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The Unbinding Core for Coalitional Form Games

Author

Listed:
  • Takaaki Abe

    (JSPS Research Fellow. Graduate School of Economics, Waseda University.)

  • Yukihiko Funaki

    (School of Political Science and Economics, Waseda University.)

Abstract

In this paper, we introduce a new concept of core by extending the definition of deviation. The traditional definition of deviation allows for players to deviate if some profitable allocation exists after their deviation, while our new definition requires that all possible allocations are profitable. Hence, our core becomes a superset of the traditional core. We examine some properties that our new core satisfies and provide a sufficient condition for being nonempty. Moreover, we apply Ray's (1989) credibility to our core.

Suggested Citation

  • Takaaki Abe & Yukihiko Funaki, 2018. "The Unbinding Core for Coalitional Form Games," Working Papers 1805, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:1805
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    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    2. Takaaki Abe, 2018. "Consistency and the core in games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 133-154, March.
    3. Konishi, Hideo & Quint, Thomas & Wako, Jun, 2001. "On the Shapley-Scarf economy: the case of multiple types of indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 1-15, February.
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    5. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    6. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
    7. Takaaki Abe & Yukihiko Funaki, 2017. "The non-emptiness of the core of a partition function form game," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 715-736, August.
    8. László Kóczy, 2007. "A recursive core for partition function form games," Theory and Decision, Springer, vol. 63(1), pages 41-51, August.
    9. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
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    11. Shapley, Lloyd & Vohra, Rajiv, 1991. "On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 108-116, January.
    12. Yukihiko Funaki & Takehiko Yamato, 1999. "The core of an economy with a common pool resource: A partition function form approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 157-171.
    13. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 185-187.
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    More about this item

    Keywords

    cooperative game; core; credibility; deviation;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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