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The Farsighted Stable Set

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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Paper provided by Brown University, Department of Economics in its series Working Papers with number 2013-11.

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Date of creation: 2013
Date of revision:
Handle: RePEc:bro:econwp:2013-11
Contact details of provider: Postal: Department of Economics, Brown University, Providence, RI 02912

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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. MAULEON, Ana & VANNETELBOSCH, Vincent J. & VERGOTE, Wouter, . "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," CORE Discussion Papers RP 2337, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. 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.
  4. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer, vol. 18(2), pages 185-87.
  5. Hideo Konishi & Debraj Ray, 2000. "Coalition Formation as a Dynamic Process," Boston College Working Papers in Economics 478, Boston College Department of Economics, revised 15 Apr 2002.
  6. Anindya Bhattacharya & Victoria Brosi, 2011. "An existence result for farsighted stable sets of games in characteristic function form," International Journal of Game Theory, Springer, vol. 40(2), pages 393-401, May.
  7. Effrosyni Diamantoudi & Licun Xue, . "Farsighted Stability in Hedonic Games," Economics Working Papers 2000-12, School of Economics and Management, University of Aarhus.
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