A New Algorithm for Constructing a Characteristic Function

Abstract The following paper studies the problem of fairly sharing jointly generated revenues. Firstly, we construct a characteristic function of the joint production. We provide a new approach to constructing the characteristic function of a TU game. For the computation of the game we interpret the constructed characteristic function as a vector and we describe an algorithm for constructing them. Secondly, we provide an empirical application to the Premier League, the English Football League. Therefore, we use the Shapley value and an egalitarian solution to identify a fair share in a TU game with a large number of players. We show that the Shapley value of one of our models yields outcomes close to the current Premier League allocation.