A condition for non-emptiness of the epsilon-core of a nontransferable utility fuzzy game and computational schemes

Zhao (2001) suggested a new condition for non-emptiness of the core of a cooperative game. At first, a necessary and sufficient condition was found by Zhao for a particular case of games with transferable utility. In this case, as was shown by Zhao, the condition can be easily used for construction of a computational scheme which decides if the core of a game is empty or non-empty and gives imputations belonging to the core if the core is non-empty. Then, the condition was generalized by Zhao for games with nontransferable utility. In this paper, the results are generalized in few directions. The problem of non-emptiness of the epsilon-core which is somewhat more general than the problem of non-emptiness of the core is studied. Games with fuzzy payoffs are considered. For some classes of games with nontransferable utility, possibility of construction of a computational scheme which is similar to the computational scheme for games with transferable utility is established.