Analysis of Dual-channel Pricing and Utility Optimization under a Subsidy Mechanism

Government subsidies profoundly influence the pricing strategies and profit distribution of dual channels by altering channel cost structures and consumer choice behaviors, ultimately forming a complex landscape where online and offline channels coexist through both collaboration and competition. A dual-channel Stackelberg game model composed of the government, online retailers, offline retailers, and consumers was constructed. Differentiated subsidy mechanisms were introduced, and backward induction was employed to derive the equilibrium pricing strategies, channel effort levels, and consumer utilities. A threshold-based adjustment mechanism was proposed to reveal the indirect pathways through which subsidies influence channel choices and system coordination. Quantitative analysis of dual-channel pricing and coordination strategies was achieved via MATLAB-based numerical simulations. The results indicate that when channel effort costs are high, increased consumer preference for online channels drives online prices upward while pushing offline prices downward, with channel profits being simultaneously influenced by both the effort cost coefficient and cross-price elasticity. While moderate subsidies are found to enhance overall profits by reducing marginal costs, excessive online subsidies tend to trigger rapid channel cost escalation and erode system profits, whereas offline subsidies demonstrate stronger sustainability and stability. A critical point of diminishing returns is identified in channel advertising investment; although subsidies can delay the emergence of this threshold, efficiency losses resulting from excessive resource allocation require vigilance. Accordingly, governments are advised to rationally control online subsidy intensity to prevent the risk of cost escalation, fully leverage the sustained profit-enhancing effect of offline subsidies, and guide enterprises to identify the critical point of resource allocation for optimizing channel effort strategies. This study provides theoretical foundations and decision-making support for enterprises in coordinating channel conflicts under subsidy policies and for governments in formulating differentiated subsidy policies.