Strategic bidding in electricity pools with short-lived bids: an application to the Spanish market

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Abstract

We generalize von der Fehr and Harbord’s [Econ. J. 103 (1993) 531] multi-unit auction model for the case of a deterministic demand allowing for any technology mix and elastic demand in order to account for demand-side bidding. We obtain a general characterization of the equilibrium and show that this is bounded above by the Cournot equilibrium. We simulate the Spanish electricity pool and show that price–cost margins substantially increased with the 1996 merger that took the industry from a six-firm structure to its current four-firm structure. Our results show that, in terms of market power, this is similar to a nearly symmetric duopoly. The introduction of demand-side bidding is not likely to change this situation.

Introduction

Electricity pools are at the core of electricity deregulation processes throughout the world. After the pioneering case of England and Wales, several other spot wholesale markets for electricity were created in order to introduce competition into the generation of electricity. Argentina, California, the Scandinavian region, Spain and the states of Victoria and New South Wales in Australia currently have electricity spot markets in operation, while several are in the process of creation.1

The common characteristic of all electricity pools is that generators make bids to supply a given amount of electricity at a certain price. A market operator orders these bids from highest to lowest, constructing the market offer curve, and the intersection of this offer curve with a demand curve yields a price at which all trade occurs. An important characteristic of pool markets is the period of time for which bids are fixed and cannot be altered. In certain pools, such as the Argentinian pool, firms place bids every six months, in the England and Wales pool the bidding is daily, while in Spain, California and Nordpool firms submit bids for each hour.2 In this paper we develop a methodology for the analysis of competition in electricity spot markets where firms make bids valid for short periods of time. We consider the bid life to be short when demand does not vary significantly during the period of time for which the bid is valid, i.e. when firms bid facing a certain demand.

In a seminal paper, Green and Newbery (1992) analyze the behavior of firms in the England and Wales electricity pool. These authors assume that firms have a continuously differentiable cost function and submit continuously differentiable bid functions to the pool and apply Klemperer and Meyer’s (1989) results to obtain a range of equilibrium supply functions. Their analysis assumes that bids are fixed for a period during which demand shifts in a given interval. The equilibrium prices range from Cournot to perfect competition. They apply this methodology to simulate the England and Wales pool assuming that firms coordinate on the highest pricing equilibrium. Klemperer and Meyer (1989) show that any price above marginal cost can be sustained in a supply function equilibrium if there is no uncertainty. Accordingly, in pools where firms make bids for periods of time in which demand hardly varies, the supply function approach has extremely limited predictive power.3

Alternatively, von der Fehr and Harbord (1993) model electric pools as multi-unit auctions where generating firms face constant marginal costs up to capacity and demand is inelastic. They analyze a specific example with two firms for deterministic and uncertain demand cases and extract some general conclusions. In this paper we generalize von der Fehr and Harbord’s (1993) approach for the case of deterministic demand. In particular, we allow for multiple asymmetric firms with increasing step cost functions. We also allow for a downward sloping demand function that represents the existence of demand-side bidding. However, we do not model a double auction where consumers’ behavior is determined endogenously. This effectively assumes price-taking behavior by consumers. For instance, in the Spanish case, this is justified by the small size of eligible consumers with respect to total demand, and the fact that distributors, although large in aggregate, supply customers that face a fixed tariff and therefore are not price responsive.

We obtain a characterization of the pure strategy equilibria for this model and find that firms’ asymmetries in size and technology significantly affect price–cost margins. In particular, very strong asymmetries lead to a single equilibrium price with a dominant firm where small firms behave competitively, while the market leader maximizes profits given its residual demand. Also, symmetric market structures generally lead to a single equilibrium price but to lower average price–cost margins. Intermediate situations lead to multiple equilibrium prices since any of several different firms can adopt a dominant role and set the market price.

We implement a simple algorithm to identify equilibria in a simulation for the Spanish pool. The object of the simulation is to identify problems of market power in the generation of electricity in Spain and, in particular, to quantify the effect of the 1996 merger that took the industry from a six-firm structure to a four-firm structure.

To our knowledge, the only previous attempts to simulate firms’ behavior in electricity pools with deterministic demand are those of Borenstein and Bushnell (1999) and Ocaña and Romero (1998) that use the Cournot model to simulate the Californian and the Spanish pools, respectively. The main drawback of this analysis is that it does not exploit all the information available on how firms interact in the pool; that is, it ignores the pool market institution.4 It is reasonable to believe that taking into account the pool auction mechanism will lead to closer predictions of the generating firms’ strategic behavior. When comparing our results with those derived from the Cournot model, we observe that Cournot yields significantly higher mark-ups except when demand is very elastic or the industry is very fragmented, two situations which are extremely unlikely in the electricity industry.

The results of our simulation for the Spanish case show that market power measured by price–cost margins substantially increased with the 1996 merger that took the industry from a six-firm structure to its current four-firm structure. In fact, our simulation shows that the current situation is, in terms of market power, nearly equivalent to a symmetric duopoly. We also show that the introduction of demand-side bidding may not be enough to curb market power in the Spanish spot market for electricity.

Our simulation estimates variations in market power following changes in market and cost structure. This cannot be tested empirically because they have not taken place, or have taken place before the pool was in operation. However, some of the simulation results for the current four-firm structure could be contrasted with empirical observations, such as the identity of the firm that determines the system marginal price and the individual firms’ hourly production shares. Unfortunately, it is not possible to compare our simulation results with current data for two reasons. First, while the Spanish pool started operation in 1998, it is going through a transition period designed to allow firms to recover their stranded costs. We do not explicitly model this stranded cost recovery mechanism but rather analyse firms’ behavior in the pool once this transition period is over. Second, much of the necessary data is unavailable. The market operator only publishes the pool price and the total quantity despatched for each hour. Agents’ individual bids, sales and purchases, as well as the identity of the firm that determines the system marginal price, are not publicly available.

Section snippets

The model

In this section we present a model of an electricity pool as a multiple unit first price competitive auction with complete information.5

The simulation

For a given period, the simulation is conducted as follows. We define Gi as the set of non-differentiable points of vi(p). Gi includes pmax, cu for all uUi and all the prices where the profits are kinked due to the discontinuity of the marginal cost function of firm i. By assuming demand is differentiable from Theorem 2 we obtain Corollary 3.

Corollary 3

Let p1 and p2 be two consecutive prices in Gi. If Mi>0 and p1<p*<p2, then p* verifies the following first-order condition:D′(p*)(p*−C′(D(p*)−O−i(p*

Conclusions

In this paper we extend the results of von der Fehr and Harbord (1993) to analyze an electricity pool with short bidding periods. The model also accounts for the effect of demand-side bidding by including a positively sloped demand. We obtain a characterization of the pure strategy equilibria for this model and we implement a simple algorithm to identify them. Our theoretical results suggest that asymmetries among generating firms, both in size and costs, play a crucial role in determining

Acknowledgements

We would like to thank CNSE for technical assistance and financial support. We are particularly indebted to Arturo Romero and Raul Yunta. We would also like to thank Luis Corchón, Juan Delgado, Ma Angeles de Frutos, Richard Green, Diego Moreno, Richard Sicotte and an anonymous referee for their comments and encouragement. The usual disclaimer applies.

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