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Maximality in the Farsighted Stable Set

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  • Debraj Ray
  • Rajiv Vohra

Abstract

The stable set of von Neumann and Morgenstern imposes credibility on coalitional deviations. Their credibility notion can be extended to cover farsighted coalitional deviations, as proposed by Harsanyi (1974), and more recently reformulated by Ray and Vohra (2015). However, the resulting farsighted stable set suffers from a conceptual drawback: while coalitional deviations improve on existing outcomes, coalitions might do even better by moving elsewhere. Or other coalitions might intervene to impose their favored moves. We show that every farsighted stable set satisfying some reasonable, and easily verifiable, properties is unaffected by the imposition of this stringent maximality requirement. These properties are satisfied by many, but not all, known farsighted stable sets.Creation-Date: 2017

Suggested Citation

  • Debraj Ray & Rajiv Vohra, "undated". "Maximality in the Farsighted Stable Set," Working Papers 2017-4, Brown University, Department of Economics.
    • Handle: RePEc:bro:econwp:2017-4
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    References listed on IDEAS

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    1. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
    2. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954, Decembrie.
    3. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    4. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May.
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