The Egalitarian Shapley value: a generalization based on coalition sizes

Choudhury, Dhrubajit; Borkotokey, Surajit; Kumar, Rajnish; Sarangi, Sudipta

doi:10.1007/s10479-020-03675-9

Cited by 17 publications

(6 citation statements)

References 18 publications

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“…Several values are introduced in the literature through which solidarity among players is achieved. Examples include the Solidarity value (Nowak and Radzik, 1994), The Egalitarian Shapley value (Joosten, 1996), the Generalized Egalitarian Shapley value (Choudhury et al, 2020), the Solidarity value due to (Béal et al, 2017), the discounted Shapley value (Joosten, 1996) and their respective characterizations, (Casajus and Huettner, 2013;Béal et al, 2017;Kamijo and Kongo, 2012;Radzik, 2013;Casajus and Huettner, 2014;van den Brink, 2007;van den Brink et al, 2013;van den Brink and Funaki, 2015;Weber, 1988;Yokote and Funaki, 2017;Young, 1985) etc., just to name a few. We assume here that players form groups within coalitions to indulge in interactions which we call multilateral interactions.…”

Section: -Stephen Jay Gouldmentioning

confidence: 99%

“…The null player axiom of the Shapley value (Shapley, 1953) blocks all sorts of egalitarianism in the distribution of the wealth. Thus, combining the axioms of efficiency, symmetry and linearity 4 with a property that replaces the null player axiom has been accepted as essential for ensuring solidarity, take for example the Average null-player property for the Solidarity value, (Nowak and Radzik, 1994), the Null player in a productive environment for the Egalitarian Shapley value, (Casajus and Huettner, 2013), the null player in a null environment for positive game for the Solidarity value (Béal et al, 2017), the null player in a non-negative environment for the Generalized Egalitarian Shapley value (Choudhury et al, 2020), the Invariance from proportional and quasi proportional deletion for the Equal Division and Solidarity value (Kamijo and Kongo, 2012), the δ-reducing property for the discounted Shapley value (van den Brink and Funaki, 2015) etc., to name just a few.…”

Section: -Stephen Jay Gouldmentioning

confidence: 99%

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Solidarity induced by group contributions: the MI$$^k$$-value for transferable utility games

et al. 2020

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The most popular values in cooperative games with transferable utilities are perhaps the Shapley and the Shapley like values which are based on the notion of players' marginal productivity. The equal division rule on the other hand, is based on egalitarianism where resource is equally divided among players, no matter how productive they are. However none of these values explicitly discuss players' multilateral interactions with peers in deciding to form coalitions and generate worths. In this paper we study the effect of multilateral interactions of a player that accounts for her contributions with her peers not only at an individual level but also on a group level. Based on this idea, we propose a value called the MI k -value and characterize it by the axioms of linearity, anonymity, efficiency and a new axiom: the axiom of MN k -player. An MN kplayer is one whose average marginal contribution due to her multilateral interactions upto level k is zero and can be seen as a generalization of the standard null player axiom of the Shapley value. We have shown that the MI k -value on a variable player set is asymptotically close to the equal division rule. Thus our value realizes solidarity among players by incorporating both their individual and group contributions.

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Section: -Stephen Jay Gouldmentioning

confidence: 99%

Section: -Stephen Jay Gouldmentioning

confidence: 99%

Solidarity induced by group contributions: the MI$$^k$$-value for transferable utility games

et al. 2020

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“…In Abe and Nakada (2019) the ED is generalized to obtain a weighted division and the corresponding axiomatization is obtained. For a comprehensive study of all these values, we refer to Béal et al (2017), Borkotokey et al (2020a, 2020b), Casajus (2011, 2012), Choudhury et al (2020), Kakoty et al (2021), and Nowak and Radzik (1994).…”

Section: Introductionmentioning

confidence: 99%

A new value for cooperative games based on coalition size

Borkotokey

Choudhury

Kumar

et al. 2023

Int J of Economic Theory

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We propose and characterize a new value for TU cooperative games based on egalitarian distribution of worths in smaller coalitions and players' marginal productivity in larger coalitions. This value belongs to the class of Procedural values due to Malawski. Our value is identical with the Shapley value on one extreme and the Equal Division rule on the other extreme. We show that our value is identical with the solidarity value due to Bèal et al. of the dual game. However, by duality, our characterization intuitively improves over the axiomatization of this solidarity value. We also provide a mechanism that implements our value in sub‐game perfect Nash equilibrium. Finally, a generalized version of this value is proposed followed by its characterizations.

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“…In section 2, this idea is illustrated with a numerical example. More examples can be found in [12], where the authors introduce the Generalized egalitarian Shapley value in the cooperative framework that reflects the flexibility in choosing the level of marginality based on the coalition size.…”

Section: Introductionmentioning

confidence: 99%

The component-wise egalitarian Myerson value for Network Games

Borkotokey¹,

Goala²,

Kakoty³

et al. 2022

Preprint

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We introduce the component-wise egalitarian Myerson value for network games. This new value being a convex combination of the Myerson value and the component-wise equal division rule is a playerbased allocation rule. In network games under the cooperative framework, the Myerson value is an extreme example of marginalism, while the equal division rule signifies egalitarianism. In the proposed component-wise egalitarian Myerson value, a convexity parameter combines these two attributes and determines the degree of solidarity to the players. Here, by solidarity, we mean the mutual support or compensation among the players in a network. We provide three axiomatic characterizations of the value. Further, we propose an implementation mechanism for the component-wise egalitarian Myerson value under subgame perfect Nash equilibrium.

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The Egalitarian Shapley value: a generalization based on coalition sizes

Cited by 17 publications

References 18 publications

Solidarity induced by group contributions: the MI$$^k$$-value for transferable utility games

Solidarity induced by group contributions: the MI$$^k$$-value for transferable utility games

A new value for cooperative games based on coalition size

The component-wise egalitarian Myerson value for Network Games

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