On the Effect of Bounded Rationality in Electricity Markets

TL;DR

This paper challenges the full rationality assumption in electricity market analysis by applying level-$k$ bounded rationality to a two-firm Cournot model with a social planner. It derives closed-form level-$k$ strategies, reveals that welfare is maximized when the planner is exactly one level smarter than the opponent, and shows that bounded rationality can both exceed and fall short of Nash equilibrium welfare depending on network constraints. It develops three planner strategies under different information conditions (optimal, expectation-maximizing, robust maximin) and demonstrates welfare gains via a utility-design approach that blends the planner’s payoff with the opponent’s. Numerical studies corroborate these insights, quantify information value, and derive the optimal cooperation level for welfare improvement, highlighting practical implications for policy design in constrained power networks.

Abstract

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.

Figures (12)

• Figure 1: A 3-bus network example.
• Figure 2: Other network topologies.
• Figure 3: The comparison of level-k performance and equilibrium performance.
• Figure 4: The effect of social planner's rationality level on social welfare performance.
• Figure 5: Social welfare comparison when assuming the summation of two firms' rationality levels remains the same.

Theorems & Definitions (48)

• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Lemma 4
• proof
• Theorem 1
• proof