The weighted Shapley-egalitarian value for cooperative games with a coalition structure

Xun-Feng Hu ()
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Xun-Feng Hu: Guangzhou University

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2020, vol. 28, issue 1, No 11, 193-212

Abstract: Abstract In this paper, we study a solution, the weighted Shapley-egalitarian value, for transferable utility cooperative games with a coalition structure. It first distributes the worth of the grand coalition among a priori unions of the coalition structure with the weighted Shapley value, with the sizes of unions acting as weights. And then, it allocates the payoff of every union among its players with the equal division value, thus players inside a union exhibit a greater degree of solidarity than players in different unions. We give several equivalent definitions of the value, particularly show its relationship with the collective value. We apply the value to the recent field of airport cost pooling game, and find that the Shapley value therein can be viewed as a special case of our value, if we view an airport cost pooling game as a transferable utility cooperative game with a coalition structure. Finally, to further highlight the differences between our value and the collective value, we provide parallel axiomatizations of the two values, by replacing the collective balanced contributions axiom with two intuitive axioms.

Keywords: Cooperative game; Coalition structure; Shapley-solidarity value; Collective value; Airport cost pooling game; 91A06; 91A12 (search for similar items in EconPapers)
JEL-codes: C71 D63 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s11750-019-00530-4

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