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

Abstract

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.

Keywords: TU game, Shapley's value, axiomatics, probability of coalition formation

JEL Classification: C71, D70