An energy provider faced with energy generation risks and a large homogeneous pool of customers designs its energy price as a time-varying function of a risk-related quantile of the total energy demand, which generalizes pricing through the mean of the total energy demand. In the infinite population limit, we model the pricing problem with a class of linear quadratic Gaussian quantilized mean field games. For these quantilized mean field games, we show existence and uniqueness of an equilibrium which reveals the price trajectory, as well as an approximate Nash property when the quantilized mean field game’s feedback control functions are applied to the large but finite game and the rate of convergence of the Nash deviation to zero as a function of the population size and the quantile is provided. Finally, the use of this class of quantilized mean field games is illustrated in the context of equivalent thermal parameter models for households heater and an energy provider using solar generation.

中文翻译：

---

一类线性二次高斯量化平均场博弈


面临能源发电风险和大量同质客户的能源供应商将其能源价格设计为总能源需求的风险相关分位数的时变函数，从而通过总能源需求的平均值来概括定价。在无限人口限制下，我们用一类线性二次高斯量化平均场博弈对定价问题进行建模。对于这些量化平均场博弈，我们展示了揭示价格轨迹的均衡的存在性和唯一性，以及当量化平均场博弈的反馈控制函数应用于大型但有限的博弈和收敛速度时的近似纳什性质提供了纳什偏差为零作为总体规模和分位数的函数。最后，在家庭加热器和使用太阳能发电的能源供应商的等效热参数模型的背景下说明了此类量化平均场游戏的使用。