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Analysis of Stochastic Matching Markets

Author

Listed:
  • Peter Biro

    () (Institute of Economics - Hungarian Academy of Sciences)

  • Gethin Norman

    () (School of Computing Science - University of Glasgow)

Abstract

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.

Suggested Citation

  • Peter Biro & Gethin Norman, 2011. "Analysis of Stochastic Matching Markets," IEHAS Discussion Papers 1132, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  • Handle: RePEc:has:discpr:1132
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    References listed on IDEAS

    as
    1. James Boudreau, 2008. "Preference Structure and Random Paths to Stability in Matching Markets," Economics Bulletin, AccessEcon, vol. 3(67), pages 1-12.
    2. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
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    4. 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).
    5. Joana Pais & Agnes Pinter & Robert F. Veszteg, 2012. "Decentralized Matching Markets: A Laboratory Experiment," Working Papers Department of Economics 2012/08, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    6. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
    7. Ma, Jinpeng, 1996. "On Randomized Matching Mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 377-381, August.
    8. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
    9. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Blum, Yosef & Rothblum, Uriel G., 2002. ""Timing Is Everything" and Marital Bliss," Journal of Economic Theory, Elsevier, vol. 103(2), pages 429-443, April.
    15. Iñarra García, María Elena & Larrea Jaurrieta, María Concepción & Molis Bañales, Elena, 2007. "The Stability of the Roommate Problem Revisited," IKERLANAK 2007-30, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    16. 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.
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    Cited by:

    1. Newton, Jonathan & Sawa, Ryoji, 2015. "A one-shot deviation principle for stability in matching problems," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1-27.
    2. Bolle Friedel & Otto Philipp E., 2016. "Matching as a Stochastic Process," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 236(3), pages 323-348, May.
    3. Joana Pais & Ágnes Pintér & Róbert F. Veszteg, 2017. "Decentralized Matching Markets With(out) Frictions: A Laboratory Experiment," Working Papers REM 2017/03, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

    More about this item

    Keywords

    roommates problem; marriage problem; stochastic processes; core convergence; probabilistic model checking;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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