论文标题
竞争与合作：一类可解决的平均场脉冲控制问题
Competition versus Cooperation: A class of solvable mean field impulse control problems
论文作者
论文摘要
我们讨论了一类明确的经济解释的明确解决平均现场类型控制问题/平均现场游戏。更确切地说，我们考虑长期平均脉冲控制问题，其基本的一般一维扩散过程是由自然资源管理中最佳收获问题所激发的。我们通过允许使用平均场结构来依赖市场状况来扩展经典的随机浮士特模型。在竞争性的市场模型中，我们证明，在自然条件下，存在阈值类型的均衡策略，此外，明确特征了阈值。如果代理人彼此合作，我们将面临平均场类型控制问题。使用Lagrange类型参数，我们证明此非标准脉冲控制问题的优化器也是阈值类型的，并且表征了最佳阈值。此外，我们比较解决方案并说明了一个示例中的发现。
We discuss a class of explicitly solvable mean field type control problems/mean field games with a clear economic interpretation. More precisely, we consider long term average impulse control problems with underlying general one-dimensional diffusion processes motivated by optimal harvesting problems in natural resource management. We extend the classical stochastic Faustmann models by allowing the prices to depend on the state of the market using a mean field structure. In a competitive market model, we prove that, under natural conditions, there exists an equilibrium strategy of threshold-type and furthermore characterize the threshold explicitly. If the agents cooperate with each other, we are faced with the mean field type control problem. Using a Lagrange-type argument, we prove that the optimizer of this non-standard impulse control problem is of threshold-type as well and characterize the optimal threshold. Furthermore, we compare the solutions and illustrate the findings in an example.
