Allocating fixed costs using multi-coalition epsilon equilibrium

In this paper, a multi-coalition fixed cost allocation (MCFCA) is considered. The problem is solved using epsilon equilibrium (also called e-Nash equilibrium) concept and data envelopment analysis framework. The MCFCA epsilon equilibrium involves tradeoffs between satisfying objectives of cooperative coalitions and conflicts arising from inter-coalitions objectives. First, it is shown that a simple single objective fixed cost allocation problem is an easy problem to solve and multiple solutions satisfying traditional Nash equilibrium can be trivially obtained. Second, the MCFCA problem is proposed by using different coalitions' objective criteria highlighted in previous studies. Third, the MCFCA problem is solved using a genetic algorithm (GA) procedure. Several real-world datasets from different domains are used to test the procedure and two different types of GA fitness functions - raw and scaled - are used. The results indicate that different fitness functions perturb solutions around the epsilon equilibrium so that multiple statistically similar solutions can be obtained to aid subjective managerial solution selection among multiple similar solutions.