Аксиоматизация вектора Шепли в играх с априорными вероятностями образования коалиций

A new, generalized model of a cooperative game with transferable utility (TP game) is introduced and studied, in which, in addition to the characteristic function, two additional functions are used: relations between players and the probability of coalition formation, which reflect the main features of the interaction of people in specific groups. Various properties of the probability function are studied, and it is proved which of them are sufficient for its transformation into a probability measure. The generalized Shapley vector is defined for a new class of games as the mathematical expectation of a player from his marginal contribution to coalitions. Necessary and sufficient conditions are given for the generalized Shapley vector to completely coincide with the classical one introduced by Shapley himself. An axiomatization of value functions on a new class of games is proposed, which is also an extension of existing axioms in original TP games. It is proved that the (generalized) Shapley vector and only it corresponds to the introduced axioms.