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 imply that the corresponding stochastic processes are absorbing Markov chains. 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. Copyright Springer-Verlag Berlin Heidelberg 2013
Volume (Year): 42 (2013)
Issue (Month): 4 (November)
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- 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.
- 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).
- James Boudreau, 2008.
"Preference Structure and Random Paths to Stability in Matching Markets,"
AccessEcon, vol. 3(67), pages 1-12.
- James W. Boudreau, 2008. "Preference Structure and Random Paths to Stability in Matching Markets," Working papers 2008-29, University of Connecticut, Department of Economics.
- Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
- Peter Biro & Flip Klijn, 2011.
"Matching with Couples: a Multidisciplinary Survey,"
IEHAS Discussion Papers
1139, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
- Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999.
"Core in a Simple Coalition Formation Game,"
Boston College Working Papers in Economics
449, Boston College Department of Economics.
- 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).
- Blum, Yosef & Rothblum, Uriel G., 2002. ""Timing Is Everything" and Marital Bliss," Journal of Economic Theory, Elsevier, vol. 103(2), pages 429-443, April.
- 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.
- 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.
- László Á. Kóczy & Luc Lauwers, 2001.
"The Coalition Structure Core is Accessible,"
Game Theory and Information
0110001, EconWPA, revised 26 Jun 2002.
- Ma, Jinpeng, 1996.
"On Randomized Matching Mechanisms,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 377-81, August.
- 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.
- Bo Chen & Satoru Fujishige & Zaifu Yang, 2011. "Decentralized Market Processes to Stable Job Matchings with Competitive Salaries," Discussion Papers 11/03, Department of Economics, University of York.
- 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.
- 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.
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