Remarks on the reasonable set of outcomes in a general coalition function form game
type: Item
instance of: scholarly article
title: Remarks on the reasonable set of outcomes in a general coalition function form game
zbMATH Open document ID: 0632.90095
DOI: 10.1007/BF01780637
author: Shmuel Zamir
author: Louis-André Gérard-Varet
published in: International Journal of Game Theory
publication date: 1987-01-01T00:00:00Z
review text: In the present paper the authors first define a ``reasonable payoff correspondence'' by what they believe are unquestionable axioms. The result catches the intuition of ``reasonable'' that they have in mind. They obtain that for a superadditive game the reasonable interval for a player is the set of individually rational payoff levels that do not exceed the upper bound introduced by Milnor in 1952, namely the player's largest marginal contribution. They try to use the set to learn about coalition structure. Perhaps a natural modification of one of the axioms allows to extend the theory. In a second part they go further. Their suggested set of ``reasonable outcomes'' being such that a point outside is nonplausible, it is natural to test plausibility of alternative solution concepts by verifying whether or not they are included in the set. This is done for well-known, solution concepts such as Shapley value, stable sets, the core, the bargaining set, the kernel and the nucleolus, however extended to non- trivial coalition structures and considered for games which are not necessarily super-additive. A systematic treatment of such tests is worthwhile.
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 4029308
zbMATH Keywords: axiomatic approach
zbMATH Keywords: reasonable payoff correspondence
zbMATH Keywords: coalition structure
reviewed by: Ezio Marchi
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01780637
OpenAlex ID: W2006071255
description: scientific article; zbMATH DE number 4029308