The Nash Equilibrium (NE) estimation in bidding games of electricity markets is the key concern of both generation companies (GENCOs) for bidding strategy optimization and the Independent System Operator (ISO) for market surveillance. However, existing methods for NE estimation in emerging modern electricity markets (FEM) are inaccurate and inefficient because the priori knowledge of bidding strategies before any environment changes, such as load demand variations, network congestion, and modifications of market design, is not fully utilized. In this paper, a Bayes-adaptive Markov Decision Process in FEM (BAMDP-FEM) is therefore developed to model the GENCOs' bidding strategy optimization considering the priori knowledge. A novel Multi-Agent Generative Adversarial Imitation Learning algorithm (MAGAIL-FEM) is then proposed to enable GENCOs to learn simultaneously from priori knowledge and interactions with changing environments. The obtained NE is a Bayesian Nash Equilibrium (BNE) with priori knowledge transferred from the previous environment. In the case study, the superiority of this proposed algorithm in terms of convergence speed compared with conventional methods is verified. It is concluded that the optimal bidding strategies in the obtained BNE can always lead to more profits than NE due to the effective learning from the priori knowledge. Also, BNE is more accurate and consistent with situations in real-world markets.

翻译：电力市场竞价博弈中的纳什均衡估计是发电公司优化报价策略及独立系统运营商进行市场监管的关键问题。然而，现有方法在估计新兴现代电力市场中的纳什均衡时存在精度不足与效率低下问题，其根源在于未充分利用环境变化（如负荷需求波动、网络阻塞及市场设计调整）前的报价策略先验知识。为此，本文首先构建了适用于新兴现代电力市场的贝叶斯自适应马尔可夫决策过程，用以建模考虑先验知识的发电公司报价策略优化。进而提出一种新颖的多智能体生成对抗模仿学习算法，使发电公司能够同时从先验知识及与动态环境的交互中学习。由此获得的纳什均衡即为融合前序环境先验知识的贝叶斯纳什均衡。案例研究表明，该算法在收敛速度上优于传统方法。结论指出，由于有效利用了先验知识，贝叶斯纳什均衡中的最优报价策略总能带来高于纳什均衡的收益，且该均衡更能准确反映真实市场情境。