Fixed cost and minimum compensation allocations in two-stage systems: A DEA-dual game framework

Abstract

Though data envelopment analysis (DEA) is widely utilized in two-stage systems for fixed cost allocation, it often overlooks the payoffs of decision-making units (DMUs) deriving from undertaking the cost and receiving compensation. This paper puts forward a dual game approach to determine the Nash equilibrium-based fixed cost and minimum total compensation allocations in two-stage systems. The dual game involves the competition game among DMUs engaging in cost and compensation allocations and the non-cooperation and cooperation games between two stages. The Nash equilibrium allocation under the non-cooperation game maximizes the payoffs of DMUs' two stages sequentially, while the Nash equilibrium allocation under the cooperation game maximizes the payoffs of DMUs' two-stage systems simultaneously. To ensure all DMUs are efficient in the Nash equilibrium allocations, the possible sets of allocations under both cooperation and non-cooperation games between two stages maximizing both the payoffs and efficiencies of all DMUs are proved to be always non-empty. Furthermore, minimum total compensation allocations are obtained from these possible sets respectively. Finally, an application case study is conducted to demonstrate the practical application and benefits of the proposed approach.