Existence of an Aumann–Maschler fuzzy bargaining set and fuzzy kernels in TU fuzzy games
Fuzzy Sets and Systems
In this paper, we first give fuzzy extensions of the well-known solution concepts of kernel and prekernel for a transferable utility (TU) game and establish the existence of fuzzy kernels in TU fuzzy games which generalizes the corresponding result for classical TU games by Davis and Maschler . We then prove that the fuzzy kernel is a subset of the fuzzy bargaining set in a TU fuzzy game, which gives the fuzzy counterpart of the corresponding fact for classical TU games by Davis and Maschler. As a consequence, we establish the existence of fuzzy Aumann–Maschler fuzzy bargaining sets for TU fuzzy games which generalizes the well-known existence theorem for bargaining sets by Aumann and Maschler and Peleg .
Link to Published Version
Liu, J., Liu, X., Huang, Y., & Yang, W. (2018). Existence of an Aumann–Maschler fuzzy bargaining set and fuzzy kernels in TU fuzzy games. Fuzzy Sets and Systems, 349J, 53–63. https://doi.org/10.1016/j.fss.2018.01.010