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arxiv: 2605.16794 · v1 · pith:PAQSBNM6new · submitted 2026-05-16 · 📡 eess.SY · cs.SY

Modeling Coincident Peak Pricing in Electricity Markets: Challenges and Peak Shaving Effectiveness

Qian Zhang , Sadie Zhao , Lucy Diao , Conleigh Byers , Yiling Chen , Derya Cansever , Le Xie This is my paper

Pith reviewed 2026-05-19 21:17 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords coincident peak pricingpeak shavingload shiftinggame theoryelectricity marketsERCOTbest-response dynamicsfictitious play
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The pith

Fictitious-play dynamics in a game model of coincident peak pricing reliably reduce system peaks, while best-response dynamics can increase them under tight capacity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper builds a behavioral game-theoretic framework to model how electricity consumers shift their loads in response to coincident peak pricing, a method used to allocate capacity costs based on usage at peak times. It compares two ways consumers might update their decisions: best-response dynamics, reacting to current conditions, and fictitious-play dynamics, based on historical averages. Simulations using ERCOT peak-day data show that fictitious play consistently lowers overall system peaks, whereas best response leads to more variable results and can actually raise peaks when capacity is limited. The analysis also finds that allowing finer adjustments in load and using certain price signals to avoid herding behavior improves outcomes, while the total number of participants matters less if total flexibility stays the same. These insights matter for designing electricity markets that encourage peak shaving without unintended consequences.

Core claim

Using a nonlinear cost-allocation model coupled with day-ahead and real-time decision processes, the paper establishes that fictitious-play dynamics reliably reduce system peaks in coincident peak pricing, in contrast to best-response dynamics which are more variable and can increase peaks under tight-capacity conditions. Finer action resolution improves peak shaving, participant numbers are neutral at fixed aggregate flexibility, and smoothed or diverse signals outperform herding-inducing ones.

What carries the argument

A behavioral game-theoretic framework coupling a nonlinear cost-allocation model with one-shot day-ahead and sequential real-time decision processes under best-response and fictitious-play update rules.

If this is right

  • Finer action resolution improves peak shaving.
  • The number of participants is largely neutral when aggregate flexibility is fixed.
  • Smoothed information signals enhance coordination and reduce peaks.
  • Response-aware or diverse signals improve peak shaving compared to those causing herding.
  • System operators can enhance outcomes by broadcasting smoothed CP signals and setting minimum controllable-capacity thresholds.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The relative advantage of fictitious-play over best-response may extend to other cost-allocation mechanisms in networked resource markets.
  • Real deployments could combine CP pricing with granular control technologies to test whether the simulated gains in peak reduction materialize.
  • Signal design choices might interact with other demand-response programs, potentially multiplying or diluting the coordination benefits identified here.

Load-bearing premise

Real consumers update their load-shifting decisions according to the modeled best-response or fictitious-play dynamics rather than other behavioral patterns.

What would settle it

Field observations from an ISO like ERCOT showing increased peaks after consumers respond in a best-response manner during tight-capacity periods would challenge the reliability of FPD over BRD.

Figures

Figures reproduced from arXiv: 2605.16794 by Conleigh Byers, Derya Cansever, Le Xie, Lucy Diao, Qian Zhang, Sadie Zhao, Yiling Chen.

Figure 1
Figure 1. Figure 1: The energy price (red) and demand baseline (black) [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of the system peak under BRD and FPD [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Final demand curves under BRD and FPD (continuous [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Final peak reduction versus the number of players for [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: BRD peak dynamics under different flexibility levels [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Fine-grained action library for a single agent: [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Peak dynamics under coarse (dotted) and fine (solid) [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: System demand profiles under Naive (red solid) vs. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Peak reduction sensitivity to population awareness level [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The peak reduction under different numbers of players [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
read the original abstract

Coincident Peak (CP) pricing is widely used in U.S. electricity markets to allocate capacity and transmission costs. This paper develops a behavioral game-theoretic framework for CP-driven load shifting that couples a nonlinear cost-allocation model with day-ahead (one-shot) and real-time (sequential-learning) decision processes. We examine two update rules, namely best-response dynamics (BRD) and fictitious-play dynamics (FPD), across continuous and finite action spaces to quantify how flexibility, action resolution, and participation influence peak outcomes. Using ERCOT peak-day data, we find that FPD reliably reduces system peaks, whereas BRD is more variable and can increase peaks under tight-capacity conditions. Finer action resolution improves peak shaving, while the number of participants is largely neutral when aggregate flexibility is fixed. Meanwhile, information-provider signals can induce herding, whereas response-aware or diverse signals improve peak shaving. These results highlight both the potential and limits of CP pricing: smoothing information and enabling granular control are as important as the amount of available flexibility. The framework offers practical guidance for system operators and consumers: For ISOs, broadcasting smoothed CP signals and setting minimum controllable-capacity thresholds enhance coordination. For consumers, greater flexibility and finer control resolution improve both cost savings and peak-shaving performance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper develops a behavioral game-theoretic framework coupling a nonlinear coincident-peak cost-allocation model with best-response dynamics (BRD) and fictitious-play dynamics (FPD) for day-ahead and real-time load-shifting decisions. Simulations on ERCOT peak-day data are used to compare peak-shaving performance under varying flexibility, action resolution, participation, and signal designs, concluding that FPD reliably reduces peaks while BRD is more variable and can increase peaks under tight capacity.

Significance. If the modeled update rules capture actual consumer behavior, the results provide concrete guidance on CP pricing design, particularly the value of smoothed signals and granular control. The distinction between BRD and FPD and the use of real ERCOT data are strengths that could inform ISO practice, though the findings remain conditional on the behavioral assumptions.

major comments (2)
  1. [§4 (Numerical Experiments and ERCOT Case Study)] The central empirical-style claim (FPD reliably reduces peaks while BRD can increase them under tight capacity) is obtained from forward simulations that assume consumers follow exactly the BRD or FPD update rules described in the framework. No calibration to observed ERCOT consumer responses, no sensitivity analysis to alternative behavioral rules (myopic thresholds, delayed response), and no validation against actual load data are reported, rendering the peak-shaving distinction sensitive to this untested modeling choice.
  2. [§3.2 (Real-time Sequential Learning Dynamics)] The nonlinear cost-allocation model and its coupling to the iterative dynamics are load-bearing for all reported outcomes, yet the manuscript provides insufficient detail on convergence criteria, step-size selection, and how equilibria are identified in the continuous versus finite action spaces.
minor comments (2)
  1. [§4.3 (Results)] Simulation results lack error bars, confidence intervals, or sensitivity tables with respect to the aggregate-flexibility parameter, making it difficult to judge robustness of the reported peak reductions.
  2. [Abstract] The abstract states that 'the number of participants is largely neutral when aggregate flexibility is fixed,' but the corresponding figure or table is not referenced, and the precise definition of 'neutral' (e.g., change in peak < X %) is not given.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the detailed and constructive comments. The feedback highlights important aspects of the behavioral assumptions and technical details in our framework. We address each major comment below, clarifying the scope of our simulation study and outlining specific revisions to improve clarity and transparency.

read point-by-point responses

  1. Referee: [§4 (Numerical Experiments and ERCOT Case Study)] The central empirical-style claim (FPD reliably reduces peaks while BRD can increase them under tight capacity) is obtained from forward simulations that assume consumers follow exactly the BRD or FPD update rules described in the framework. No calibration to observed ERCOT consumer responses, no sensitivity analysis to alternative behavioral rules (myopic thresholds, delayed response), and no validation against actual load data are reported, rendering the peak-shaving distinction sensitive to this untested modeling choice.

    Authors: We agree that the reported outcomes are conditional on the specific behavioral update rules (BRD and FPD) and that the study does not include empirical calibration or validation against observed ERCOT consumer responses. Our framework is a behavioral game-theoretic exploration designed to illustrate how different learning dynamics can affect peak-shaving outcomes under CP pricing, rather than a predictive model of actual consumer behavior. The contrast between FPD and BRD is intended to demonstrate the sensitivity of results to behavioral assumptions, which itself provides guidance on the risks of assuming myopic best-response behavior in practice. In the revision, we will add a dedicated limitations subsection in the discussion that explicitly acknowledges the untested nature of the dynamics, the absence of calibration to real load-shifting data, and the value of future empirical work. We will also incorporate limited sensitivity checks to alternative rules (e.g., simple myopic threshold responses) within the existing simulation setup. Full calibration and validation against disaggregated ERCOT consumer data is not feasible in this revision, as it would require proprietary individual-level response datasets. revision: partial

  2. Referee: [§3.2 (Real-time Sequential Learning Dynamics)] The nonlinear cost-allocation model and its coupling to the iterative dynamics are load-bearing for all reported outcomes, yet the manuscript provides insufficient detail on convergence criteria, step-size selection, and how equilibria are identified in the continuous versus finite action spaces.

    Authors: We thank the referee for pointing out the need for greater implementation detail. In the revised manuscript we will expand §3.2 with explicit statements of the convergence criteria (e.g., strategy change below a numerical tolerance), the step-size rules used for both continuous and discrete updates, and the precise procedures for locating equilibria: fixed-point iteration for the continuous case and exhaustive best-response mapping for the finite-action case. We will also include pseudocode and additional equations clarifying the coupling between the nonlinear cost-allocation function and the iterative dynamics. revision: yes

standing simulated objections not resolved
  • Full calibration to observed ERCOT consumer responses and validation against actual load-shifting data, which would require access to proprietary disaggregated consumer datasets not available for this study.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper constructs a game-theoretic model coupling a nonlinear CP cost-allocation function with explicitly defined behavioral update rules (best-response dynamics and fictitious-play dynamics) and then runs forward simulations on external ERCOT peak-day data. Peak-shaving outcomes are generated by iterating these stated dynamics rather than fitting any parameters to reproduce target peak values or deriving results tautologically from the inputs. No self-citations, uniqueness theorems, or ansatzes are invoked as load-bearing steps in the provided text, and the central empirical-style claims rest on the simulation outputs under the openly stated behavioral assumptions. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on behavioral assumptions about how agents update strategies and on the accuracy of the nonlinear cost-allocation model; these are not derived from first principles but selected as modeling choices.

free parameters (1)
  • aggregate flexibility
    Fixed in analyses to isolate effects of participation and resolution; value not specified in abstract.
axioms (1)
  • domain assumption Consumers follow best-response or fictitious-play update rules in day-ahead and real-time decisions
    Invoked to define the sequential decision processes in the framework.

pith-pipeline@v0.9.0 · 5776 in / 1331 out tokens · 62452 ms · 2026-05-19T21:17:12.161853+00:00 · methodology

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Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages

  1. [1]

    Incentive properties of coincident peak pricing,

    R. Baldick, “Incentive properties of coincident peak pricing,”Journal of Regulatory Economics, vol. 54, no. 2, pp. 165–194, 2018

    work page 2018

  2. [2]

    Manual M-20: ISO New England Manual for the Forward Capacity Market (FCM), Revision 27,

    ISO New England Inc., “Manual M-20: ISO New England Manual for the Forward Capacity Market (FCM), Revision 27,” April 2023, effective date: April 6, 2023. [Online]. Avail- able: https://www.iso-ne.com/static-assets/documents/2023/04/manual 20 forward capacity market rev27 2023 04 06.pdf

    work page 2023

  3. [3]

    Priorities for the evolution of an energy-only electricity market design in ercot,

    W. W. Hogan and S. Pope, “Priorities for the evolution of an energy-only electricity market design in ercot,”FTI Consulting, 2017

    work page 2017

  4. [4]

    Demand responses in ercot,

    P. Du, N. Lu, and H. Zhong, “Demand responses in ercot,” inDemand Response in Smart Grids. Springer, 2019, pp. 85–119

    work page 2019

  5. [5]

    Re- view Transmission Access Charge Structure: Revised Straw Proposal,

    California Independent System Operator (CAISO), “Re- view Transmission Access Charge Structure: Revised Straw Proposal,” April 4 2018, accessed: 2025- 08-10. [Online]. Available: https://www.caiso.com/Documents/ RevisedStrawProposal-ReviewTransmissionAccessChargeStructure.pdf

    work page 2018

  6. [6]

    Load Forecast vs. Actual: Current Day,

    Electric Reliability Council of Texas (ERCOT), “Load Forecast vs. Actual: Current Day,” 2025. [Online]. Available: https://www.ercot. com/content/cdr/html/loadForecastVsActualCurrentDay.html

    work page 2025

  7. [7]

    Overview of demand response in ercot,

    K. ¨Ogelman, “Overview of demand response in ercot,” Electric Reliability Council of Texas (ERCOT), April 2023. [On- line]. Available: https://www.ercot.com/files/docs/2023/05/19/ERCOT Demand Response Summary Spring 2023-update.pdf

    work page 2023

  8. [8]

    Predicting peak- demand days in the ontario peak reduction program for large con- sumers,

    Y . H. Jiang, R. Levman, L. Golab, and J. Nathwani, “Predicting peak- demand days in the ontario peak reduction program for large con- sumers,” inProceedings of the 5th international conference on Future energy systems, 2014, pp. 221–222

    work page 2014

  9. [9]

    Analyzing the impact of the 5cp ontario peak reduction program on large consumers,

    ——, “Analyzing the impact of the 5cp ontario peak reduction program on large consumers,”Energy policy, vol. 93, pp. 96–100, 2016

    work page 2016

  10. [10]

    Coincident peak predic- tion for capacity and transmission charge reduction,

    R. Carmona, X. Yang, and C. Zeng, “Coincident peak predic- tion for capacity and transmission charge reduction,”arXiv preprint arXiv:2407.04081, 2024

    work page arXiv 2024

  11. [11]

    Gaming on coincident peak shaving: Equilibrium and strategic behavior,

    L. Chen, J. Sethuraman, and B. Xu, “Gaming on coincident peak shaving: Equilibrium and strategic behavior,”arXiv preprint arXiv:2501.02792, 2025

    work page arXiv 2025

  12. [12]

    Leveraging evolutionary game theory for cleaner production: Strategic 12 insights for sustainable energy markets, electric vehicles, and carbon trading,

    L. Cheng, P. Peng, P. Huang, M. Zhang, X. Meng, and W. Lu, “Leveraging evolutionary game theory for cleaner production: Strategic 12 insights for sustainable energy markets, electric vehicles, and carbon trading,”Journal of Cleaner Production, vol. 512, p. 145682, Jun. 2025

    work page 2025

  13. [13]

    Game- theoretic evolution in renewable energy systems: Advancing sustainable energy management and decision optimization in decentralized power markets,

    L. Cheng, F. Yu, P. Huang, G. Liu, M. Zhang, and R. Sun, “Game- theoretic evolution in renewable energy systems: Advancing sustainable energy management and decision optimization in decentralized power markets,”Renewable and Sustainable Energy Reviews, vol. 217, p. 115776, Jul. 2025

    work page 2025

  14. [14]

    The response of large industrial energy consumers to four coincident peak (4cp) transmission charges in the texas (ercot) market,

    J. Zarnikau and D. Thal, “The response of large industrial energy consumers to four coincident peak (4cp) transmission charges in the texas (ercot) market,”Utilities Policy, vol. 26, pp. 1–6, 2013

    work page 2013

  15. [15]

    Peak and off-peak demand for electricity: Is there a potential for load shifting?

    R. Br ¨annlund and M. Vesterberg, “Peak and off-peak demand for electricity: Is there a potential for load shifting?”Energy Economics, vol. 102, p. 105466, 2021

    work page 2021

  16. [16]

    Estimation of peak demand reduction using smart thermostats: A texas case study,

    D. Kim, A. K. Karngala, and L. Xie, “Estimation of peak demand reduction using smart thermostats: A texas case study,” in2025 IEEE PES Grid Edge Technologies Conference & Exposition (Grid Edge). IEEE, 2025, pp. 1–5

    work page 2025

  17. [17]

    Design of a battery energy management system for capacity charge reduction,

    D. Wu, X. Ma, T. Fu, Z. Hou, P. Rehm, and N. Lu, “Design of a battery energy management system for capacity charge reduction,”IEEE Open Access Journal of Power and Energy, vol. 9, pp. 351–360, 2022

    work page 2022

  18. [18]

    Auction design in day-ahead electricity markets,

    J. Contreras, O. Candiles, J. I. De La Fuente, and T. Gomez, “Auction design in day-ahead electricity markets,”IEEE Transactions on power Systems, vol. 16, no. 1, pp. 88–96, 2002

    work page 2002

  19. [19]

    Gridstatus ercot 4cp prediction,

    GridStatus, “Gridstatus ercot 4cp prediction,” https://www.gridstatus.io/ apps/ercot-4cp

    work page

  20. [20]

    Enverus load forecast nails every ercot coincident peak,

    Enverus, “Enverus load forecast nails every ercot coincident peak,” https: //tinyurl.com/enverus, 2025

    work page 2025

  21. [21]

    Coincident peak notifications with gridpredict,

    P. Power, “Coincident peak notifications with gridpredict,” https://peakpowerenergy.com/energy-storage-management/ coincident-peak-notifications/

    work page

  22. [22]

    ERCOT real-time market,

    “ERCOT real-time market,” https://www.ercot.com/mktinfo/rtm, Electric Reliability Council of Texas

    work page

  23. [23]

    ERCOT four coincident peak calculations,

    “ERCOT four coincident peak calculations,” https://www.ercot.com/ mktinfo/data agg/4cp, Electric Reliability Council of Texas

    work page

  24. [24]

    Energy Information Administration

    U.S. Energy Information Administration. (2024, October 3) Data centers and cryptocurrency mining in texas drive strong power demand growth. [Online]. Available: https://www.eia.gov/todayinenergy/detail. php?id=63344

    work page 2024

  25. [25]

    Computability of global solutions to factorable nonconvex programs: Part i—convex underestimating problems,

    G. P. McCormick, “Computability of global solutions to factorable nonconvex programs: Part i—convex underestimating problems,”Math- ematical Programming, vol. 10, no. 1, pp. 147–175, 1976

    work page 1976

  26. [26]

    ERCOT’s 4CP summer demand roller coaster takes off as storage flips outcomes,

    C. Waldoch, “ERCOT’s 4CP summer demand roller coaster takes off as storage flips outcomes,” https://blog.gridstatus.io/ercot-4cp-2025-june/, Jun. 2025

    work page 2025

  27. [27]

    Designing markets for prediction,

    Y . Chen and D. M. Pennock, “Designing markets for prediction,”AI Magazine, vol. 31, no. 4, pp. 42–52, 2010

    work page 2010