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Evolutionary Dynamics and Fast Convergence in the Assignment Game

  • Bary S.R. Pradelski
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    We study decentralized learning dynamics for the classic assignment game with transferable utility.� At random points in time firms and workers match, break up, and re-match in the sesarch for better opportunities.� We propose a simple learning process in which players have no knowledge about other players' payoffs or actions and they update their behavior in a myopic fashion.� Behavior fluctuates according to a random variable that reflects current market conditions: sometimes the firms exhibit greater price stickiness than the workers, and at other times the reverse holds.� We show that this stochastic learning process converges in polynomial time to the core.� While convergence to the core is known for some types of decentralized dynamics this paper is the first to prove fast convergence, a crucial feature from a practical standpoint.� The proof relies on novel results for random walks on graphs, and more generally suggests a fruitful connection between the theory of random walks and matching theory.

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    Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 700.

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    Date of creation: 03 Mar 2014
    Date of revision:
    Handle: RePEc:oxf:wpaper:700
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    1. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    2. 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.
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    7. 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.
    8. Murali Agastia, . "Adaptive Play in Multiplayer Bargaining Situations," ELSE working papers 007, ESRC Centre on Economics Learning and Social Evolution.
    9. 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, vol. 36(3), pages 473-488, March.
    10. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-50, March.
    11. Agastya, Murali, 1999. "Perturbed Adaptive Dynamics in Coalition Form Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 207-233, December.
    12. Marek Pycia, 2012. "Stability and Preference Alignment in Matching and Coalition Formation," Econometrica, Econometric Society, vol. 80(1), pages 323-362, 01.
    13. Arnold, Tone & Schwalbe, Ulrich, 2002. "Dynamic coalition formation and the core," Journal of Economic Behavior & Organization, Elsevier, vol. 49(3), pages 363-380, November.
    14. 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.
    15. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
    16. Sawa, Ryoji, 2014. "Coalitional stochastic stability in games, networks and markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 90-111.
    17. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.
    18. 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.
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