🤖 AI Summary
本文通过结合CKLS需求不确定性、私人信息、不可逆进入决策等要素，利用贝叶斯信号传递和路径积分控制方法解决市场条件不确定下的进入决策问题。
📝 Abstract
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.