A New Solution of Cooperative Games with Random Coalitional Payoffs

In this paper, a class of cooperative games with random payoffs is studied, a new solution which is called expected value based on players´ contributions for the coalitions they belong to is introduced. Meanwhile, its uncertainty is defined, and their formulas are introduced. Then the properties of expected value are studied, and some of them are proved in detail. In the end, an example is computed and the conclusion is made that players´ expected value and its uncertainty decreases while the scale of game augments, which is similar to the Shapley value in classic cooperative game theory.