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

TL;DR

This paper compares Pay-as-Bid and Pay-as-Clear energy market mechanisms, revealing that PB is more robust to strategic behavior and often results in lower prices, supported by theoretical analysis and simulations.

Contribution

It provides the first theoretical comparison showing PB's robustness and lower worst-case prices relative to PC, with extensive simulation validation.

Findings

PB outperforms PC in worst-case equilibrium prices

No mechanism uniformly dominates the other

Simulations show lower average prices with PB

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.