A note on the nonuniqueness of the Equal Profit Method

When a set of players cooperate, they need to decide how the collective cost should be allocated among them. Cooperative game theory provides several methods or solution concepts, that can be used as a tool for cost allocation. In this note, we consider a specific solution concept called the Equal Profit Method (EPM). In some cases, a solution according to the EPM is any one of infinitely many solutions. That is, it is not always unique. This leads to a lack of clarity in the characterization of the solutions obtained by the EPM. We present a modified version of the EPM, which unlike its precursor ensures a unique solution. In order to illustrate the differences, we present some numerical examples and comparisons between the two concepts.