Whose deletion does not affect your payoff? the difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value

Yoshio Kamijo, Takumi Kongo

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

Abstract

This study provides a unified axiomatic characterization method of one-point solutions for cooperative games with transferable utilities. Any one-point solution that satisfies efficiency, the balanced cycle contributions property (BCC), and the axioms related to invariance under a player deletion is characterized as a corollary of our general result. BCC is a weaker requirement than the well-known balanced contributions property. Any one-point solution that is both symmetric and linear satisfies BCC. The invariance axioms necessitate that the deletion of a specific player from games does not affect the other players' payoffs, and this deletion is different with respect to solutions. As corollaries of the above characterization result, we are able to characterize the well-known one-point solutions, the Shapley, egalitarian, and solidarity values, in a unified manner. We also studied characterizations of an inefficient one-point solution, the Banzhaf value that is a well-known alternative to the Shapley value.

Original languageEnglish
Pages (from-to)638-646
Number of pages9
JournalEuropean Journal of Operational Research
Volume216
Issue number3
DOIs
Publication statusPublished - 2012 Feb 1
Externally publishedYes

Keywords

  • Axiomatization
  • Banzhaf value
  • Egalitarian value
  • Game theory
  • Shapley value
  • Solidarity value

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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