Nash equilibrium is a common solution concept that captures strategic interaction in electricity market analysis. However, it requires a fundamental but impractical assumption that all market participants are fully rational, implying unlimited computational resources and cognitive abilities. To tackle the limitation, level-k reasoning is proposed and studied to model the bounded rational behaviors. In this paper, we consider a Cournot competition in electricity markets with two suppliers, both following level-k reasoning. One is a self-interested firm and the other serves as a benevolent social planner. First, we observe that the optimal strategy of the social planner corresponds to a particular rationality level, where being either less or more rational may both result in reduced social welfare. We then investigate the effect of bounded rationality on social welfare performance and find that it can largely deviate from that at the Nash equilibrium point. From the perspective of the social planner, we characterize optimal, expectation maximizing and robust maximin strategies, when having access to different information. Finally, by designing its utility function, we find that social welfare is better off if the social planner cooperates with or fights the self-interested firm. Numerical experiments further demonstrate and validate our findings.

翻译：纳什均衡是电力市场分析中捕捉策略互动的常用解概念。然而，它需要一个基本但不切实际的假设，即所有市场参与者都是完全理性的，这意味着无限的计算资源和认知能力。为克服这一局限，本文提出并研究了k层推理以建模有限理性行为。在本文中，我们考虑一个双供应商的电力市场古诺竞争模型，两个供应商均遵循k层推理。其中一个是自利型企业，另一个则作为仁慈的社会计划者。首先，我们观察到社会计划者的最优策略对应一个特定的理性层级，在该层级上，无论理性程度过高或过低都可能导致社会福利下降。随后，我们研究了有限理性对社会福利表现的影响，发现其可能显著偏离纳什均衡点的结果。从社会计划者视角出发，我们刻画了在获取不同信息时的最优策略、期望最大化策略以及鲁棒最大最小策略。最后，通过设计社会计划者的效用函数，我们发现当社会计划者选择与自利型企业合作或对抗时，社会福利状况均能得到改善。数值实验进一步验证了我们的研究结论。