Stochastic differential game in the closed-loop supply chain with fairness concern retailer

Abstract

This paper addresses the stochastic used-product return problem in a closed-loop supply chain consisting of one manufacturer and one retailer concerned with fairness. We resolve the equilibrium feedback control strategies with no fairness concern retailer, gap fairness concern retailer, and self-due fairness concern retailer. We find only under a specific condition, the feedback Markov equilibrium exists, and the expected return rate would approach to the stable state, regardless of the fairness type the retailer is. The equilibrium prices are decreasing over the return rate, and the equilibrium collecting control strategy is increasing over the return rate. The increasing of stochastic disturbance intensity can be beneficial to the supply chain members. The manufacturer should shift profit to the retailer since the retailer is fairness concern. By the comparison analysis, we find the gap fairness concern retailer is more aggressive, while the self-due fairness concern retailer is more reasonable for both the manufacturer and the retailer. Furthermore, we design a hybrid coordinate contract for the manufacturer to coordinate with the retailer.