This study revisits the strategic delegation game in a duopoly setting by generalizing the managerial incentives. Prior studies considered only the case when firms’ managers are incentivized by a linear combination of profits and a specific objective such as revenue or market share. By extending managerial incentives to a linear combination of profits and a quadratic function of firm outputs, we aim to determine the type of managerial incentives that can achieve the highest profit. We show the following results. First, in any managerial incentive structure, the equilibrium profit is equal to or greater than that in the revenue-oriented case. Second, when the coefficient of the squared term is equal to the coefficient of the product of both firms’ outputs, the equilibrium profit is equal to that in the revenue-oriented case. Third, the firm achieves the highest profit with a managerial incentive consisting of a linear combination of profits and functions that increase with the product of both firms’ outputs and decrease with its output but that do not depend on the squared term of its output. Fourth, the equilibrium profit is strictly less than that in the no delegation case.

这项研究通过概括管理激励措施，在双头垄断环境下重新审视了战略授权博弈。以前的研究仅考虑了通过利润和特定目标（例如收入或市场份额）的线性组合激励公司经理的情况。通过将管理人员激励扩展到利润和企业产出的二次函数的线性组合，我们的目标是确定可以实现最高利润的管理人员激励的类型。我们显示以下结果。首先，在任何管理激励结构中，均衡利润等于或大于以收入为导向的情况下的均衡利润。其次，当平方项的系数等于两家公司产出的乘积系数时，均衡利润等于以收入为导向的情况下的均衡利润。第三，公司通过管理激励获得最高利润，该激励由利润和函数的线性组合组成，线性组合随两家公司产出的乘积而增加，随其产出减少，但不依赖于其产出的平方项。第四，均衡利润严格小于无授权情况下的均衡利润。