A solidarity value forn-person transferable utility games

Nowak, Adam; Radzik, Tadeusz

doi:10.1007/bf01242845

Cited by 133 publications

(98 citation statements)

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“…On the other hand, the division resulting from applying procedure 4 to the game v is . More generally, the value determined by procedure 4 is the solidarity value σ defined by Nowak and Radzik (1994) as…”

Section: Procedures 2cmentioning

confidence: 99%

“Procedural” values for cooperative games

Malawski

2012

Int J Game Theory

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This paper introduces a new notion of a "procedural" value for cooperative TU games. A procedural value is determined by an underlying procedure of sharing marginal contributions to coalitions formed by players joining in random order. We consider procedures under which players can only share their marginal contributions with their predecessors in the ordering, and study the set of all resulting values. The most prominent procedural value is, of course, the Shapley value obtaining under the simplest procedure of every player just retaining his entire marginal contribution. But different sharing rules lead to other interesting values, including the "egalitarian solution" and the Nowak and Radzik "solidarity value". All procedural values are efficient, symmetric and linear. Moreover, it is shown that these properties together with two very natural monotonicity postulates characterize the class of procedural values. Some possible modifications and generalizations are also discussed. In particular, it is shown that dropping one of monotonicity axioms is equivalent to allowing for sharing marginal contributions with both predecessors and successors in the ordering.

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Section: Procedures 2cmentioning

confidence: 99%

“Procedural” values for cooperative games

Malawski

2012

Int J Game Theory

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“…Example 2 The solidarity value Sol(N , v) of a game N , v is defined by some expected average marginal contribution over all coalitions containing the player as follows (Nowak 1994):…”

Section: Discussionmentioning

confidence: 99%

Associated consistency and values for TU games

Driessen

2010

Int J Game Theory

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In the framework of the solution theory for cooperative transferable utility games, Hamiache axiomatized the well-known Shapley value as the unique one-point solution verifying the inessential game property, continuity, and associated consistency. The purpose of this paper is to extend Hamiache's axiomatization to the class of efficient, symmetric, and linear values, of which the Shapley value is the most important representative. For this enlarged class of values, explicit relationships to the Shapley value are exploited in order to axiomatize such values with reference to a slightly adapted inessential game property, continuity, and a similar associated consistency. The latter axiom requires that the solutions of the initial game and its associated game (with the same player set, but a different characteristic function) coincide.

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“…Among the various one-point solutions for TU games, the Shapley value [1] and the solidarity value [2] are perhaps the most popular ones. The Shapley value builds on the axioms of efficiency, linearity, anonymity, and the null player.…”

Section: Introductionmentioning

confidence: 99%

Solidarity Value and Solidarity Share Functions for TU Fuzzy Games

Biswakarma

Borkotokey

Mesiar

2018

Advances in Fuzzy Systems

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TU games under both crisp and fuzzy environments describe situations where players make full (crisp) or partial (fuzzy) binding agreements and generate worth in return. The challenge is then to decide how to distribute the profit among them in a rational manner: we call this a solution. In this paper, we introduce the notion of solidarity value and the solidarity share function as a suitable solution to TU fuzzy games. Two special classes of TU fuzzy games, namely, TU fuzzy games in Choquet integral form and in multilinear extension form, are studied and the corresponding solidarity value and the solidarity share functions are characterized.

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A solidarity value forn-person transferable utility games

Cited by 133 publications

References 1 publication

“Procedural” values for cooperative games

“Procedural” values for cooperative games

Associated consistency and values for TU games

Solidarity Value and Solidarity Share Functions for TU Fuzzy Games

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