Individual weighted excess and least square values

Xia Zhang, Rene van den Brink, Arantza Estevez-Fernandez and Hao Sun
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Xia Zhang: Vrije Universiteit Amsterdam
Rene van den Brink: Vrije Universiteit Amsterdam
Arantza Estevez-Fernandez: Vrije Universiteit Amsterdam
Hao Sun: Northwestern Polytechnical University

No 20-033/II, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This work deals with the weighted excesses of players in cooperative games which are obtained by summing up all the weighted excesses of all coalitions to which they belong. We first show that lexicographically minimizing the individual weighted excesses of players gives the same minimal weighted excess for every player. Moreover, we show that the associated payoff vector is the corresponding least square value. Second, we show that minimizing the variance of the players' weighted excesses on the preimputation set, again yields the corresponding least square value. Third, we show that these results give rise to lower and upper bounds for the core payoff vectors and, using these bounds, we define the weighted super core as a polyhedron that contains the core. It turns out that the least square values can be seen as a center of this weighted super core, giving a third new characterization of the least square values. Finally, these lower and upper bounds for the core inspire us to introduce a new solution for cooperative TU games that has a strong similarity with the Shapley value.

Keywords: Individual weighted excess; Prenucleolus; Least square value; Weighted super core; Shapley value (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2020-06-20
New Economics Papers: this item is included in nep-gth
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