On the Effect of Bounded Rationality in Electricity Markets

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.