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The Farsighted Stable Set

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Harsanyi (1974) criticized the von Neumann-Morgenstern notion of a stable set on the grounds that it implicitly assumes coalitions to be shortsighted in evaluating their prospects. He proposed a modification of the dominance relation to incorporate farsightedness. In doing so, however, Harsanyi 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 S. This implicitly gives an objecting coalition complete power to arrange the payoffs of players elsewhere, which is clearly unsatisfactory. While this assumption is absolutely innocuous for the classical stable set, it is of crucial significance for farsighted dominance. Our proposed modification of the Harsanyi set respects “coalitional sovereignty.” The resulting farsighted stable set is very different, both from that of Harsanyi or of von Neumann and Morgenstern. We provide a necessary and sufficient condition for the existence of a farsighted stable set containing just a single payoff allocation. This condition is weaker than assuming that the relative interior of the core is non-empty, but roughly establishes an equivalence between core allocations and the union of allocations over all singlepayoff farsighted stable sets. We state two conjectures: that farsighted stable sets exist in all transferable-utility games, and that when a single-payoff farsighted stable set exists, there are no farsighted stable sets containing multiple payoff allocations.

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  • Debraj Ray & Rajiv Vohra, 2013. "The Farsighted Stable Set," Working Papers 2013-11, Brown University, Department of Economics.
  • Handle: RePEc:bro:econwp:2013-11
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    1. Béal, Sylvain & Durieu, Jacques & Solal, Philippe, 2008. "Farsighted coalitional stability in TU-games," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 303-313, November.
    2. Anindya Bhattacharya & Victoria Brosi, 2011. "An existence result for farsighted stable sets of games in characteristic function form," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 393-401, May.
    3. Vannetelbosch, Vincent J. & Mauleon, Ana & Vergote, Wouter, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    4. Lucas, William F., 1992. "Von Neumann-Morgenstern stable sets," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 17, pages 543-590 Elsevier.
    5. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    6. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 185-187.
    7. Effrosyni Diamantoudi & Licun Xue, 2003. "Farsighted stability in hedonic games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 39-61, August.
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    Cited by:

    1. Jean-Jacques Herings, P. & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Stable sets in matching problems with coalitional sovereignty and path dominance," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 14-19.
    2. Francis Bloch & Anne van den Nouweland, 2017. "Farsighted Stability with Heterogeneous Expectations," Working Papers 2017.31, Fondazione Eni Enrico Mattei.
    3. Kai A. Konrad & Florian Morath, 2015. "To deter or to moderate? Alliance formation in contests with incomplete information," Working Papers tax-mpg-rps-2015-15, Max Planck Institute for Tax Law and Public Finance.
    4. repec:spr:sochwe:v:49:y:2017:i:1:d:10.1007_s00355-017-1057-5 is not listed on IDEAS
    5. repec:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0538-6 is not listed on IDEAS

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