AI 中文总结
研究encroaching供应商如何通过Stackelberg博弈平衡双重角色，确定最优配置与定价。考虑客户需求响应中的价格替代及忠诚度，得出不同产品特性和客户回落率下的最优策略，还开发数值程序并发现两个意外结果。
AI 中文摘要
供应商常常通过运营内部生产单位同时继续向独立生产单位供货来向下游拓展。我们通过Stackelberg博弈研究了一个平衡这双重角色的encroaching供应商的最优配置，包括最优定价。集成供应商确定向外包生产单位收取的批发价格和自身产品的零售价格，外包单位做出最优响应。客户需求响应包含基于价格的替代（两个生产单位之间）和忠诚度（对单个单位）。对于联盟的最优选择，在客户忠诚度高和产品为奢侈品时，两个单位能盈利共存。而当产品变得必需时，最优策略取决于客户回落率。在低回落率下，联盟要么以最高价格维持共存，要么使外包单位保本运营；在高回落率下，最优做法是关闭内部单位或淘汰外包单位。我们得出了识别上述情况的两个因素。还开发了一个数值程序来确定任何给定参数集的最优状态。有两个令人惊讶的结果：外包单位更高的市场潜力可能成为其保本运营的原因；联盟可能发现让内部单位亏损运营是有益的，特别是对于既非高度必需也非奢侈品类别的产品。
英文摘要
Suppliers often encroach downstream by operating in-house production-units while continuing to supply independent production-units. We study the optimal configuration, including optimal pricing, for an encroaching supplier that balances these dual roles through a Stackelberg game. The integrated supplier determines the wholesale price charged to the outsourced production unit and the retail price of its own product, while the outsourced unit responds optimally. Customer demand-response incorporates both price-based substitutions (of the two production-units) and loyalty (towards individual units). With strong customer loyalty and luxury products, at the optimal choice for the coalition, both units co-exist profitably. In contrast, when the products become essential, the optimal strategy depends upon customer-fallback rates (fraction of the exiting production-unit's market that falls-back to other). Under low fallback, the coalition either sustains co-existence at maximum prices or disciplines the out-house to operate at break-even---with high fallback it is optimal to shut-down the in-house or eliminate the out-house---we derive two factors that identify the above. We further develop a numerical procedure to identify the optimal regime for any given set of parameters. Two surprising results are---higher market potential of the out-house can become a reason for it to operate at break-even---and the coalition may find it beneficial to operate its in-house at losses, particularly for products that are neither highly essential nor in the luxury category.
