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Second-order productivity, second-order payoffs, and the Banzhaf value

Author

Listed:
  • André Casajus

    (HHL Leipzig Graduate School of Management
    Dr. Hops Craft Beer Bar)

  • Rodrigue Tido Takeng

    (Université de Caen Normandie, CREM, UMR 6211)

Abstract

First, we suggest and discuss second-order versions of properties for solutions for TU games used to characterize the Banzhaf value, in particular, of standardness for two-player games, of the dummy player property, and of 2-efficiency. Then, we provide a number of characterizations of the Banzhaf value invoking the following properties: (i) [second-order standardness for two-player games or the second-order dummy player property] and 2-efficiency, (ii) standardness for one-player games, standardness for two-player games, and second-order 2-efficiency, (iii) standardness for one-player games, [second-order standardness for two-player games or the second-order dummy player property], and second-order 2-efficiency. These characterizations also work within the classes of simple games, of superadditive games, and of simple superadditive games.

Suggested Citation

  • André Casajus & Rodrigue Tido Takeng, 2024. "Second-order productivity, second-order payoffs, and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 989-1004, September.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:3:d:10.1007_s00182-024-00893-4
    DOI: 10.1007/s00182-024-00893-4
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    References listed on IDEAS

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    More about this item

    Keywords

    TU game; Banzhaf value; Second-order marginal contributions; Second-order payoffs; Amalgamation;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

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