Christoph Graf

All Publications

• Unlocking Transmission Flexibility Under Uncertainty: Getting Dynamic Line Ratings Into Electricity Markets IEEE TRANSACTIONS ON ENERGY MARKETS POLICY AND REGULATION Zhou, Z., Graf, C., Dvorkin, Y. 2026; 4 (2): 274-291

  View details for DOI 10.1109/TEMPR.2025.3636820

  View details for Web of Science ID 001795874800002

• Simplified short-term electricity market designs: Evidence from Europe ELECTRICITY JOURNAL Graf, C. 2026; 39 (1)

  View details for DOI 10.1016/j.tej.2025.107486

  View details for Web of Science ID 001754485400001

• Cost-Effective Capacity Markets ENERGY JOURNAL Graf, C., Holt, C., Unel, B. 2025

  View details for DOI 10.1177/01956574251379783

  View details for Web of Science ID 001594640800001

• Multi-Objective Transmission Expansion: An Offshore Wind Power Integration Case Study IEEE TRANSACTIONS ON ENERGY MARKETS POLICY AND REGULATION Khanal, S., Graf, C., Liang, Z., Dvorkin, Y., Unel, B. 2024; 2 (4): 519-535

  View details for DOI 10.1109/TEMPR.2024.3390760

  View details for Web of Science ID 001485009900004

• Computational Performance of Deep Reinforcement Learning to Find Nash Equilibria. Computational economics Graf, C., Zobernig, V., Schmidt, J., Klöckl, C. 2024; 63 (2): 529-576

  Abstract

  We test the performance of deep deterministic policy gradient-a deep reinforcement learning algorithm, able to handle continuous state and action spaces-to find Nash equilibria in a setting where firms compete in offer prices through a uniform price auction. These algorithms are typically considered "model-free" although a large set of parameters is utilized by the algorithm. These parameters may include learning rates, memory buffers, state space dimensioning, normalizations, or noise decay rates, and the purpose of this work is to systematically test the effect of these parameter configurations on convergence to the analytically derived Bertrand equilibrium. We find parameter choices that can reach convergence rates of up to 99%. We show that the algorithm also converges in more complex settings with multiple players and different cost structures. Its reliable convergence may make the method a useful tool to studying strategic behavior of firms even in more complex settings.

  View details for DOI 10.1007/s10614-022-10351-6

  View details for PubMedID 38304891

  View details for PubMedCentralID PMC10827988

• Frequent Auctions for Intraday Electricity Markets ENERGY JOURNAL Graf, C., Kuppelwieser, T., Wozabal, D. 2024; 45 (1): 231-256

  View details for DOI 10.5547/01956574.45.1.cgra

  View details for Web of Science ID 001196096900007

• Computational Performance of Deep Reinforcement Learning to Find Nash Equilibria (Jan 2023, 10.1007/s10614-022-10351-6) COMPUTATIONAL ECONOMICS Graf, C., Zobernig, V., Schmidt, J., Kloeckl, C. 2023

  View details for DOI 10.1007/s10614-023-10360-z

  View details for Web of Science ID 001011236900001

• Computational Performance of Deep Reinforcement Learning to Find Nash Equilibria COMPUTATIONAL ECONOMICS Graf, C., Zobernig, V., Schmidt, J., Kloeckl, C. 2023

  View details for DOI 10.1007/s10614-022-10351-6

  View details for Web of Science ID 000906829600001

• Is Daylight Saving Time worth it in tourist regions?* TOURISM MANAGEMENT PERSPECTIVES Graf, C., Rossello-Nadal, J., Sanso-Rosselo, A. 2023; 45

  View details for DOI 10.1016/j.tmp.2022.101068

  View details for Web of Science ID 000922700900001

• (Machine) learning from the COVID-19 lockdown about electricity market performance with a large share of renewables JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT Graf, C., Quaglia, F., Wolak, F. A. 2021; 105

  View details for DOI 10.1016/j.jeem.2020.102398

  View details for Web of Science ID 000607089900003

• Installation entries and exits in the EU ETS: patterns and the delay effect of closure provisions ENERGY ECONOMICS Verde, S. F., Graf, C., Jong, T. 2019; 78: 508-524

  View details for DOI 10.1016/j.eneco.2018.11.032

  View details for Web of Science ID 000462105100038

• Renewable energy and its impact on thermal generation ENERGY ECONOMICS Graf, C., Marcantonini, C. 2017; 66: 421-430

  View details for DOI 10.1016/j.eneco.2017.07.009

  View details for Web of Science ID 000412033900040

• The effect of intermittent renewables on the electricity price variance OR SPECTRUM Wozabal, D., Graf, C., Hirschmann, D. 2016; 38 (3): 687-709

  View details for DOI 10.1007/s00291-015-0395-x

  View details for Web of Science ID 000378820400007