Uncertain Core for Coalitional Game with Uncertain Payos

Coalitional game deals with situations that involve cooperations among the players. There are dierent solution concepts such as core, Shapley value and nucleolus. This paper investigates uncertain coalitional game in which the payos are uncertain variables. Within the framework of uncertainty theory, two denitions of uncertain core are proposed. Meanwhile, a sucient and necessary condition is provided for nding the uncertain core. Finally, an example is provided for illustrating purpose.