Mathematical Problems in Engineering (2020-01-01)

Procedural Implementation and Axiomatization of the Weighted Nonseparable Cost Value

  • Hui Yang,
  • Wenna Wang,
  • Zhengsheng Ding

Journal volume & issue
Vol. 2020


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The paper defines a new value called the weighted nonseparable cost value (weighted-NSC value), which divides the nonseparable cost on the ground of an exogenous attached weight and compromises egalitarianism and utilitarianism of a value flexibly. First, we construct an optimization model to minimize the deweighted variance of complaint and define its optimal solution to be the weighted-NSC value. Second, a process is set up to acquire the weighted-NSC value, which enlarges the traditional procedural values. In the process, one player’s marginal contribution is divided up by all participants rather than merely restricted within his precursors. Lastly, adopting the weight in defining a value destructs the classical symmetry. This promotes the definition of ω-symmetry for the grand-marginal normalized game to defend against the effect of weight and axiomatically sculptures the weighted-NSC value. Dual dummifying player property is also applied to characterize the new defined value.