Applications of cooperative games to business activities

Abstract

We show several applications of the cooperative game theory and the Shapley value to business activities. Among them we emphasize on the sharing of costs or profits. In the theoretical part, the axiomatic setting proposed by Shapley is described and the properties of the value are studied. It is also shown the usefulness of simple games to describe and analyze collective decision systems ruled by voting. Many of these systems admit a representation as weighted majority games, a class of simple games. One of the most interesting problems in this case is to define a measure of the power distribution among the agents involved in the system. This problem receives a nice solution by means of the Shapley–Shubik index of power, which is the restriction of the Shapley value to simple games.