用样条逼近计算供给函数均衡
Computing Supply Function Equilibria via Spline Approximations
摘要：
供应函数均衡（SFE）是一种市场竞争模型，每个公司都提供一个价格和数量表来面对需求的不确定性，并已成功地应用于批发电力市场。然而，表征的SFE是困难的，无论是分析和数值。在本文中，我们首先提出了一个专门的算法容量约束的仿射成本的非对称双寡头市场。我们发现，解决一阶条件（一个系统的微分方程）使用样条逼近是等价于解决一个最小二乘问题，这使得算法非常有效。我们还建议使用样条作为一种方法来改善最近推出的通用算法，使平衡可以更容易和更快地找到较少的用户干预。我们证明了这两种算法的近似解的渐近收敛，并通过数值例子说明了它们的性能。
英文摘要：
The supply function equilibrium (SFE) is a model for competition in markets where each firm offers a schedule of prices and quantities to face demand uncertainty, and has been successfully applied to wholesale electricity markets. However, characterizing the SFE is difficult, both analytically and numerically. In this paper, we first present a specialized algorithm for capacity constrained asymmetric duopoly markets with affine costs. We show that solving the first order conditions (a system of differential equations) using spline approximations is equivalent to solving a least squares problem, which makes the algorithm highly efficient. We also propose using splines as a way to improve a recently introduced general algorithm, so that the equilibrium can be found more easily and faster with less user intervention. We show asymptotic convergence of the approximations to the true equilibria for both algorithms, and illustrate their performance with numerical examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
