AI 中文总结
本研究构建整合CKLS需求不确定性等要素的连续时间进入威慑博弈，用路径积分控制方法刻画均衡，实证验证模型策略机制，为进入决策提供新计算方案。
AI 中文摘要
我们构建了一个连续时间的进入威慑博弈，其中市场需求遵循Chan-Karolyi-Longstaff-Sanders（CKLS）随机微分方程演化，允许均值回复和状态依赖波动率。拥有私人已知实力的在位企业会策略性地选择广告和促销支出，以影响潜在进入者的信念；而进入者则面临成本高昂且不可逆转的进入决策，会最优地等待直至市场条件适合参与。在动态斯塔克尔伯格框架内，贝叶斯学习、不对称信息、随机需求和策略性控制共同决定了进入与信号传递行为。我们采用费曼型路径积分控制公式，刻画了企业支出策略的马尔可夫纳什反馈均衡。本研究的贡献在于，将CKLS需求不确定性、私人信息、不可逆转进入、贝叶斯信念更新以及路径积分反馈控制整合到统一的连续时间进入威慑框架中，同时提供了一种替代直接汉密尔顿-雅可比-贝尔曼（HJB）方法的计算方案。我们利用2010-2024年Enterprise Products Partners和Targa Resources的收入数据对该框架进行实证说明，所得轨迹在性质上与模型预测一致，表现出持续性、不利冲击后的恢复以及与不同竞争地位相关的差异化反应，同时验证了模型在不确定性下的策略机制。
英文摘要
We develop a continuous-time entry-deterrence game in which market demand evolves according to the Chan-Karolyi-Longstaff-Sanders (CKLS) stochastic differential equation, allowing mean reversion and state-dependent volatility. An incumbent with privately known strength strategically chooses advertising and promotional expenditures to influence a potential entrant's beliefs, while the entrant faces a costly, irreversible entry decision and optimally waits until market conditions justify participation. Within a dynamic Stackelberg setting, Bayesian learning, asymmetric information, stochastic demand, and strategic controls jointly determine entry and signaling behavior. Using a Feynman-type path-integral control formulation, we characterize a Markovian Nash feedback equilibrium for the firms' expenditure strategies. Our contribution is to integrate CKLS demand uncertainty, private information, irreversible entry, Bayesian belief updating, and path-integral feedback control within a unified continuous-time entry-deterrence framework, while providing a computational alternative to direct Hamilton-Jacobi-Bellman (HJB) approach. We illustrate the framework empirically using 2010-2024 revenue data for Enterprise Products Partners and Targa Resources. The resulting trajectories are qualitatively consistent with the model's predictions, exhibiting persistence, recovery after adverse shocks, and distinct responses associated with different competitive positions, while supporting the model's strategic mechanisms under uncertainty.
Comments88 pages, 11 figures, 4 tables
