Gain measurement and payoff allocation for the internal resource sharing based on DEA approach

As an effective strategy for improving resource utilization and increasing profits, resource sharing exists not only between independent systems but also between sub-systems in the same system. Many researchers study the external cooperation among independent systems through building Data Envelopment Analysis (DEA) games. However, they do not consider the internal resource sharing between sub-systems and think players possess the same risk attitudes for gain and loss when allocating potential gains, which may be inconsistent with practice. To fill these gaps and answer the question: "For the system containing multiple independent DMUs, how to measure and allocate the potential gains derived from the internal resource sharing", we construct an internal resource-sharing DEA game based on the DEA approach and propose a novel payoff allocation method considering players' bounded rationality. Our proposed game is super-additive, monotone, not necessarily convex, and has a non-empty core. By the proposed payoff method, we obtain a unique, efficient, stable, and fair payoff allocation. Finally, to validate our method, we conduct a numerical experiment with inland transportation systems and compare the novel payoff allocation method with the core, Shapley value, and nucleolus.