An existence result for farsighted stable sets of games in characteristic function form
type: Item
instance of: scholarly article
title: An existence result for farsighted stable sets of games in characteristic function form
zbMATH Open document ID: 1233.91013
author: Anindya Bhattacharya
author: Victoria Brosi
published in: International Journal of Game Theory
publication date: 2011-06-28T00:00:00Z
review text: This paper considers NTU games, that is, the class of cooperative games where the utility can be non transferable among the players. Interesting real situations, as for example market problems, can be modelled using NTU games. One important result in the literature of game theory is that there exist games that admit no von Neumann-Morgenstern solution (cf. [\textit{W. Lucas}, ``A game with no solution'', Bull. Am. Math. Soc. 74, 237--239 (1968; Zbl 0157.51101)]) with respect to the classical direct dominance relation. One significant development in this literature were the two notions of indirect dominance (cf. [\textit{J. C. Harsanyi}, ``An equilibrium-point interpretation of stable sets and a proposed alternative definition'', Manage. Sci., Theory 20, 1472--1495 (1974; Zbl 0335.90063)]) that take into account the fact that the players may be farsighted while making a move, they may take into account the further moves by other groups of players that may ensue. In this paper, the second of such notions is used. In stark contrast to that for the direct dominance relation, at least one stable set with respect to the indirect (or farsighted) dominance relation exists for every cooperative game where the utility is transferable among the agents (cf. [\textit{S. Béal, J. Durieu} and \textit{P. Solal}, ``Farsighted coalitional stability in TU-games'', Math. Soc. Sci. 56, No. 3, 303--313 (2008; Zbl 1155.91308)]). This paper generalizes that result to the setting of NTU games under an innocuous condition. Let \((N,V)\) be an NTU game. For any \(S\subset N\) and any \(x,y\in V(N)\) \(y\prec_Sx\) means that \(y_i<x_i\) for every \(i\in S\). A pay-off vector is an imputation if it is individually rational as well as efficient. \(I(N,V)\) denotes the set of imputations. A coalition \(S\) can enforce an imputation \(x\) from an (and any) imputation \(z\), denoted as \(z\to_S x\), if and only if \(x |_S \in V(S)\). The notion of indirect dominance used in the paper is the followi…
reviewed by: Balbina Casas-Méndez
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 5913907
zbMATH Keywords: coalitional games
zbMATH Keywords: farsighted stable sets
MaRDI profile type: Publication
full work available at URL: s00182-010-0262-6
OpenAlex ID: W1980026806
cites work: Von Neumann-Morgenstern solutions to cooperative games without side payments
cites work: Farsighted coalitional stability in TU-games
cites work: Farsighted coalitional stability
cites work: Farsighted stability in hedonic games
cites work: (Sophisticated) stable sets in exchange economies
cites work: An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition
cites work: A game with no solution
cites work: von Neumann-Morgenstern farsightedly stable sets in two-sided matching
cites work: Q4369419
cites work: The Core of an N Person Game
DOI: 10.1007/S00182-010-0262-6
description: scientific article; zbMATH DE number 5913907