Fixed cost allocation using asymmetrical core-Nash bargaining DEA game

Abstract

This paper introduces cooperative game theory into the data envelopment analysis (DEA) method for building a novel fixed cost allocation (FCA) approach from group and individual consciousness. We start by acknowledging the divergences of decision-making units (DMUs) and propose an asymmetrical Nash bargaining DEA game, where DMUs’ bargaining powers are defined through the functions of cross-efficiency and operation scale. However, the asymmetrical Nash bargaining solution is proposed from an individual perspective, without providing the theoretical support of full cooperation. To narrow this gap, we further introduce the core concept of a coalitional cooperative game into the built asymmetrical Nash bargaining DEA game, resulting in the asymmetrical core-Nash bargaining DEA game. The asymmetrical core-Nash bargaining solution is based on the common weights, with the properties of stability, fairness, Pareto-efficiency, and invariance to affine transformation. Furthermore, our proposed approach inherently ensures the uniqueness of the fixed cost scheme. Finally, numerical analysis and case study are provided to show the concrete application of the new method.