Analysis of Stochastic Matching Markets
Suppose that the agents of a matching market contact each other randomly and form new pairs if is in their interest. Does such a process always converge to a stable matching if one exists? If so, how quickly? Are some stable matchings more likely to be obtained by this process than others? In this paper we are going to provide answers to these and similar questions, posed by economists and computer scientists. In the first part of the paper we give an alternative proof for the theorems by Diamantoudi et al. and Inarra et al. which implies that the corresponding stochastic processes are absorbing Markov chains. Our proof is not only shorter, but also provides upper bounds for the number of steps needed to stabilise the system. The second part of the paper proposes new techniques to analyse the behaviour of matching markets. We introduce the Stable Marriage and Stable Roommates Automaton and show how the probabilistic model checking tool PRISM may be used to predict the outcomes of stochastic interactions between myopic agents. In particular, we demonstrate how one can calculate the probabilities of reaching different matchings in a decentralised market and determine the expected convergence time of the stochastic process concerned. We illustrate the usage of this technique by studying some well-known marriage and roommates instances and randomly generated instances.
|Date of creation:||Jul 2011|
|Date of revision:|
|Contact details of provider:|| Postal: 1112 Budapest, Budaorsi ut 45.|
Phone: (+36-1) 309-2652
Fax: (36-1) 319-3136
Web page: http://econ.core.hu
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.:
- INARRA, Elena & LARREA, Conchi & MOLIS, Elena, 2010.
"The stability of the roommate problem revisited,"
CORE Discussion Papers
2010007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- László Á. Kóczy & Luc Lauwers, 2001.
"The Coalition Structure Core is Accessible,"
Game Theory and Information
0110001, EconWPA, revised 26 Jun 2002.
- Jinpeng Ma, 1996.
"On randomized matching mechanisms (*),"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 377-381.
- Blum, Yosef & Roth, Alvin E. & Rothblum, Uriel G., 1997. "Vacancy Chains and Equilibration in Senior-Level Labor Markets," Journal of Economic Theory, Elsevier, vol. 76(2), pages 362-411, October.
- Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001.
"Core in a simple coalition formation game,"
Social Choice and Welfare,
Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
- James W. Boudreau, 2008.
"Preference Structure and Random Paths to Stability in Matching Markets,"
2008-29, University of Connecticut, Department of Economics.
- James Boudreau, 2008. "Preference Structure and Random Paths to Stability in Matching Markets," Economics Bulletin, AccessEcon, vol. 3(67), pages 1-12.
- Péter Biró & Flip Klijn, 2013.
"Matching With Couples: A Multidisciplinary Survey,"
International Game Theory Review (IGTR),
World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1340008-1-1.
- Péter Biró & Katarína Cechlárová & Tamás Fleiner, 2008. "The dynamics of stable matchings and half-matchings for the stable marriage and roommates problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 333-352, March.
- Fuhito Kojima & M. Ünver, 2008. "Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 473-488, March.
- Blum, Yosef & Rothblum, Uriel G., 2002. ""Timing Is Everything" and Marital Bliss," Journal of Economic Theory, Elsevier, vol. 103(2), pages 429-443, April.
- E. Inarra & C. Larrea & E. Molis, 2008. "Random paths to P-stability in the roommate problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 461-471, March.
- Klaus Bettina & Klijn Flip & Walzl Markus, 2008.
"Stochastic Stability for Roommate Markets,"
010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
- Joana Pais & Agnes Pinter & Robert F. Veszteg, 2012. "Decentralized Matching Markets: A Laboratory Experiment," Working Papers Department of Economics 2012/08, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
- Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
When requesting a correction, please mention this item's handle: RePEc:has:discpr:1132. 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: (Adrienn Foldi)
If references are entirely missing, you can add them using this form.