Cooperative Benefit and Cost Games under Fairness Concerns


1 Industrial Engineering, IIslamic Azad University

2 Industrial Engineering, University of Tehran

3 Industrial Engineering, South Tehran Branch, Islamic Azad University


Solution concepts in cooperative games are based on either cost games or benefit games. Although cost games and benefit games are strategically equivalent, that is not the case in general for solution concepts. Motivated by this important observation, a new property called invariance property with respect to benefit/cost allocation is introduced in this paper. Since such a property can be regarded as a fairness criterion in cooperative games when deciding on choosing the solution concepts in coordination contracts, it is crucially important for players to check if the solution concepts available in contract menu possesses this property. To this end, we showed that some solution concepts such as the Shapley value, and the  -value satisfy invariance property with respect to benefit/cost allocation but some others such as Equal Cost Saving Method (ECSM) and Master Problem variant I ( ), do not. Furthermore, a measure for fairness with respect to equitable payoffs and utility is defined and related to invariance property. To validate the proposed approach, a numerical example extracted from the existing literature in benefit/cost cooperative games is solved and analyzed. The results of this research can be generalized for all solution concepts in cooperative games and is applicable for n-person games.