The Family of Ideal Values for Cooperative Games

Wenna Wang, Hao Sun, René van den Brink, Genjiu Xu

Research output: Contribution to JournalArticleAcademicpeer-review

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, the corresponding ideal value is characterized by efficiency, linearity, an equal-expectation player property and a nullifying player punishment property, and also interpreted by a dynamic process. As two dual cases in the family of ideal values, the center of gravity of imputation set value and the equal allocation of nonseparable costs value are raised from new axiomatic angles.

Original languageEnglish
Pages (from-to)1065–1086
Number of pages22
JournalJournal of Optimization Theory and Applications
Volume180
Issue number3
DOIs
Publication statusPublished - 2019

Fingerprint

Cooperative Game
Coalitions
Reward
Coefficient
Centre of gravity
Nonseparable
Imputation
Dynamic Process
Linearity
Profit
Least Squares
Profitability
Gravitation
Deviation
Angle
Family
Cooperative game
Costs

Keywords

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

Cite this

Wang, Wenna ; Sun, Hao ; van den Brink, René ; Xu, Genjiu. / The Family of Ideal Values for Cooperative Games. In: Journal of Optimization Theory and Applications. 2019 ; Vol. 180, No. 3. pp. 1065–1086.
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The Family of Ideal Values for Cooperative Games. / Wang, Wenna; Sun, Hao; van den Brink, René; Xu, Genjiu.

In: Journal of Optimization Theory and Applications, Vol. 180, No. 3, 2019, p. 1065–1086.

Research output: Contribution to JournalArticleAcademicpeer-review

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