The Farsighted Stable Set

Debraj Ray, Rajiv Vohra

    Research output: Contribution to journalArticle

    Abstract

    Harsanyi (1974) criticized the von Neumann-Morgenstern (vNM) stable set for its presumption that coalitions are myopic about their prospects. He proposed a new dominance relation incorporating farsightedness, but retained another feature of the stable set: that a coalition S can impose any imputation as long as its restriction to S is feasible for it. This implicitly gives an objecting coalition complete power to arrange the payoffs of players elsewhere, which is clearly unsatisfactory. While this assumption is largely innocuous for myopic dominance, it is of crucial significance for its farsighted counterpart. Our modification of the Harsanyi set respects "coalitional sovereignty." The resulting farsighted stable set is very different from both the Harsanyi and the vNM sets. We provide a necessary and sufficient condition for the existence of a farsighted stable set containing just a single-payoff allocation. This condition roughly establishes an equivalence between core allocations and the union of allocations over all single-payoff farsighted stable sets. We then conduct a comprehensive analysis of the existence and structure of farsighted stable sets in simple games. This last exercise throws light on both single-payoff and multi-payoff stable sets, and suggests that they do not coexist.

    Original languageEnglish (US)
    Pages (from-to)977-1011
    Number of pages35
    JournalEconometrica
    Volume83
    Issue number3
    DOIs
    StatePublished - May 1 2015

    Fingerprint

    Stable set
    Farsightedness
    Von Neumann-Morgenstern stable set
    Equivalence
    Exercise
    Sovereignty
    Imputation
    Simple game
    Core allocation

    Keywords

    • Coalition formation
    • Core
    • Farsightedness
    • Simple games
    • Stable set
    • Veto players

    ASJC Scopus subject areas

    • Economics and Econometrics

    Cite this

    Ray, D., & Vohra, R. (2015). The Farsighted Stable Set. Econometrica, 83(3), 977-1011. https://doi.org/10.3982/ECTA12022

    The Farsighted Stable Set. / Ray, Debraj; Vohra, Rajiv.

    In: Econometrica, Vol. 83, No. 3, 01.05.2015, p. 977-1011.

    Research output: Contribution to journalArticle

    Ray, D & Vohra, R 2015, 'The Farsighted Stable Set', Econometrica, vol. 83, no. 3, pp. 977-1011. https://doi.org/10.3982/ECTA12022
    Ray D, Vohra R. The Farsighted Stable Set. Econometrica. 2015 May 1;83(3):977-1011. https://doi.org/10.3982/ECTA12022
    Ray, Debraj ; Vohra, Rajiv. / The Farsighted Stable Set. In: Econometrica. 2015 ; Vol. 83, No. 3. pp. 977-1011.
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