- Bettina Klaus & Flip Klijn, 2004.
"Paths to Stability for Matching Markets with Couples,"
156, Barcelona Graduate School of Economics.
- Klaus, Bettina & Klijn, Flip, 2007. "Paths to stability for matching markets with couples," Games and Economic Behavior, Elsevier, vol. 58(1), pages 154-171, January.
- Bettina Klaus & Flip Klijn, 2004. "Paths to Stability for Matching Markets with Couples," UFAE and IAE Working Papers 604.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 01 Dec 2005.
- Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
- Sotomayor, Marilda, 2003. "Some further remark on the core structure of the assignment game," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 261-265, December.
- Gabrielle Demange & David Gale, 1985.
"The Strategy Structure of Two Sided Matching Markets,"
- Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-88, July.
- Milgrom, Paul, 1998.
"Putting auction theory to work : the simultaneous ascending auction,"
Policy Research Working Paper Series
1986, The World Bank.
- Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
- Paul Milgrom, . "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Working Papers 98002, Stanford University, Department of Economics.
- Peter Biro & Matthijs Bomhoff & Walter Kern & Petr A. Golovach & Daniel Paulusma, 2012. "Solutions for the Stable Roommates Problem with Payments," IEHAS Discussion Papers 1211, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
- Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-80, November.
- Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, vol. 48(1), pages 18-28, July.
- Gabrielle Demange & Gale David & Marilda Sotomayor, 1986.
- Jun Wako, 2006. "Another proof that assignment games have singleton cores only if multiple optimal matchings exist," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 213-217, September.
- John William Hatfield & Scott Duke Kominers & Alexandru Nichifor & Michael Ostrovsky & Alexander Westkamp, 2013. "Stability and Competitive Equilibrium in Trading Networks," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 966 - 1005.
- Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
- Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
- Schwarz, Michael & Yenmez, M. Bumin, 2011. "Median stable matching for markets with wages," Journal of Economic Theory, Elsevier, vol. 146(2), pages 619-637, March.
When requesting a correction, please mention this item's handle: RePEc:lau:crdeep:13.14. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Gaëlle Sarda)
If references are entirely missing, you can add them using this form.