Критерий непустоты эпсилон-ядер для нечетких игр с нетрансферабельной полезностью и вычислительные процедуры

Информатика и ее применения. 2022. Т. 16. № 3. С. 2–6.

Shvedov A. S.

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 solves is the core of a game 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 non-transferable utility. In this paper, the results are generalized in few directions. A problem of non-emptiness of the epsilon-core, which is somewhat more general than a problem of non-emptiness of the core, is studied. Games with fuzzy payoffs are considered. For some classes of games with non-transferable utility, possibility of construction of a computational scheme, which is similar with the computational scheme for games with transferable utility, is established.

Keywords: нечеткое множество, кооперативная игра, cooperative game, fuzzy set, epsilon-core, эпсилон-ядро, comprehensive set, исчерпывающее множество