Price-coupling games and the generation expansion planning problem
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Price-coupling games and the generation expansion planning problem Mathew P. Abraham1 · Ankur A. Kulkarni2 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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 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. Keywords Price-coupling game · Stackelberg game · Generalized Nash game · Generation expansion planning
A preliminary version of the paper was presented at Indian Control Conference 2018, Kanpur (Abraham and Kulkarni 2018b). This work was supported by the grant YSS/2014/000910 of the Science and Engineering Research Board, Department of Science and Technology, Government of India.
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Ankur A. Kulkarni [email protected] Mathew P. Abraham [email protected]
1
Department of Electrical and Electronics Engineering, TKM College of Engineering, Kollam, India
2
Systems and Control Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
123
Annals of Operations Research
1 Introduction The recent past has seen the stupendous growth of market mechanisms involving buyers and sellers in markets as complex as commodity markets (like electricity) or service markets like transportation. Unlike in old-school markets, the price that suppliers see in these modern markets is itself determined by a fairly complicated decision problem. For example, in the electricity industry, the price is determined by the independent system operator such a way so as to procure electricity at the lowest cost for the consumer. In on-demand tran
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