Modeling Electricity Markets as Two-Stage Capacity Constrained Price Competition Games under Uncertainty

The last decade has seen an increasing application of game theoretic tools in the analysis of electricity markets and the strategic behavior of market players. This paper focuses on the model examined by Fabra et al. (2008), where the market is described by a two-stage game with the firms choosing their capacity in the first stage and then competing in prices in the second stage. By allowing the firms to endogenously determine their capacity, through the capacity investment stage of the game, they can greatly affect competition in the subsequent pricing stage. Extending this model to the demand uncertainty case gives a very good candidate for modeling the strategic aspect of the investment decisions in an electricity market. After investigating the required assumptions for applying the model in electricity markets, we present some numerical examples of the model on the resulting equilibrium capacities, prices and profits of the firms. We then proceed with two results on the minimum value of price caps and the minimum required revenue from capacity mechanisms in order to induce adequate investments

Modeling Electricity Markets as Two-Stage Capacity Constrained Price Competition Games under Uncertainty

The last decade has seen an increasing application of game theoretic tools in the analysis of electricity markets and the strategic behavior of market players. This paper focuses on the model examined by Fabra et al. (2008), where the market is described by a two-stage game with the firms choosing their capacity in the first stage and then competing in prices in the second stage. By allowing the firms to endogenously determine their capacity, through the capacity investment stage of the game, they can greatly affect competition in the subsequent pricing stage. Extending this model to the demand uncertainty case gives a very good candidate for modeling the strategic aspect of the investment decisions in an electricity market. After investigating the required assumptions for applying the model in electricity markets, we present some numerical examples of the model on the resulting equilibrium capacities, prices and profits of the firms. We then proceed with two results on the minimum value of price caps and the minimum required revenue from capacity mechanisms in order to induce adequate investments.Capacity Constraints; Electricity Markets; Regulatory Policy; Strategic Behaviour;

Price capping in partially monopolistic electricity markets

In this paper we consider an oligopolistic market in which one firm can be monopolist on her residual demand function and derive implications on the shape of her profit function, which we show may not be concave in price. We propose a simple price-capping rule that induce the pivotal operator to compete for quantity instead of taking advantage of her monopoly. Then, we analyze the bidding behaviour of the dominant electricity producer oper- ating in the Italian wholesale power market (IPEX). This firm is vertically integrated and in many instances she acts as a monopolist on the residual demand. We find that, contrary to expectations, this pivotal firm refrains to exploit totally her unilateral market power and, therefore, bids at levels well below the cap. We discuss such a behaviour and derive implications for the setting of the price cap.Electricity auctions, capacity constraints, price cap, optimal bidding

Unique Supply Function Equilibrium with Capacity Constraints

Consider a market where producers submit supply functions to a procurement auction — e.g. an electric power auction — under uncertainty, before demand has been realized. In the Supply Function Equilibrium (SFE), every firm commits to the supply function maximizing his expected profit given the supply functions of the competitors. The presence of multiple equilibria is one basic weakness of SFE. This paper shows that with (i) symmetric producers, (ii) inelastic demand, (iii) a reservation price, and (iiii) capacity constraints that bind with a positive probability, there is a unique symmetric SFE.Supply function equilibrium; auction; oligopoly; capacity constraint; wholesale electricity market

Electricity Pricing and Market Power - Evidence from Germany

The aim of this paper is to develop a methodology for measuring the exercise of potential market power in liberalized electricity markets. We therefore investigate producer behavior in the context of electricity pricing with respect to fundamental time-dependent marginal cost (TMC), i.e. CO2- and fuel cost. In doing so, we do not - in contrast to most current approaches to market power investigation - rely on an estimate of the entire generation cost, which inevitably suffers from the lack of appropriate available data. Applying an analytical model of a day-ahead electricity market, we derive work-on rates, which provide information about the impact of TMC variations on electricity prices in the market constellations of perfect competition, quasi-monopoly and monopoly. Comparing these model-based work-on rates with actual work-on rates, estimated by an adjusted first-differences regression model of German power prices on the cost for hard coal, natural gas and emission allowances, we find evidence of the exercise of market power in the period 2006 to 2008. However, our results reveal that German market competitiveness increases marginally. We confirm our results by simulating a TMC-driven diffusion model of futures power prices estimated by maximum-likelihood.energy; electricity; market power analysis; spot-futuresprice relation

Electricity pricing and market power: Evidence from Germany

The aim of this paper is to develop a methodology for measuring the exercise of potential market power in liberalized electricity markets. We therefore investigate producer behavior in the context of electricity pricing with respect to fundamental time-dependent marginal cost (TMC), i.e. CO2- and fuel cost. In doing so, we do not - in contrast to most current approaches to market power investigation - rely on an estimate of the entire generation cost, which inevitably suffers from the lack of appropriate available data. Applying an analytical model of a day-ahead electricity market, we derive work-on rates, which provide information about the impact of TMC variations on electricity prices in the market constellations of perfect competition, quasi-monopoly and monopoly. Comparing these model-based work-on rates with actual work-on rates, estimated by an adjusted first-differences regression model of German power prices on the cost for hard coal, natural gas and emission allowances, we find evidence of the exercise of market power in the period 2006 to 2008. However, our results reveal that German market competitiveness increases marginally. We confirm our results by simulating a TMC-driven diffusion model of futures power prices estimated by maximum-likelihood. --

Uncertainty and Speculators in an Auction for Emissions Permits

Auctions have become popular as means of allocating emissions permits in the emissions trading schemes developed around the world. Mostly, only a subset of the regulated polluters participate in these auctions along with speculators, creating a market with relatively few participants and, thus, incentive for strategic bidding. I characterize the bidding behavior of the polluters and the speculators, examining the effect of the latter on the profits of the former and on the auction outcome. It turns out that in addition to bidding for compliance, polluters also bid for speculation in the aftermarket. While the presence of the speculators forces the polluters to bid closer to their true valuations, it also creates a trade-off between increasing the revenue accrued to the regulator and reducing the profits of the auction-participating polluters. Nevertheless, the profits of the latter increase in the speculators' risk aversion

Supply Function Auction for Linear Asymmetric Oligopoly: Equilibrium and Convergence

AbstractWe study the supply function auction for an asymmetric oligopoly with uncertain linear demand function and linear marginal cost functions of producers. We examine existence of a supply function equilibrium (SFE) in the model and convergence of the best response dynamics to this equilibrium. We show that the dynamics converges to the SFE for a duopoly, but in general the SFE and the strong best response do not exist in the model

When are Auctions Best?

We compare the two most common bidding processes for selling a company or other asset when participation is costly to buyers. In an auction all entry decisions are made prior to any bidding. In a sequential bidding process earlier entrants can make bids before later entrants choose whether to compete. The sequential process is more efficient because entrants base their decisions on superior information. But pre-emptive bids transfer surplus from the seller to buyers. Because the auction is more conducive to entry in several ways it usually generates higher expected revenue.auctions, jump bidding, sequential sales, procurement, entry.

When are Auctions Best?

We compare the two most common bidding processes for selling a company or other asset when participation is costly to buyers. In an auction all entry decisions are made prior to any bidding. In a sequential bidding process earlier entrants can make bids before later entrants choose whether to compete. The sequential process is more efficient because entrants base their decisions on superior information. But pre-emptive bids transfer surplus from the seller to buyers. Because the auction is more conducive to entry in several ways it usually generates higher expected revenue.