快速还是持久？战略投资要求的多面性
Quick or Persistent? Strategic Investment Demanding Versatility
AI总结：
本文分析了双寡头在不确定性下的投资动态模型，探讨了企业切换市场的策略，通过混合策略子博弈完美均衡证明了预emption和attrition均可能发生，并通过数值示例展示了投资在attrition和preemption区域的相对概率。
摘要：
本文分析了在双寡头中面临不确定性的投资动态模型，其中每家企业都有机会从当前市场切换到新市场。我们构建了混合策略下的子博弈完美均衡，并证明在典型均衡路径中，预emption和attrition均可发生。为了确定attrition区域，需要解决一个二维约束最优停止问题，我们刻画了状态空间中的非平凡停止边界。我们明确确定了attrition区域中的马尔可夫均衡停止率，并证明了最终预emption总是具有正概率，与确定性模型形成对比。基于模拟的数值示例展示了该模型并展示了投资在attrition和preemption区域的相对可能性。
英文摘要：
In this paper we analyse a dynamic model of investment under uncertainty in a duopoly, in which each firm has an option to switch from the present market to a new market. We construct a subgame perfect equilibrium in mixed strategies and show that both preemption and attrition can occur along typical equilibrium paths. In order to determine the attrition region a two-dimensional constrained optimal stopping problem needs to be solved, for which we characterize the non-trivial stopping boundary in the state space. We explicitly determine Markovian equilibrium stopping rates in the attrition region and show that there is always a positive probability of eventual preemption, contrasting the deterministic version of the model. A simulation-based numerical example illustrates the model and shows the relative likelihoods of investment taking place in attrition and preemption regions.
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