A note on equivalence of consistency and bilateral consistency through converse consistency

Theo Driessen, Cheng-Cheng Hu

Research output: Contribution to journalArticle

Abstract

In the framework of (set-valued or single-valued) solutions for coalitional games with transferable utility, the three notions of consistency, bilateral consistency, and converse consistency are frequently used to provide axiomatic characterizations of a particular solution (like the core, prekernel, prenucleolus, Shapley value). Our main equivalence theorem claims that a solution satisfies consistency (with respect to an arbitrary reduced game) if and only if the solution satisfies both bilateral consistency and converse consistency (with respect to the same reduced game). The equivalence theorem presumes transitivity of the reduced game technique as well as difference independence on payoff vectors for two-person reduced games.

Original languageEnglish
Pages (from-to)644-648
Number of pages5
JournalGames and Economic Behavior
Volume65
Issue number2
DOIs
Publication statusPublished - 2009 Mar 1

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Converse consistency
Equivalence
Reduced game
Bilateral
Equivalence theorem
Axiomatic characterization
Coalitional games
Transferable utility
Shapley value
Transitivity

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics
  • Finance

Cite this

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A note on equivalence of consistency and bilateral consistency through converse consistency. / Driessen, Theo; Hu, Cheng-Cheng.

In: Games and Economic Behavior, Vol. 65, No. 2, 01.03.2009, p. 644-648.

Research output: Contribution to journalArticle

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