Group contributions in TU-games: A class of k-lateral Shapley values

Borkotokey, Surajit; Choudhury, Dhrubajit; Gogoi, Loyimee; Kumar, Rajnish

doi:10.1016/j.ejor.2020.03.054

Cited by 10 publications

(7 citation statements)

References 27 publications

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“…where the parameter α ∈ [0, 1] makes the reconciliation between marginalism and egalitarianism. Various axiomatizations of the Shapley value, the Equal Division rule and the α-Egalitarian Shapley value can be found in the literature (see [1,2,3,4,11,15,16,17,18]).…”

Section: Preliminariesmentioning

confidence: 99%

The Egalitarian Shapley value: a generalization based on coalition sizes

et al. 2020

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In designing solution concepts for cooperative games with transferable utilities, consolidation of marginalism and egalitarianism has been widely studied. The α-Egalitarian Shapley value is one such solution that combines the Shapley value and the Equal Division rule, the two most popular extreme instances of marginalism and egalitarianism respectively. This value gives the planner the flexibility to choose the level of marginality for the players by varying the convexity parameter α. In this paper, we define the Generalized Egalitarian Shapley value that gives the planner more flexibility in choosing the level of marginality based on the coalition size. We then provide two characterizations of the Generalized Egalitarian Shapley value.

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Section: Preliminariesmentioning

confidence: 99%

The Egalitarian Shapley value: a generalization based on coalition sizes

et al. 2020

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“…All the siblings in an undivided family, which can include up to several generations, have equal rights on the property of the family. The inheritance rights do not depend on the marginal contribution of the family members, see for example (Borkotokey et al, 2020). Other examples include the allocation of Health and Social care.…”

Section: -Stephen Jay Gouldmentioning

confidence: 99%

“…Obviously, the share to a player from her group contributions is directly proportional to the size of the coalition. The idea is similar to the one proposed in (Borkotokey et al, 2020), but the two values differ by their counting process proposed therein. Unlike ours, the counting process in (Borkotokey et al, 2020) is based on the original Shapley's rule of counting, where the players are allowed to enter a room to form the grand coalition, following an order and then determine their contributions in groups.…”

Section: -Stephen Jay Gouldmentioning

confidence: 99%

“…The idea is similar to the one proposed in (Borkotokey et al, 2020), but the two values differ by their counting process proposed therein. Unlike ours, the counting process in (Borkotokey et al, 2020) is based on the original Shapley's rule of counting, where the players are allowed to enter a room to form the grand coalition, following an order and then determine their contributions in groups. The standard null player axiom of the Shapley value requires zero payment to players whose marginal contribution vector is zero, see (Casajus and Huettner, 2013).…”

Section: -Stephen Jay Gouldmentioning

confidence: 99%

“…UCU members at 61 universities in the UK have recently launched a four week strike, to protest against planned changes to their pensions which they say will mean a typical lecturer will receive £10, 000 a year less in retirement (The Guardian, 15 February, 2018).2 Universal basic income: renaissance for a 500-year-old idea, Martin Sandbu, Financial Times, December 8, 20173 A similar concept was proposed in(Borkotokey et al, 2015) for a class of fixed and flexible network allocation rules and recently in(Borkotokey et al, 2020) which introduces the notion of group contributions within coalitions.4 We can take additivity in stead of linearity as any value that is symmetric and additive is also linear.…”

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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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The α-Egalitarian Myerson value of games with communication structure

Meng

2023

Math Meth Oper Res

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Group contributions in TU-games: A class of k-lateral Shapley values

Cited by 10 publications

References 27 publications

The Egalitarian Shapley value: a generalization based on coalition sizes

The Egalitarian Shapley value: a generalization based on coalition sizes

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

The α-Egalitarian Myerson value of games with communication structure

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