The Family of Ideal Values for Cooperative Games

Tinbergen Institute Discussion Paper 2018-002/II

27 Pages Posted: 17 Jan 2018

See all articles by Wenna Wang

Wenna Wang

Northwestern Polytechnical University, China

Hao Sun

Northwestern Polytechnical University, China

Rene van den Brink

Vrije Universiteit Amsterdam, School of Business and Economics

Genjiu Xu

Northwestern Polytechnical University, China

Date Written: January 11, 2018

Abstract

In view of the nature of pursuing profit, a selfish coefficient function is employed to describe the degrees of selfishness of players in different coalitions, which is the desired rate of return to the worth of coalitions. This function brings in the concept of individual expected reward to every player. Built on different selfish coefficient functions, the family of ideal values can be obtained by minimizing deviations from the individual expected rewards. Then we show the relationships between the family of ideal values and two other classical families of values: the procedural values and the least square values. For any selfish coefficient function m, the m-ideal value is characterized by efficiency, linearity, m-equal-expectation player property and nullifying player m-punishment property. We also provide an interpretation of a dynamic process for the m-ideal value. As two dual cases in the family of ideal values, the center-of-gravity of imputation-set value (CIS value) and the equal allocation of nonseparable costs value (EANS value) are raised from new axiomatic angles.

Keywords: Game theory, m-Individual expected reward, The family of ideal values, Dynamic process, CIS and EANS values

JEL Classification: C71

Suggested Citation

Wang, Wenna and Sun, Hao and van den Brink, Rene and Xu, Genjiu, The Family of Ideal Values for Cooperative Games (January 11, 2018). Tinbergen Institute Discussion Paper 2018-002/II, Available at SSRN: https://ssrn.com/abstract=3100168 or http://dx.doi.org/10.2139/ssrn.3100168

Wenna Wang (Contact Author)

Northwestern Polytechnical University, China ( email )

127# YouYi Load
XiAn, Shaanxi 710072
China

Hao Sun

Northwestern Polytechnical University, China ( email )

127# YouYi Load
XiAn, Shaanxi 710072
China

Rene Van den Brink

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Genjiu Xu

Northwestern Polytechnical University, China ( email )

127# YouYi Load
XiAn, Shaanxi 710072
China

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