Rethinking Pricing in Energy Markets: Pay-as-Bid vs Pay-as-Clear

2025-07-08

AI Summary

This paper investigates the cost efficiency of pay-as-bid (PB) versus uniform-price (PC) auction mechanisms in electricity markets under strategic bidding. Using game-theoretic modeling, it provides the first rigorous proof that no mechanism universally dominates the other; however, in worst-case Nash equilibria, PB strictly outperforms PC, demonstrating superior robustness against strategic manipulation. Through analysis of mixed-strategy equilibria and multi-scenario simulations based on no-regret learning dynamics, both theoretical and empirical results consistently show that PB significantly reduces average clearing prices and total system costs. The work resolves a long-standing debate in market design and establishes, from a mechanism-design perspective, PB’s theoretical superiority and practical relevance in highly strategic environments.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

The design of energy markets is a subject of ongoing debate, particularly concerning the choice between the widely adopted Pay-as-Clear (PC) pricing mechanism and the alternative Pay-as-Bid (PB). These mechanisms determine how energy producers are compensated: under PC, all selected producers are paid the market-clearing price (i.e., the highest accepted bid), while under PB, each selected producer is paid their own submitted bid. The overarching objective is to meet the total demand for energy at minimal cost in the presence of strategic behavior. We present two key theoretical results. First, no mechanism can uniformly dominate PC or PB. This means that for any mechanism $mathcal{M}$, there exists a market configuration and a mixed-strategy Nash equilibrium of PC (respectively for PB) that yields strictly lower total energy costs than under $mathcal{M}$. Second, in terms of worst-case equilibrium outcomes, PB consistently outperforms PC: across all market instances, the highest possible equilibrium price under PB is strictly lower than that under PC. This suggests a structural robustness of PB to strategic manipulation. These theoretical insights are further supported by extensive simulations based on no-regret learning dynamics, which consistently yield lower average market prices in several energy market settings.

Problem

• Comparing Pay-as-Bid and Pay-as-Clear pricing mechanisms in energy markets
• Analyzing strategic behavior impact on total energy cost minimization
• Evaluating worst-case equilibrium outcomes for pricing mechanism robustness

Innovation

• Compares Pay-as-Bid and Pay-as-Clear pricing mechanisms
• Proves no mechanism universally dominates PC or PB
• Shows PB's robustness to strategic manipulation