Nonadditive Integration and Some Solutions of Cooperative Games

The paper proposes three non-additive integration schemes based on various extensions of integrable functions and nonadditive set functions to the corresponding symmetric powers of the original measurable spaces. Within the framework of the developed schemes, integral representations of some classical objects of the theory of cooperative games are given. A unified approach to the consideration of finite and infinite games is proposed. Particular attention is paid to the Shapley vector, the generalized Owen extension, and the support function of the core of a convex game.