Comparing auction designs where suppliers have uncertain costs and uncertain pivotal status

• Date: 01 December 2018
• Author: Pär Holmberg,Frank A. Wolak
• DOI: http://doi.org/10.1111/1756-2171.12259
• Published date: 01 December 2018

RAND Journal of Economics

Vol.49, No. 4, Winter 2018

pp. 995–1027

Comparing auction designs where suppliers

have uncertain costs and uncertain pivotal

status

P¨

ar Holmberg∗

and

Frank A. Wolak∗∗

We analyze how market design influences bidding in multiunit procurement auctions where

suppliers have asymmetric information about production costs. Our analysis is particularly

relevant to wholesale electricity markets, because it accounts for the risk that a supplier is

pivotal; market demand is larger than the total production capacity of its competitors. With

constant marginal costs, expected welfare improves if the auctioneer restricts offers to be flat. We

identify circumstances where the competitiveness of market outcomes improves with increased

market transparency. We also find that, for buyers, uniform pricing is preferable to discriminatory

pricing when producers’ private signals are affiliated.

1. Introduction

Multiunit auctions are used to trade commodities, securities, emission permits, and other

divisible goods. This article focuses on electricity markets, where producers submit offers before

the level of demand and amount of availableproduction capacity are fully known. Due to demand

shocks, unexpected outages, transmission-constraints, and intermittent output from renewable

energy sources, it often arises that an electricity producer is pivotal, that is, that realized demand

is larger than the realized total production capacity of its competitors. A producer that is certain

to be pivotal possess a substantial ability to exercise marketpower because it can withhold output

∗Research Institute of Industrial Economics (IFN), Associate Researcher of the Energy Policy Research Group (EPRG),

University of Cambridge; par.holmberg@ifn.se.

∗∗Program on Energy and Sustainable Development (PESD) and Stanford University; wolak@zia.stanford.edu.

Note that an earlier version of this article has the title. “Electricity markets: designing auctions where suppliers have

uncertain costs.” We are grateful to Mark Armstrong, Chlo´

eLeCoq,MarioBl

´

azquez de Paz, Philippe Gillen, and

referees for very helpful comments. We also want to acknowledge great comments from participants at a seminar at

the Research Institute of Industrial Economics (IFN) (March 2016), at the IAEE conference in Bergen (June 2016),

the Swedish Workshop on Competition and Procurement Research in Stockholm (November 2016), the AEA meeting

in Chicago (January 2017), and participants at the Mannheim Energy Conference (May 2017). Holmberg has been

financially supported by Jan Wallanderand Tom Hedelius’ Research Foundations, the TorstenS ¨

oderberg Foundation,and

the Swedish Energy Agency.

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and push the price up to the reservation price of the consumers. We are interested in how such

markets perform and how they are influenced by the auction design. Most electricity markets

use uniform pricing, where the highest accepted offer sets the transaction price for all accepted

production. A few markets, such as the British real-time market, use discriminatory pricing,

where each accepted offer is instead paid its own offer price.1There have been calls to switch

from uniform to discriminatory pricing in a number of electricity markets (Kahn et al., 2001).

Our model accounts for asymmetric information in suppliers’ production costs. Our analysis

is, for example, of relevance for European wholesale electricity markets, where the European

Commission has introduced regulations that increase the market transparency, so that uncertain-

ties and information asymmetries are reduced.2Long before delivery, in forward markets, the

uncertainty about future fuel prices is to a large extent a common uncertainty among producers.

The relative size of this common uncertainty typically decreases closer to the delivery. In the

electricity spot market, an owner of a thermal plant has private information about the actual price

paid for its input fuel. Daily natural gas prices can have large uncertainties due to local conges-

tion and local storage constraints in gas pipelines. These circumstances can be even more severe

in regions with significant amounts of intermittent wind and solar generation capacity, because

natural gas units must make up for any renewable energy shortfall relative to system demand.

Moreover, the owner of a thermal plant has private information about the efficiency of its plant,

which depends on the ambient temperature, and how the plant is maintained and operated.

The cost uncertainty and the information asymmetry between firms can also be significant

in hydro-dominated markets. The opportunity cost of using water stored in the reservoir behind

a specific generation unit is normally estimated by solving a stochastic dynamic program based

on estimates of the probability distribution of future water inflows and future offer prices of

thermal generation units. These firm-specific estimated opportunity costs typically have a sig-

nificant common component across suppliers. The stochastic simulations also leaves significant

scope for differences across market participants in their estimates of the generation unit-specific

opportunity cost of water. The uncertainty in this opportunity cost is exacerbated by the possibil-

ity of regulatory intervention, especially during extreme system conditions, and each producer’s

subjective beliefs about the probability of these events occurring during the planning period.

Our model of an electricity market with asymmetric information about supplier costs assumes

a multiunit auction with two capacity-constrained producers facing an inelastic demand. Each

producer also has an uncertain amount available of generation capacity that is realized after offers

are submitted. Demand is also uncertain and realized after offers have been submitted. Both of

these sources of uncertainty and when they are realized is consistent with how spot electricity

markets operate. Similar to the electricity market model by vonder Fehr and Harbord (1993), each

firm has a flat marginal cost (independent of output) up to the capacity constraint and must make

a flat offer. This is also similar to the Colombian electricity market, where each supplier chooses

one offer price for the entire capacity of each generation unit (Wolak, 2009). We generalize

von der Fehr and Harbord (1993) by introducing uncertain interdependent costs. Analogous to

Milgrom and Weber’s (1982) auction for single objects as well as Ausubel et al.’s (2014) and

Vives’ (2011) models of multiunit auctions, each firm makes its ownestimate of production costs

based on the private information that it receives, and then submits an offer.3As is customary

in game theory, we refer to this private information as a private signal. We solve for a unique

1In addition, some special auctions in the electricity market, such as counter-trading in the balancing market and/or

the procurement of power reserves, sometimes use discriminatory pricing (Holmberg and Lazarczyk, 2015; Anderson,

Holmberg, and Philpott, 2013).The US Treasury is an important exception, but otherwise most treasury auctions around

the world use discriminatory pricing (Bartolini and Cottarelli, 1997; Brenner, Galai, and Sade, 2009).

2According to EU No. 543/2013, the hourlyproduction in every single plant should be published. EU No. 1227/2011

(REMIT) mandates all electricity market participants to disclose insider information, such as the scheduled availability

of plants.

3Milgrom and Weber (1982) and Ausubel et al. (2014) analyze sales auctions, so in their settings, each agent

estimates the value of the good that the auctioneer is selling.

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Bayesian Nash Equilibrium (BNE) when signals are drawn from a bivariate distribution that is

known to the suppliers.

In our setting with flat marginal costs, inelastic demand, and ex ante symmetric producers,

the bid constraint that offers must also be flat improves expected welfare. A comparison of our

results to Vives (2011) suggests that the bid constraint is particularly beneficial for uniform-price

auctions where producers have large common uncertainties in their costs. This is mainly relevant

for uniform-price auctions of forward contracts and hydro-dominated electricity markets, where

the opportunity cost has a significant common uncertainty and is approximately flat for a wide

range of outputs.4

For an auction with our bid constraint, we show that the auctioneer would prefer uniform

to discriminatory pricing if signals of producers are affiliated. This is related to Milgrom and

Weber’s (1982) ranking of first- and second-price single-object auctions. In the special case where

signals are independent, we find that the two auction formats are revenue-equivalent. This is a

generalization of revenue-equivalence results for single-object auctions by Myerson (1981) and

Riley and Samuelson (1981). Our results also generalize Fabra,von der Fehr, and Harbord (2006),

who prove revenue equivalence for our setting when costs are common knowledge.

Equilibrium offers in a discriminatory auction are determined by the expected sales of

the highest and lowest bidder, respectively. A smaller difference between these sales means

that both producers are pivotal by a larger margin and equilibrium offers increase. Under our

modelling assumptions, the variance in sales after offers have been submitted—due to demand

shocks, outages and intermittent renewable production—will not influence the bidding behavior

of producers or their expected payoffs in the discriminatory auction. Results are similar for

uniform-price auctions, but equilibrium offers in that auction are more sensitive to the variance

in sales. The variance in sales due to demand shocks and outages does not influence the ranking

of auctions.

We extend our basic model to consider the case that the auctioneer has private cost-relevant

information that it can disclose to the two suppliers. For a discriminatory auction, we can show

that the auctioneer would benefit from disclosing its information, if its signal and the producers’

signals are all affiliated. Intuitively, this should also hold for uniform-price auctions, but in

this case, we are only able to prove this when the signals of producers are independent. This

is related to the publicity effect that was proven by Milgrom and Weber (1982) for single-

object auctions. Vives (2011) finds that markups decrease when nonpivotal producers receive

less noisy cost information before competing in a uniform-price auction. It is known from

Perry and Reny (1999) that the publicity effect may not hold in multiunit auctions. Still, taken

together, these results suggest that publicly available information of relevance for production

costs—such as fuel prices, prices of emission permits, and water levels in reservoirs—is likely

to improve the competitiveness of market outcomes in electricity markets. Similarly, disclosing

detailed historical bid data and/or detailed production data are likely to make production costs

more transparent.5In addition, information provision about outcomes from financial markets just

ahead of the operation of related physical markets should lowerthe market uncertainty. Similarly,

trading of long-term contracts, which help producers predict future electricity prices, should

reduce the extent of informational asymmetries among suppliers about the opportunity cost of

water.

Extending this logic further,our results suggest that regulator y risks that increase information

asymmetries among players about the opportunity cost of water are particularly harmful for

competition in hydro-dominated wholesale electricity markets, especially when water is scarce.

Thus, we recommend clearlydefined contingency plans for intervention by the regulator in case of

4Analogously,bidders’ marginal valuation of securities is fairly insensitive to the purchased volume and often have

a large common value component. This indicates that bid constraints have the potential to increase welfare and auction

sales revenues in uniform-price security auctions.

5Note that disclosure of individual offers wouldgive detailed information on all plants, not only the marginal plant,

for every auction outcome.

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