We study competition in a dual-channel supply chain in which a single supplier sells a single product through its own direct channel and through two different duopolistic retailers. The two retailers have three competitive behaviour patterns: Cournot, Collusion and Stackelberg. Three models are respectively constructed for these patterns, and the optimal decisions for the three patterns are obtained. These optimal solutions are compared, and the effects of certain parameters on the optimal solutions are examined for the three patterns by considering two scenarios: a special case and a general case. In the special case, the equilibrium supply chain structures are analysed, and the optimal quantity and profit are compared for the three different competitive behaviours. Furthermore, both parametric and numerical analyses are presented, and some managerial insights are obtained. We find that in the special case, the Stackelberg game allows the supplier to earn the highest profit, the retailer playing the Collusion game makes the supplier earn the lowest profit, and the Stackelberg leader can gain a first-mover advantage as to the follower. In the general case, the supplier can achieve a higher profit by raising the maximum retail price or holding down the self-price sensitivity factor.

中文翻译：

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考虑行为不同的双寡头零售商的双渠道供应链竞争

我们研究了双渠道供应链中的竞争，其中单个供应商通过自己的直接渠道以及通过两个不同的双寡头零售商出售单个产品。两家零售商具有三种竞争行为模式：古诺，共谋和斯塔克尔贝格。针对这些模式分别构建了三个模型，并获得了针对这三种模式的最优决策。比较这些最优解，并通过考虑两种情况（特殊情况和一般情况）来检查三种模式下某些参数对最优解的影响。在特殊情况下，分析了均衡供应链结构，并比较了三种不同竞争行为的最优数量和利润。此外，还提供了参数分析和数值分析，并获得一些管理见解。我们发现在特殊情况下，Stackelberg游戏可以使供应商获得最高利润，玩Collusion游戏的零售商可以使供应商获得最低利润，并且Stackelberg领导者可以获得追随者的先发优势。在一般情况下，供应商可以通过提高最高零售价或压低自我价格敏感性因素来获得更高的利润。