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Complementarity formulation of games with random payoffs

Author

Listed:
  • Rossana Riccardi

    (University of Brescia)

  • Giorgia Oggioni

    (University of Brescia)

  • Elisabetta Allevi

    (University of Brescia)

  • Abdel Lisser

    (Université Paris-Saclay)

Abstract

We consider an n-player non-cooperative game where the payoff function of each player follows a multivariate distribution. This formulation is adopted to model a zonal electricity market in which generators operate by running conventional and renewable-based plants. The players in the market compete as in a Cournot model. We formulate this problem as a chance-constrained game by defining the payoff function of each player using a chance constraint. A full empirical analysis has been conducted on the Italian electricity market to test the impact of renewable generators in the light of decarbonization of the market and the impact of the volatility of the cost of conventional plants, mainly related to the volatility of gas prices. We finally test the robustness of the chance constraint formulation with an out of sample analysis.

Suggested Citation

  • Rossana Riccardi & Giorgia Oggioni & Elisabetta Allevi & Abdel Lisser, 2023. "Complementarity formulation of games with random payoffs," Computational Management Science, Springer, vol. 20(1), pages 1-32, December.
    • Handle: RePEc:spr:comgts:v:20:y:2023:i:1:d:10.1007_s10287-023-00467-x
    DOI: 10.1007/s10287-023-00467-x
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    1. Genc, Talat S. & Reynolds, Stanley S. & Sen, Suvrajeet, 2007. "Dynamic oligopolistic games under uncertainty: A stochastic programming approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(1), pages 55-80, January.
    2. WEI, Jing-Yuan & SMEERS, Yves, 1999. "Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices," LIDAM Reprints CORE 1454, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Farzad Hassanzadeh Moghimi & Yihsu Chen & Afzal S. Siddiqui, 2023. "Flexible supply meets flexible demand: prosumer impact on strategic hydro operations," Computational Management Science, Springer, vol. 20(1), pages 1-35, December.
    4. Daniel De Wolf & Yves Smeers, 1997. "A Stochastic Version of a Stackelberg-Nash-Cournot Equilibrium Model," Management Science, INFORMS, vol. 43(2), pages 190-197, February.
    5. Morales, Juan M. & Pineda, Salvador, 2017. "On the inefficiency of the merit order in forward electricity markets with uncertain supply," European Journal of Operational Research, Elsevier, vol. 261(2), pages 789-799.
    6. Paul J. Burke and Ashani Abayasekara, 2018. "The Price Elasticity of Electricity Demand in the United States: A Three-Dimensional Analysis," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    7. Lanot, Gauthier & Vesterberg, Mattias, 2021. "The price elasticity of electricity demand when marginal incentives are very large," Energy Economics, Elsevier, vol. 104(C).
    8. OGGIONI, Giorgia & SMEERS, Yves, 2013. "Market failures of market coupling and counter-trading in Europe: an illustrative model based discussion," LIDAM Reprints CORE 2553, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Vikas Vikram Singh & Abdel Lisser, 2018. "A Characterization of Nash Equilibrium for the Games with Random Payoffs," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 998-1013, September.
    10. Roger A. Blau, 1974. "Random-Payoff Two-Person Zero-Sum Games," Operations Research, INFORMS, vol. 22(6), pages 1243-1251, December.
    11. Wei Jing-Yuan & Yves Smeers, 1999. "Spatial Oligopolistic Electricity Models with Cournot Generators and Regulated Transmission Prices," Operations Research, INFORMS, vol. 47(1), pages 102-112, February.
    12. Bert Willems, 2002. "Modeling Cournot Competition in an Electricity Market with Transmission Constraints," The Energy Journal, , vol. 23(3), pages 95-125, July.
    13. Gabriel, Steven A. & Zhuang, Jifang & Egging, Ruud, 2009. "Solving stochastic complementarity problems in energy market modeling using scenario reduction," European Journal of Operational Research, Elsevier, vol. 197(3), pages 1028-1040, September.
    14. Hoang Nam Nguyen & Abdel Lisser & Vikas Vikram Singh, 2022. "Random Games Under Elliptically Distributed Dependent Joint Chance Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 249-264, October.
    15. Vikas Vikram Singh & Abdel Lisser, 2018. "Variational inequality formulation for the games with random payoffs," Journal of Global Optimization, Springer, vol. 72(4), pages 743-760, December.
    16. Tanaka, Makoto, 2009. "Transmission-constrained oligopoly in the Japanese electricity market," Energy Economics, Elsevier, vol. 31(5), pages 690-701, September.
    17. De Wolf, D. & Smeers, Y., 1997. "A stochastic version of a Stackelberg-Nash-Cournot equilibrium model," LIDAM Reprints CORE 1257, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Giorgia Oggioni and Yves Smeers, 2012. "Degrees of Coordination in Market Coupling and Counter-Trading," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    19. R. G. Cassidy & C. A. Field & M. J. L. Kirby, 1972. "Solution of a Satisficing Model for Random Payoff Games," Management Science, INFORMS, vol. 19(3), pages 266-271, November.
    20. Pineda, Salvador & Boomsma, Trine K. & Wogrin, Sonja, 2018. "Renewable generation expansion under different support schemes: A stochastic equilibrium approach," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1086-1099.
    21. Shen Peng & Navnit Yadav & Abdel Lisser & Vikas Vikram Singh, 2021. "Chance-constrained games with mixture distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 71-97, August.
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