Shapley's Value and Its Axiomatization in Games with Prior Probabilities of Coalition Formation

A new model of TU game is introduced and studied. Here apart from the characteristic function, two additional functions are used: relations between the players and the probability of coalition formation. We suggest and study the sufficient properties of the probability function to transform it into a probability measure. The generalized Shapley's value is defined for a new class of games by analogy with the original Shapley approach. For the games under study, we give the axiomatization of value functions. It unambiguously characterizes the (generalized) Shapley's value.