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The stochastic stability of decentralized matching on a graph

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  • Boncinelli, Leonardo
  • Pin, Paolo

Abstract

We provide a perturbed evolutionary model of matching on a graph. First, we obtain that maximal matchings are the singleton recurrent classes of the model without perturbations. Then, we apply stochastic stability analysis considering two different error models: the link-error model, where mistakes directly hit links, and the agent-error model, where mistakes hit agents' decisions, and indirectly links. We find that stochastic stability is ineffective for refinement purposes in the link-error model – where all maximal matchings are stochastically stable – while it proves effective in the agent-error model – where all and only maximum matchings are stochastically stable.

Suggested Citation

  • Boncinelli, Leonardo & Pin, Paolo, 2018. "The stochastic stability of decentralized matching on a graph," Games and Economic Behavior, Elsevier, vol. 108(C), pages 239-244.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:239-244
    DOI: 10.1016/j.geb.2017.06.005
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    References listed on IDEAS

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    1. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 17-45.
    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.
    3. 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.
    4. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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    6. Boncinelli, Leonardo & Pin, Paolo, 2012. "Stochastic stability in best shot network games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 538-554.
    7. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    8. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
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    Cited by:

    1. Ennio Bilancini & Leonardo Boncinelli, 2020. "The evolution of conventions under condition-dependent mistakes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 497-521, March.
    2. Leonardo Boncinelli & Alessio Muscillo & Paolo Pin, 2022. "Efficiency and Stability in a Process of Teams Formation," Dynamic Games and Applications, Springer, vol. 12(4), pages 1101-1129, December.
    3. Sawa, Ryoji, 2019. "Stochastic stability under logit choice in coalitional bargaining problems," Games and Economic Behavior, Elsevier, vol. 113(C), pages 633-650.

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    More about this item

    Keywords

    Matching; Graph; Stochastic stability; Maximal matching; Maximum matching;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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