Second-order productivity, second-order payoffs, and the Banzhaf value - André Casajus; Rodrigue Tido Takeng (International Journal of Game Theory, 2024)
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.
Additional information: C71;D60
Keywords: 330; TU game; Banzhaf value; Second-order marginal contributions; Second-order payoffs; Amalgamation