The equilibrium models over the years have become the mainstream tool for evaluating different design options for electricity markets, analysis of electricity bids by market monitoring agencies, and also preparation of bids by traders. Equilibrium models have been successfully calibrated against actual market price outcomes.<sup>19</sup> These models have also been used for merger analysis and a number of litigation cases around market power since the late 1990s.<sup>20</sup> Equilibrium models internally account for profit-maximizing decisions of each company, assuring that the modeled bidding reflects real-life behavior. Thus, it allows us to evaluate, and gain some insights into, the impact of strategic behavior on the market outcomes and the impact of various market designs on the players' behavior (in both production and investment stages). In the remainder of this section, we discuss the possible modeling constructs for each of the market design proposals focusing on the ability of the modeling framework to deal with energy transition issues, including modeling of bidding behavior by generators, representation of physical realities transmission, RE, storage, ancillary services, etc. as well as specific market design constructs including representation of physical and financial contracts they may entail.

# <mark>ENERGY-ONLY MARKETS</mark>

Significant works in this area paving the way for the most recent developments and applications were presented between 1994 and 2005. In 1994 (Scott & Read, 1996) used the Cournot duopoly model to represent the hydro reservoir operation in wholesale markets and the impact of contracts. In 1995, (Borenstein et al., 1995) suggested using the Cournot oligopoly equilibrium to analyze the Californian energy industry while undergoing restructuring. The authors suspected market power abuse and concluded that the Cournot model would be a suitable methodology. In 1997, (Borenstein et al., 1997) deployed the Nash-Cournot model to evaluate the New Jersey electricity market. The model was used to assess the impact of the line congestion and the amount of time congestion is likely to be a problem. In 1999, (Jing-yuan & Smeers, 1999) presented a similar model with Cournot players and regulated transmission prices. A variational inequality (VI) approach was used to compute the equilibrium solution. In 2001, (Hobbs, 2001) presented two Cournot models of imperfect competition among electricity producers formulated as MCP.

An equilibrium model based on Cournot competition has been used for over twenty years to describe energy-only markets. Using these basic principles, we may represent the basic principles of this model by utilizing individual optimization problems for producers, as shown in Eq. (1). Assuming that the set represents players participating in the market, each player simultaneously chooses their profitmaximizing production (revenues obtained through market price minus costs ), assuming the output ii of other competitors as constant. ii λλ CC max (1) QQii<sup>ππ(QQii) = QQiiλλ(QQ) −CCii(QQii)</sup>

> 19 See for example, J. Bushnell,  E. Mansur, and C. Saravia, Vertical Arrangements, Market Structure, and Competition: An Analysis of Restructured U.S. Electricity Markets. CSEM WP 126, University of California Energy Institute, 2005. And also, E. G. Read, J. Tipping, and D. Chattopadhyay, “Incorporating bottom-up structure into top-down electricity market models,” in Proc. Int. Assoc. Energy Economics, IAEE Int. Conf., Wellington, New Zealand, 2007 present a calibration outcome for the New Zealand electricity market.

> 20 Please refer to the FERC document on Inquiry Concerning the Commission's Policy on the Use of Computer Models in Merger Analysis: https://www.govinfo.gov/content/pkg/FR-1998-04-24/html/98-10687.htm

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