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

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  • Driessen, Theo
  • Hu, Cheng-Cheng

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.

Suggested Citation

  • Driessen, Theo & Hu, Cheng-Cheng, 2009. "A note on equivalence of consistency and bilateral consistency through converse consistency," Games and Economic Behavior, Elsevier, vol. 65(2), pages 644-648, March.
    • Handle: RePEc:eee:gamebe:v:65:y:2009:i:2:p:644-648
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    References listed on IDEAS

    as
    1. Theo Driessen & Elena Yanovskaya, 2002. "Note On linear consistency of anonymous values for TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 601-609.
    2. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
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