Playing with Peaks: A Game-Theoretic Comparison of Electricity Pricing Mechanisms

TL;DR

Problem: evaluate which peak-pricing mechanism best reduces peak demand in grids with flexible loads. Approach: a game-theoretic model of an electricity market with AP, CP, and a progressive mechanism PP, plus theoretical and simulation analysis under deterministic and stochastic baselines. Key findings: with deterministic baselines, CP never exceeds AP (P_CP ≤ P_AP); with stochastic baselines, AP can outperform CP; PP matches CP under deterministic baselines (P_CP = P_PP) and often outperforms CP under uncertainty (P_PP ≤ P_CP for many delta>1); simulations show PP is robust across distributions. Significance: results guide mechanism design for demand response by balancing coordination benefits and miscoordination risks, and point to progressive charges as a practical robust alternative.

Abstract

As electricity consumption grows, reducing peak demand--the maximum load on the grid--has become critical for preventing infrastructure strain and blackouts. Pricing mechanisms that incentivize consumers with flexible loads to shift consumption away from high-demand periods have emerged as effective tools, yet different mechanisms are used in practice with unclear relative performance. This work compares two widely implemented approaches: anytime peak pricing (AP), where consumers pay for their individual maximum consumption, and coincident peak pricing (CP), where consumers pay for their consumption during the system-wide peak period. To compare these mechanisms, we model the electricity market as a strategic game and characterize the peak demand in equilibrium under both AP and CP. Our main result demonstrates that with perfect information, equilibrium peak demand under CP never exceeds that under AP; on the other hand, with imperfect information, the coordination introduced by CP can backfire and induce larger equilibrium peaks than AP. These findings demonstrate that potential gains from coupling users' costs (as done in CP) must be weighed against these miscoordination risks. We conclude with preliminary results indicating that progressive demand cost structures--rather than per-unit charges--may mitigate these risks while preserving coordination benefits, achieving desirable performance in both deterministic and stochastic settings.

Figures (3)

• Figure 1: An electricity market with $T = 2$ periods and $N = 2$ Players. The baseline load is $b = (8, 4)$. The Players' consumption requirements and actions are $r_1 = r_2 = 12$ and $a_1 = (5, 7)$, $a_2 = (6, 6)$, respectively. Under anytime peak pricing, Player $1$ pays a demand charge for their consumption in period $2$, while under coincident peak pricing, they pay a demand charge for their consumption in period $1$.
• Figure 2: An electricity market with $T = 4$ periods and $N = 2$ Players with consumption requirements $r_1 = r_2 = 24$. The bottom plot shows the baseline load $b^t$, which is independently drawn from a scaled triangular distribution with mode $4$ if $t$ is odd or $8$ if $t$ is even. The top plot shows the Players' equilibrium actions for coincident peak (darker shade) and anytime peak (lighter shade) pricing, along with a worst-case disturbance realization (dark orange); observe that the peak is larger under coincident peak pricing.
• Figure 3: Comparisons of anytime, coincident, and progressive peak pricing in an electricity market with $T = 4$ periods and $N = 2$ Players with consumption requirements $r_1 = r_2 = 24$. We consider three different baseline load distributions: conditional uniform (left), Beta (center), and triangular (right). The equilibrium peak demand (lavender) is shown for each distribution under progressive peak pricing for various values of $\delta$ (top row); observe that as $\delta$ increases, the peak decreases. The equilibrium peak demand under coincident peak pricing is the first bar in each plot (darker shade), and the equilibrium peak demand under anytime peak pricing is $24$ for all three scenarios (dashed purple line).

Theorems & Definitions (6)

• Definition 1
• Proposition 1
• Definition 2
• Theorem 2
• Theorem 3
• Proposition 4