Solutions for Non-Negatively Weighted Tu Games Derived from Extension Operators

We suggest two alternatives to the Lovász-Shapley value for non-negatively weighted TU games (Casajus and Wiese, 2017. Int. J. Game Theory 46, 295-310), the dual Lovász-Shapley value and the Shapley² value. Whereas the former is based on the Lovász extension operator for TU games (Lovász, 1983. Mathematical Programming: The State of the Art, Springer, 235--256; Algaba et al., 2004. Theory Decis. 56, 229-238), the latter two are based on extension operators that share certain economically plausible properties with the Lovász extension operator, the dual Lovász extension operator and the Shapley extension operator (Casajus and Kramm, 2021. Discrete Appl. Math. 294, 224-232), respectively