The common revenue allocation based on modified Shapley value and DEA cross-efficiency

TL;DR

This paper proposes a novel revenue allocation method combining modified Shapley value, DEA cross-efficiency, and cooperative game theory to ensure fair distribution among alliance participants, with practical application to a bank network.

Contribution

It introduces a new allocation approach integrating DEA cross-efficiency and modified Shapley value, considering optimistic and pessimistic bounds for fair revenue sharing.

Findings

The method effectively allocates revenue based on contribution levels.

Application to a bank network demonstrates practical feasibility.

Provides upper and lower bounds for revenue distribution.

Abstract

How to design a fair and reasonable allocation plan for the common revenue of the alliance is considered in this paper. We regard the common revenue to be allocated as an exogenous variable which will not participate in the subsequent production process. The production organizations can cooperate with each other and form alliances. As the DEA cross-efficiency combines self- and peer-evaluation mechanisms, and the cooperative game allows fair negotiation among participants, we combine the cross-efficiency with the cooperative game theory and construct the modified Shapley value to reflect the contribution of the evaluated participant to the alliance. In addition, for each participant, both the optimistic and the pessimistic modified Shapley values are considered, and thus the upper and lower bounds of the allocation revenue are obtained, correspondingly. A numerical example is presented to illustrate the operation procedure. Finally, we apply the approach to an empirical application concerning a city commercial bank with 18 branches in China.