标题： 一种用于容量扩展建模的平均场博弈 显示英文标题

标题： A Mean Field Game for Capacity Expansion Modeling

摘要： 本文研究了可再生能源电力生产者在竞争性市场中的最优投资行为，其中价格和安装成本均受到整个行业活动的影响。 我们使用一个均值场博弈框架来建模由此产生的拥挤效应，捕捉大量异质生产者之间的战略互动。 均衡动态通过一组耦合的哈密顿-雅可比-贝尔曼方程和福克-普朗克方程进行表征，这些方程描述了一个代表性生产者的价值函数以及安装容量分布随时间的变化。 我们分析了该模型的确定性和随机版本，在可处理的情况下提供了分析见解，并开发了数值方法来近似一般解。 模拟结果展示了总体投资如何对变化的市场条件、成本结构和外生生产率冲击做出反应。 显示英文摘要

摘要： This paper studies the optimal investment behavior of renewable electricity producers in a competitive market, where both prices and installation costs are influenced by aggregate industry activity. We model the resulting crowding effects using a mean field game framework, capturing the strategic interactions among a continuum of heterogeneous producers. The equilibrium dynamics are characterized via a coupled system of Hamilton-Jacobi-Bellman and Fokker-Planck equations, which describe the value function of a representative producer and the evolution of the distribution of installed capacities over time. We analyze both deterministic and stochastic versions of the model, providing analytical insights in tractable cases and developing numerical methods to approximate the general solution. Simulation results illustrate how aggregate investment responds to changing market conditions, cost structures, and exogenous productivity shocks.