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.
|Date of creation:||2013|
|Contact details of provider:|| Postal: Department of Economics, Brown University, Providence, RI 02912|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Béal, Sylvain & Durieu, Jacques & Solal, Philippe, 2008.
"Farsighted coalitional stability in TU-games,"
Mathematical Social Sciences,
Elsevier, vol. 56(3), pages 303-313, November.
- Sylvain Béal & Jacques Durieu & Philippe Solal, 2007. "Farsighted Coalitional Stability in TU-Games," Post-Print ujm-00162456, HAL.
- Sylvain Béal & Jacques Durieu & Philippe Solal, 2008. "Farsighted Coalitional Stability in TU-games," Post-Print hal-00334049, HAL.
- Sylvain Béal & Jacques Durieu & Philippe Solal, 2007. "Farsighted Coalitional Stability in TU-Games," Post-Print ujm-00176491, HAL.
- Béal, Sylvain & Durieu, Jacques & Solal, Philippe, 2007. "Farsighted coalitional stability in TU-games," Papers 07-57, Sonderforschungsbreich 504.
- Béal, Sylvain & Durieu, Jacques & Solal, Philippe, 2007. "Farsighted Coalitional Stability in TU-games," Sonderforschungsbereich 504 Publications 07-57, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
- Sylvain Béal & Jacques Durieu & Philippe Solal, 2007. "Farsighted Coalitional Stability in TU-Games," Post-Print ujm-00176488, HAL.
- 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.
- MAULEON, Ana & VANNETELBOSCH, Vincent J. & VERGOTE, Wouter, "undated". "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).
- Vincent Vannetelbosch & Ana Mauleon & Wouter Vergote, 2008. "Von Neumann-Morgenstern Farsightedly Stable Sets in Two-Sided Matching," Working Papers 2008.29, Fondazione Eni Enrico Mattei.
- MAULEON, Ana & VANNETELBOSCH, Vincent & VERGOTE, Wouter, 2008. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," CORE Discussion Papers 2008016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Ana, MAULEON & Vincent, VANNETELBOSCH & Wouter, VERGOTE, 2008. "Von Neuman-Morgenstern farsightedly stable sets in two-sided matching," Discussion Papers (ECON - Département des Sciences Economiques) 2008013, Université catholique de Louvain, Département des Sciences Economiques.
- Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
- 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.
- 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, 08.
- Effrosyni Diamantoudi & Licun Xue, "undated". "Farsighted Stability in Hedonic Games," Economics Working Papers 2000-12, Department of Economics and Business Economics, Aarhus University.
- 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.
- 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.
- Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 185-187. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:bro:econwp:2013-11. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Brown Economics Webmaster)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.