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Nash equilibrium is a common solution concept that captures the strategic interaction in electricity market analysis. However, it requires a fundamental but impractical assumption that all market participants are fully rational, which implies 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 is to be of a particular rationality level. Being less or more rational may both result in reduced social welfare. Then, we investigate the effect of bounded rationality on social welfare performance and find that it could largely deviate from that at the Nash equilibrium point. Finally, we characterize optimal, mean maximizing and max-min strategies for the benevolent social planner, when having access to different information. The numerical experiments further demonstrate and validate our findings.
Yi et al. (Mon,) studied this question.