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Price-coupling games and the generation expansion planning problem

Author

Listed:
  • Mathew P. Abraham

    (TKM College of Engineering)

  • Ankur A. Kulkarni

    (Indian Institute of Technology Bombay)

Abstract

In this paper, we introduce and study a class of games called price-coupling games that arise in many scenarios, especially in the electricity industry. In a price-coupling game, there is a part of the objective function of a player which has an identical form for all players and there is coupling in the cost functions of players through a price which is determined uniformly for all players by an independent entity called the price-determining player (e.g. independent system operator in an electricity market). This price appears in the objective function only in the part which is identical for all players. We study the existence of equilibria in such games under two broad categories, namely price-anticipative and price-taking formulations. In the price-anticipative formulation, the players anticipate the price and make their decisions while in the price-taking formulation, the players make their decisions considering the price as a given parameter. We model the price-anticipative case as a leader–follower formulation where the players (leaders) conjecture the price (follower’s decision) and make their decision. The price-taking formulation is modelled as an $$N+1$$ N + 1 player game with the additional player as the price-determining player. The existence of an equilibrium in such games are not easy mainly because of the coupled-constraint structure of the game and the non-convexity of the action set. We give conditions for the existence of equilibria in both formulations. We apply our results to analyze the existence of an equilibrium in the generation expansion planning problem using the above results.

Suggested Citation

  • Mathew P. Abraham & Ankur A. Kulkarni, 2020. "Price-coupling games and the generation expansion planning problem," Annals of Operations Research, Springer, vol. 295(1), pages 1-19, December.
    • Handle: RePEc:spr:annopr:v:295:y:2020:i:1:d:10.1007_s10479-020-03687-5
    DOI: 10.1007/s10479-020-03687-5
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    References listed on IDEAS

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    1. Mathew P. Abraham & Ankur A. Kulkarni, 2018. "An Approach Based on Generalized Nash Games and Shared Constraints for Discrete Time Dynamic Games," Dynamic Games and Applications, Springer, vol. 8(4), pages 641-670, December.
    2. Dane A. Schiro & Benjamin F. Hobbs & Jong-Shi Pang, 2016. "Perfectly competitive capacity expansion games with risk-averse participants," Computational Optimization and Applications, Springer, vol. 65(2), pages 511-539, November.
    3. Mathew P. Abraham & Ankur A. Kulkarni, 2019. "New results on the existence of open loop Nash equilibria in discrete time dynamic games via generalized Nash games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 157-172, April.
    4. David Pozo & Enzo Sauma & Javier Contreras, 2017. "Basic theoretical foundations and insights on bilevel models and their applications to power systems," Annals of Operations Research, Springer, vol. 254(1), pages 303-334, July.
    5. Alexander Zerrahn & Daniel Huppmann, 2017. "Network Expansion to Mitigate Market Power," Networks and Spatial Economics, Springer, vol. 17(2), pages 611-644, June.
    6. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
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    Cited by:

    1. Santosh Kumar Sahu & Prantik Bagchi & Ajay Kumar & Kim Hua Tan, 2022. "Technology, price instruments and energy intensity: a study of firms in the manufacturing sector of the Indian economy," Annals of Operations Research, Springer, vol. 313(1), pages 319-339, June.

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