  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.
