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

André Casajus () and Rodrigue Tido Takeng
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André Casajus: HHL Leipzig Graduate School of Management
Rodrigue Tido Takeng: Université de Caen Normandie, CREM, UMR 6211

International Journal of Game Theory, 2024, vol. 53, issue 3, No 12, 989-1004

Abstract: 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.

Keywords: TU game; Banzhaf value; Second-order marginal contributions; Second-order payoffs; Amalgamation; 91A12 (search for similar items in EconPapers)
JEL-codes: C71 D60 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00182-024-00893-4

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