Uncertain coalition structure game with payoff of belief structure.

The uncertain coalition structure game with payoff of belief structure (UCS game) is studied based on belief structures of D–S theory. This type of UCS games gives us the uncertainty by assigning the probability to the set composed of multiple risk situations. For the solution of UCS game, this UCS game is transferred into an interval-valued coalition structure game by the two-step method. As the value for the interval-valued UCS game, the uncertain Owen value is axiomatically characterized by Hukuhara difference. Because the uncertain Owen value does not exist, the α-risk Owen value is proposed for the general UCS games. The α-risk Owen value adopts a risk coefficient α to represent the risk tolerance of players, which is more realistic than the uncertain Owen value. Also, the payoff value of UCS game is decreasing with the increasing of risk coefficient α, and the allocation value for the UCS game is also decreasing with the increasing of risk coefficient α. The players can choose their allocation scheme according to their risk tolerance.