Compromising between the proportional and equal division values: axiomatization, consistency and implementation

Zhengxing Zou, Rene van den Brink and Yukihiko Funaki ()
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Rene van den Brink: Vrije Universiteit Amsterdam

No 20-054/II, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: We introduce a family of values for TU-games that offers a compromise between the proportional and equal division values. Each value, called an alpha-mollified value, is obtained in two steps. First, a linear function with respect to the worths of all coalitions is defined which associates a real number to every TU-game. Second, the weight assigned by this function is used to weigh proportionality and equality principles in allocating the worth of the grand coalition. We provide an axiomatic characterization of this family, and show that this family contains the affine combinations of the equal division value and the equal surplus division value as the only linear values. Further, we identify the proportional division value and the affine combinations of the equal division value and the equal surplus division value as those members of this family, that satisfy projection consistency. Besides, we provide a procedural implementation of each single value in this family.

Keywords: Cooperative game; consistency; equal division value; proportional division value (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2020-09-01
New Economics Papers: this item is included in nep-gth
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