The Myerson value for cooperative games on communication structure with fuzzy coalition

In the field of cooperative games there is an extensive literature that studies various situations of cooperation. Myerson (1977) introduced the communication structure which is an undirected graph describing the bilateral relationships among the players and the Myerson value of a game is obtained by taking the Shapley value of an auxiliary graph game on communication structure. Aubin (1981) proposed fuzzy cooperative games in which players have the possibility to cooperate with different participation levels. In this paper we consider cooperative games on communication structure with fuzzy coalition. The Myerson value and its individual rational revision are defined as the Shapley value of newly auxiliary graph games and discussed based on Choquet integral form and proportional form respectively. They are also characterized in terms of some extended component efficiency and fairness. Furthermore, by showing that the Myerson value is a fuzzy core allocation, the non-emptiness of the fuzzy core is verified for a graph game on communication structure with fuzzy coalition.