Dual-Channel Closed Loop Supply Chain Competition: A Stackelberg--Nash Approach

In many consumer electronics and appliance markets, manufacturers sell products through competing retailers while simultaneously relying on take-back programs to recover used items for remanufacturing. Designing such programs is challenging when firms compete on prices and consumers differ in their willingness to return products. Motivated by these settings, this paper develops a game theoretic framework to analyze pricing and take-back decisions in a dual-channel closed loop supply chain (CLSC) with two competing manufacturers and two competing retailers. Manufacturers act as Stackelberg leaders, simultaneously determining wholesale prices and consumer take-back bonuses, while retailers engage in Nash competition over retail prices. The model integrates three key elements: (i) segmented linear demand with cross-price effects, (ii) deterministic product returns, and (iii) an inertia responsiveness allocation mechanism governing the distribution of returned products between manufacturers. Closed form Nash equilibria are derived for the retailer subgame, along with symmetric Stackelberg equilibria for manufacturers. We derive a feasibility threshold for take-back incentives, identifying conditions under which firms optimally offer positive bonuses to consumers. The results further demonstrate that higher remanufacturing value or return rates lead the manufacturers to lower wholesale prices in order to expand sales and capture additional return volumes, while high consumer inertia weakens incentives for active collection. Numerical experiments illustrate and reinforce the analytical results, highlighting how consumer behavior, market structure and product substitutability influence prices, bonuses, and return volumes. Overall, the study provides managerial insights for designing effective take-back programs and coordinating pricing decisions in competitive circular supply chains.