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

Author

Listed:
  • André Casajus

    (HHL - Handelshochschule Leipzig - Graduate School of Management)

  • Rodrigue Tido Takeng

    (UNICAEN - Université de Caen Normandie - NU - Normandie Université, CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

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," Post-Print hal-04574752, HAL.
    • Handle: RePEc:hal:journl:hal-04574752
    DOI: 10.1007/s00182-024-00893-4
    Note: View the original document on HAL open archive server: https://hal.science/hal-04574752
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