The Farsighted Stable Set

Debraj Ray and Rajiv Vohra

No 2013-11, Working Papers from Brown University, Department of Economics

Abstract: 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 ìcoalitional sovereignty.î 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.

Keywords: # (search for similar items in EconPapers)
Date: 2013
New Economics Papers: this item is included in nep-gth, nep-mic and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://economics.brown.edu/sites/g/files/dprerj72 ... rs/2013-11_paper.pdf (application/pdf)

Related works:
Journal Article: The Farsighted Stable Set (2015)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bro:econwp:2013-11

Access Statistics for this paper

More papers in Working Papers from Brown University, Department of Economics Department of Economics, Brown University, Providence, RI 02912.
Bibliographic data for series maintained by Brown Economics Webmaster ().