TY - JOUR
T1 - Balanced externalities and the proportional allocation of nonseparable contributions
AU - van den Brink, René
AU - Chun, Youngsub
AU - Funaki, Yukihiko
AU - Zou, Zhengxing
N1 - Funding Information:
We thank the associate editor and three anonymous reviewers for valuable comments on a previous version of the paper. Youngsub Chun was supported by the Research Grant of the Center for Distributive Justice at the Institute of Economic Research, Seoul National University. Yukihiko Funaki was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grants JP17H02503 and JP22H00829 , and JSPS Core-to-Core Program CEFM. Zhengxing Zou was supported by the National Natural Science Foundation of China (Grant Nos. 72101015 and 72271016 ) and the Beijing Municipal Natural Science Foundation (No. Z220001 ).
Publisher Copyright:
© 2022 The Authors
PY - 2022
Y1 - 2022
N2 - This paper provides axiomatic characterizations of the proportional allocation of nonseparable contributions (PANSC) value for TU games, being the solution which allocates the total worth proportional to the separable contributions of the players. First, we show that the PANSC value is the only one satisfying efficiency and weak balanced externalities, the last axiom requiring that every player's payoff is the same fraction of the total externality inflicted on the other players with her presence. This is a weakening of balanced externalities studied in the context of queueing problems to characterize the Shapley value. Our second characterization is obtained by investigating the dual relation between the PANSC value and the proportional division value, showing that the PANSC value is the only one satisfying complement consistency and dual proportional standardness. In addition, we discuss the relation between the PANSC value and two methods widely used in cost allocation problems: the separable costs remaining benefits method and the alternative cost avoided method.
AB - This paper provides axiomatic characterizations of the proportional allocation of nonseparable contributions (PANSC) value for TU games, being the solution which allocates the total worth proportional to the separable contributions of the players. First, we show that the PANSC value is the only one satisfying efficiency and weak balanced externalities, the last axiom requiring that every player's payoff is the same fraction of the total externality inflicted on the other players with her presence. This is a weakening of balanced externalities studied in the context of queueing problems to characterize the Shapley value. Our second characterization is obtained by investigating the dual relation between the PANSC value and the proportional division value, showing that the PANSC value is the only one satisfying complement consistency and dual proportional standardness. In addition, we discuss the relation between the PANSC value and two methods widely used in cost allocation problems: the separable costs remaining benefits method and the alternative cost avoided method.
KW - Balanced externalities
KW - Consistency
KW - Cooperative game
KW - Game theory
KW - Proportional allocation of nonseparable contributions
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U2 - 10.1016/j.ejor.2022.10.017
DO - 10.1016/j.ejor.2022.10.017
M3 - Article
AN - SCOPUS:85140955474
JO - European Journal of Operational Research
JF - European Journal of Operational Research
SN - 0377-2217
ER -