Cooperative Situations: Representations, Games and Cost Allocations

Abstract

A cooperative situation is characterized by a group of players choosing from a set of alternatives, where each alternative results in a joint cost. In this paper we assume that an alternative with minimum total cost will be chosen and we focus on the corresponding cost allocation problem by providing a procedure to associate a given cooperative situation with an appropriate transferable utility game in a methodical way. The basis of this procedure is the introduction of an order problem representation of the cooperative situation, which we use to individualize the joint costs. For each order problem representation we also define a generalized Bird allocation which we show to be in the core of the corresponding appropriate transferable utility game. We apply the procedure to both existing and new classes of cooperative situations: sequencing situations without initial ordering, maintenance problems, minimum cost spanning tree situations, permutation situations without initial allocation, public congestion network situations, traveling salesman problems, shared taxi problems and traveling repairman problems.