Network-constrained models of liberalized electricity markets: the devil is in the details

Numerical models for electricity markets are frequently used to inform and support decisions. How robust are the results? Three research groups used the same, realistic data set for generators, demand and transmission network as input for their numerical models. The results coincide when predicting competitive market results. In the strategic case in which large generators can exercise market power, the predicted prices differed significantly. The results are highly sensitive to assumptions about market design, timing of the market and assumptions about constraints on the rationality of generators. Given the same assumptions the results coincide. We provide a checklist for users to understand the implications of different modelling assumptions

Cournot Versus Supply Functions: What does the Data Tell us?

The liberalization of the electricity sector increases the need for realistic and robust models of the oligopolistic interaction of electricity firms. This paper compares the two most popular models: Cournot and the Supply Function Equilibrium (SFE), and tests which model describes the observed market data best. Using identical demand and supply specifications, both models are calibrated to the German electricity market by varying the contract cover of firms. Our results show that each model explains an identical fraction of the observed price variation. We therefore suggest using Cournot models for short term analysis, as more market details, such as network constraints, can be accommodated. As the SFE model is less sensitive to the choice of the calibration parameters, it might be more appropriate for long term analysis, such as the study of a merger.supply function equilibrium;Cournot competition;electricity markets

Cournot versus supply functions: what does the data tell us?

The liberalization of the electricity sector increases the need for realistic and robust models of the oligopolistic interaction of electricity firms. This paper compares the two most popular models: Cournot and the Supply Function Equilibrium (SFE), and tests which model describes the observed market data best. Using identical demand and supply specifications, both models are calibrated to the German electricity market by varying the contract cover of firms. Our results show that each model explains an identical fraction of the observed price variation. We therefore suggest using Cournot models for short term analysis, as more market details, such as network constraints, can be accommodated. As the SFE model is less sensitive to the choice of the calibration parameters, it might be more appropriate for long term analysis, such as the study of a merger.supply function equilibrium, Cournot competition, electricity markets

Capacity and Price Competition in Markets with Congestion Effects

We study oligopolistic competition in service markets where firms offer a service to customers. The service quality of a firm - from the perspective of a customer - depends on the congestion and the charged price. A firm can set a price for the service offered and additionally decides on the service capacity in order to mitigate congestion. The total profit of a firm is derived from the gained revenue minus the capacity investment cost. Firms simultaneously set capacities and prices in order to maximize their profit and customers subsequently choose the services with lowest combined cost (congestion and price). For this basic model, Johari et al. (2010) derived the first existence and uniqueness results of pure Nash equilibria (PNE) assuming mild conditions on congestion functions. Their existence proof relies on Kakutani's fixed-point theorem and a key assumption for the theorem to work is that demand for service is elastic (modeled by a smooth and strictly decreasing inverse demand function). In this paper, we consider the case of perfectly inelastic demand, i.e. there is a fixed volume of customers requesting service. This scenario applies to realistic cases where customers are not willing to drop out of the market, e.g. if prices are regulated by reasonable price caps. We investigate existence, uniqueness and quality of PNE for models with inelastic demand and price caps. We show that for linear congestion cost functions, there exists a PNE. This result requires a completely new proof approach compared to previous approaches, since the best response correspondences of firms may be empty, thus standard fixed-point arguments are not directly applicable. We show that the game is C-secure (see McLennan et al. (2011)), which leads to the existence of PNE. We furthermore show that the PNE is unique, and that the efficiency compared to a social optimum is unbounded in general.Comment: A one-page abstract of this paper appeared in the proceedings of the 15th International Conference on Web and Internet Economics (WINE 2019

Cournot versus Supply Functions: What Does the Data tell us?

The liberalization of the electricity sector increases the need for realistic and robust models of the oligopolistic interaction of electricity firms. This paper compares the two most popular models: Cournot and the Supply Function Equilibrium (SFE), and tests which model describes the observed market data best. Using identical demand and supply specifications, both models are calibrated to the German electricity market by varying the contract cover of firms. Our results show that each model explains an identical fraction of the observed price variation. We therefore suggest using Cournot models for short term analysis, as more market details, such as network constraints, can be accommodated. As the SFE model is less sensitive to the choice of the calibration parameters, it might be more appropriate for long term analysis, such as the study of a merger.supply function equilibrium;Cournot competition;electricity markets

Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly

In this note we investigate stochastic Nash equilibrium problems by means of monotone variational inequalities in probabilistic Lebesgue spaces. We apply our approach to a class of oligopolistic market equilibrium problems where the data are known through their probability distributions.Comment: 19 pages, 2 table

Network-constrained models of liberalized electricity markets: the devil is in the details

Numerical models for electricity markets are frequently used to inform and support decisions. How robust are the results? Three research groups used the same, realistic data set for generators, demand and transmission network as input for their numerical models. The results coincide when predicting competitive market results. In the strategic case in which large generators can exercise market power, the predicted prices differed significantly. The results are highly sensitive to assumptions about market design, timing of the market and assumptions about constraints on the rationality of generators. Given the same assumptions the results coincide. We provide a checklist for users to understand the implications of different modelling assumptions.Market power, Electricity, Networks, Numeric models, Model comparison

Network Cournot Competition

Cournot competition is a fundamental economic model that represents firms competing in a single market of a homogeneous good. Each firm tries to maximize its utility---a function of the production cost as well as market price of the product---by deciding on the amount of production. In today's dynamic and diverse economy, many firms often compete in more than one market simultaneously, i.e., each market might be shared among a subset of these firms. In this situation, a bipartite graph models the access restriction where firms are on one side, markets are on the other side, and edges demonstrate whether a firm has access to a market or not. We call this game \emph{Network Cournot Competition} (NCC). In this paper, we propose algorithms for finding pure Nash equilibria of NCC games in different situations. First, we carefully design a potential function for NCC, when the price functions for markets are linear functions of the production in that market. However, for nonlinear price functions, this approach is not feasible. We model the problem as a nonlinear complementarity problem in this case, and design a polynomial-time algorithm that finds an equilibrium of the game for strongly convex cost functions and strongly monotone revenue functions. We also explore the class of price functions that ensures strong monotonicity of the revenue function, and show it consists of a broad class of functions. Moreover, we discuss the uniqueness of equilibria in both of these cases which means our algorithms find the unique equilibria of the games. Last but not least, when the cost of production in one market is independent from the cost of production in other markets for all firms, the problem can be separated into several independent classical \emph{Cournot Oligopoly} problems. We give the first combinatorial algorithm for this widely studied problem

Price Competition on Network

We present a model of imperfect price competition where not all firms can sell to all consumers. A network structure models the local interaction of firms and consumers. We find that aggregate surplus is maximized with a fully connected network, which corresponds to perfect competition, and decreases monotonically as the network becomes less connected until firms become local monopolists. When we study which networks are likely to form in equilibrium, we find that stable networks are not fully connected but are connected enough to rule out local monopolists. Our results extend to oligopolistic competition when consumers can either buy from a single firm or from all firms.Network markets, price competition, oligopoly competition, Bertrand competition.