TY - JOUR
T1 - Compromising between the proportional and equal division values
AU - Zou, Zhengxing
AU - van den Brink, René
AU - Funaki, Yukihiko
N1 - Publisher Copyright:
© 2021 The Author(s)
PY - 2021/12
Y1 - 2021/12
N2 - We introduce a family of values for TU-games that offers a compromise between the proportional and equal division values. Each value, called an α-mollified value, is obtained in two steps. First, linear functions are defined that associate 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.
AB - We introduce a family of values for TU-games that offers a compromise between the proportional and equal division values. Each value, called an α-mollified value, is obtained in two steps. First, linear functions are defined that associate 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.
KW - Consistency
KW - Cooperative game
KW - Equal division value
KW - Proportional division value
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U2 - 10.1016/j.jmateco.2021.102539
DO - 10.1016/j.jmateco.2021.102539
M3 - Article
AN - SCOPUS:85108777974
SN - 0304-4068
VL - 97
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
M1 - 102539
ER -