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Non-convergence to stability in coalition formation games

Author

Listed:
  • Agustín G. Bonifacio

    (Universidad Nacional de San Luis/CONICET)

  • Elena Inarra

    (University of the Basque Country)

  • Pablo Neme

    (Universidad Nacional de San Luis/CONICET)

Abstract

We study the problem of convergence to stability in coalition formation games in which the strategies of each agent are coalitions in which she/he can partici- pate and outcomes are coalition structures. Given a natural blocking dynamic, an absorbing set is a minimum set of coalition structures that once reached is never abandoned. The coexistence of single and non-single absorbing sets is what causes lack of convergence to stability. To characterize games in which both types of set are present, we first relate circularity among coalitions in preferences (rings) with circularity among coalition structures (cycles) and show that there is a ring in pref- erences if and only if there is a cycle in coalition structures. Then we identify a special configuration of overlapping rings in preferences characterizing games that lack convergence to stability. Finally, we apply our findings to the study of games induced by sharing rules.

Suggested Citation

  • Agustín G. Bonifacio & Elena Inarra & Pablo Neme, 2020. "Non-convergence to stability in coalition formation games," Working Papers 23, Red Nacional de Investigadores en Economía (RedNIE).
    • Handle: RePEc:aoz:wpaper:23
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    More about this item

    Keywords

    Coalition formation Matching markets Absorbing sets Convergence to stability;

    JEL classification:

    • 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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