Abstract
This paper presents a spreadsheet model of an
electricity market that can be used to simulate
two types of auctions, a single price auction
and a paid your bid auction. This model
can be used in a variety of pedagogical applications.
From the perspective of management science and
operations research (MS/OR), this application
emphasizes model use and integrates several important
concepts. From a business perspective, users can
explore various bidding strategies and their implications,
depending on the auction rules. From a public
policy perspective, students can learn how market
design decisions may influence market outcomes
and the exercise of market power.
The electric power industry is one of the largest
industries in a modern economy. In the United
States, the electric power industry represents
$216 billion-plus in revenues from sales to ultimate
customers and approximately 4% of the real gross
domestic product (Edison Electric Institute, 2003).
It has been undergoing fundamental changes of
late as it is restructured from a vertically integrated
and regulated industry to a mixture of market-based
generation companies and regulated transmission
companies. Thanks to almost daily coverage on
the network news programs of the electricity disaster
in California that began in June 2000, the wider
public has learned of the challenges and missteps
that have occurred with restructuring in the United
States (Borenstein, 2001).
Part of this restructuring involves creating
markets in which owners of generation units submit
bids indicating the prices at which they would
be willing to produce energy (measured in megaWatt-hours,
or MWh). The organization that administers the
wholesale markets determines the least-cost combination
of bids to meet hourly demand and thus clear supply
and demand. The bidding strategies generation
unit owners employ depend fundamentally on the
rules of the auction and the ownership profiles
of the various generation units, which determine
the profitability of exercising market power.
Here, we use the term market power to refer
to situations in which there is insufficient competition,
allowing one or more generation owners to raise
profitably the market clearing price by bidding
above marginal cost.
The electric power industry is of special interest
to MS/OR professionals. It provides a wide range
of applications spanning planning and operation.
The industry’s large-scale challenges require
the use of linear, non-linear, mixed, and stochastic
programming as well as reliability analysis. Depending
on the interests of the analysts, the application
of stock-in-trade MS/OR techniques might focus
on computational, engineering, economic, or public
policy issues. The analysis and design of auctions
is also an important MS/OR topic (e.g., Rothkopf
and Park, 2001), although
anecdotal evidence based on the authors’ experience
and a review of textbooks suggests that auction
theory is not as commonly taught at the undergraduate
and MBA levels as are other MS/OR techniques.
The model presented in this paper combines many
important MS/OR topics, which can be examined
in several contexts depending on the users’ interests.
Model users can focus on auction design, market
power, microeconomic analysis, strategic interaction,
or decision-making under uncertainty in a setting
of either a single or multiple auction rounds,
the latter allowing for the possibility of learning
by the decision maker. Courses in energy economics,
environmental operations research, public policy,
or business economics may benefit from the use
of an electricity market simulation.
The model is easy to use and explain. Its flexibility
allows it to be used in a lecture, as an in-class
group activity, or as an assignment beyond the
classroom. To use the model as a market simulation
requires at least four people in addition to someone
serving as the market administrator, who collects
the bids from the various generation unit owners,
enters them into the model, and reports the results
to the market participants. Four or more generation
owners provide sufficient competition to put some
limit on the potential for the exercise of market
power, although five to nine generation owners
is ideal. Preferably, there should be a team of
two to four people per generation owner. This
will afford users the opportunity to learn through
interaction with their teammates as they develop
bids for their portfolio of generation units.
The authors have used this model successfully
with first-year MBA students, industry and business
personnel, regulators, and attorneys. Users have
found the exercise informative and enjoyable.
By forcing users to make specific bids and then
experience the simulated market outcomes, the
model drives home key points regarding bidding
strategy, market analysis, and the ability to
exercise market power. Active learning in MS/OR
(e.g., the use of student teams to solve problems
cooperatively and discuss theoretical issues with
instructors as facilitators) has been recommended
by many authors (e.g., Ladson and Liebman, 1998;
Liebman, 1998; Powell,
1998). This group simulation
exercise is an example of how “teams will learn
how to learn together while engaging their most
important business issues” (Senge, 1990).
The authors’ experience using this simulation
confirms the benefits claimed for active learning.
The model also helps serve the MS/OR objective
to “teach business students the essential skills
of analytical reasoning, especially how to use
models to think through business problems” (Powell,
2001). The focus is
on formulating a bidding strategy to price a firm’s
output, not on the technical details of programming
an auction-clearing mechanism. In this example,
those details are not difficult and can be handled
easily in a spreadsheet (Gass et al., 2000).
The body of this paper focuses on explaining
the simulation and its classroom use for the benefit
of instructors. Appendix I provides students the
necessary information to participate in the simulation
even if they are not familiar with electricity
markets. It is a standalone document that can
be distributed electronically to students.
The electricity market auction simulation model,
Electricity Auction Spreadsheet, comprises one
spreadsheet with four worksheets. The first worksheet,
labeled Data and Bids, contains the data
for 28 generation units. The units, each of which
is named for a color, are listed alphabetically.
Data provided for each unit are total capacity
in megawatts (MW), the unit type and fuel, age
(a rough proxy for the efficiency of a unit, older
units being less efficient). This worksheet also
contains confidential information for all units
on the amount of available capacity (e.g., which
units are on outage and unavailable), variable
costs ($/MWh), expected hours of operation per
year assuming the unit bids its variable costs,
and the unit’s average fixed costs presented in
both dollars per kiloWatt ($/kW) and $/MWh. The
first units listed are baseload units, which are
expected to be dispatched (i.e., to operate) most
hours in a year. They are followed by intermediate
units, which operate roughly 40-60% of the time.
Peaking units, which typically operate up to several
hundred hours per year, are listed last.
The second portion of the Data and Bids
worksheet comprises six rounds of bidding, with
Round 3 in two parts. Each round is a single clearing
price auction, meaning that the highest bid accepted
sets the clearing price and all generators whose
bids are accepted are paid this single clearing
price. Figure 1 illustrates this type of auction.
Different generation units, represented by different
color blocks, submit energy bids (which are ranked
lowest to highest). The point at which demand
intersects supply establishes the market clearing
price. Figure 1 presents the demand curve as a
“staircase.” The vertical portion of the demand
curve reflects the lack of demand price elasticity
in wholesale electricity markets, and the two
“stairs” indicate two blocks of price-responsive
demand.
All rounds incorporate price-responsive demand.
These load blocks are defined by the amounts of
load (MW) and the price ($/MWh) that triggers
each load block not to consume electricity. For
example, a load block may consist of 50 MW that
for electricity prices of $500/MWh or higher does
not consume. When generation unit bids needed
to serve demand exceed the prices of these load
blocks, the blocks are “dispatched,” meaning that
they do not consume. Although the blocks are modeled
as “resources,” this is equivalent to load being
reduced by the size of the block. This is a commonly
used technique to model blocks of price-responsive
load, and its details do not need to be shared
with the students.
The model does handle situations in which only
a portion of a unit is needed; this occurs when
the total available capacity of the marginal unit
exceeds the amount of residual demand after all
the infra-marginal units have been selected. Sometimes,
different generation units submit the same bid,
which turns out to be the marginal bid, but the
total amount of capacity from these units is not
needed to meet demand. To avoid ties, the spreadsheet
adds a different small random number between 0
and 0.0001 to each unit’s bid. Since each random
number has 15 significant figures, it is practically
impossible that even if several generation units
have the same numerical bid, their bids randomly
adjusted by the spreadsheet would be identical.
The added number is so small that it does not
visibly affect the clearing price or the associated
revenues reported to the participants.
Round 3b, and only this round, is a paid your
bid auction clearing mechanism. In contrast
to an auction with a single clearing price, in
Round 3b winning bidders are paid their bid. This
auction design is not currently used in the United
States. We include a paid your bid auction
design to illustrate that this different design
would, at first glance, seem to produce results
substantially different from the single price
auction. Participants, however, adjust their
bids to the different auction rules, resulting
in similar results. Instructors that have the
time to employ Round 3b can use it to make sure
students understand appropriate bidding strategies
and the strategic interaction between auction
rules and competitors’ strategies.1
Instructors who do not want to focus on auction
design issues or have limited time can skip Round
3b.
A separate file, Electricity Auction Bid Sheets,
provides the bid sheets for each generation unit.
Prior to the simulation, the market administrator
prepares a sheet for each generation unit by printing
out each worksheet. Each owner of generation in
the simulation receives one of these sheets for
each generation unit in its portfolio. These sheets
contain private information pertaining to each
unit’s costs and are also used to submit bids
for each unit for each round of the simulation.
The information in these bid sheets must be kept
confidential.
Figure 1: Determining the Market Clearing
Price in a Single Clearing Price Electricity Auction
with a Staircase Demand Curve
The Results tab summarizes the market
results for each round of bidding. The information
on this tab is shared with the generation owners
after each round of the simulation. The results
report the “perfect competition price,” that is,
the price that would clear the market were each
generation unit bid its variable costs. The Actual
Price or clearing price is also reported, and
in the case of the pay your bid auction, the “Actual
Price” is the average price paid to generation
owners weighted by the capacity of accepted generation
units. The Perfect Competition Price and the Actual
Price, respectively, are then used to calculate
the “Perfect Competition” Total Margin and the
Actual Total Margin. These margins are the amount
of money above variable costs that all of the
generation units earned, assuming perfect competition
and based on the actual bids. The Change In Margin
is the difference between the Perfect Competition
Total Margin and the Actual Total Margin. Of course,
some generation units may be better or worse off
than the Perfect Competition Case; the number
of units and the collective amounts of all generation
units of being better and worse off are also reported.
In the file Electricity Auction Sample Results,
we provide actual results from a simulation involving
five rounds with both versions of Round 3. This
spreadsheet of results contains the actual bids
for each round and the overall results for each
round. We strongly recommend not providing this
spreadsheet to students.
The last tab of the simulation spreadsheet, labeled
Curve, is a graph of the supply curve assuming
all units bid their variable costs. Because it
contains proprietary cost data for each of the
competing generation units, this information is
not provided to participants until after all of
rounds of the simulation. When working through
this simulation, participants should be trying
to construct such a curve to inform their bidding
strategies.
All of the worksheets in the simulation spreadsheet
are “protected,” allowing editing only in the
cells of the Data and Bids sheet containing
bids for each round (so that bids can be entered).
Results of the simulation and other information
are presented in locked cells to avoid inadvertent
errors. Users wishing more control over the content
of the workbook can unprotect sheets as they desire
by selecting “Protection” under the Tools Menu.
Sheets are not password-protected.
We have used this simulation in several training
sessions for first-year MBA students, managers,
regulators, and attorneys in the electric power
industry. Our approach has been as follows. Divide
market participants into approximately four to
nine groups of two to four people each, depending
on the total number of participants. Assign each
group a portfolio of generation units consisting
of some baseload, intermediate, and peaking units.
The 28 generating units can be divided in any
manner to accommodate the number of participants;
however, the market administrator should seek
to ensure that each generation owner has a variety
of units with differing characteristics. In addition,
inform everyone that some generation units may
not be available due to unit outages, but do not
make this quantity public. Only the individual
groups should know whether their generation units
are available to bid into the market. The amount
of demand for each round will be known by all
participants and is listed on the unit’s bid sheet.
After explaining the basics of a single clearing
price auction and the mechanics of submitting
bids, allow each group 10-15 minutes to determine
their first-round bids for each generation unit
in their portfolio. In the first round, the discussions
among the team members usually involve gaining
an understanding of the information and figuring
out whether and how to recover a unit’s fixed
costs in its bid. The primary benefit of the first
round is to make the mechanics of the simulation
clear and begin to provide some information regarding
how the market clears given the bids of all of
the other participants. Our experience is that
most participants tend to bid in the first round
an amount close to the variable cost of each unit,
though some will include an adder in hopes of
recovering some fixed costs. Usually, the first-round
results are somewhat above the perfectly competitive
price (but not by much), with most generation
units better off as a result. Consequently, there
are usually one or two generation units that are
worse off due to bidding above their variable
costs and not being selected, despite that the
units were economic (i.e., they had a variable
cost below the market clearing price and would
have been better off producing).
In the second and third rounds, participants
begin to account for the fact that they hold a
portfolio of units and for the potential bidding
strategies of competing generation owners. After
a round or two of market clearing prices, participants
have determined – to some extent – how aggressive
other participants are bidding. That information,
combined with both the ability to coordinate the
bids of a group of generation units within their
portfolio and increasing demand in the market,
typically leads participants to experiment with
bidding margins above the Perfect Competition
Total Margin. The overall trend may be increasing
prices and margins, but generation owners that
were made worse off in earlier rounds compared
to bidding their variable costs tend to stick
close to bidding their marginal costs in an attempt
to maximize their profit. In earlier rounds, where
ample supplies tend to be available, attempts
to raise prices by raising bids often only benefits
those participants not pursuing this strategy.
As a result, competition can be quite effective
in limited bids in initial bidding rounds.
At this point, the participants have enough experience
with the single clearing price auction to switch
to a paid your bid auction. This requires participants
to make a fundamental change in their bidding
strategies. In the single clearing price auction,
a strategy exists to obtain a generation unit’s
margin (clearing price minus variable costs).
The generation unit could bid its variable costs,
which would ensure that an economic unit would
run while earning the difference between the clearing
price and its variable costs. To the extent that
the generation unit thought it could raise the
clearing price, either because that unit was the
marginal unit or because it could exercise market
power, it would raise its bid above its variable
cost. In the paid your bid auction, however, the
generation owner must estimate the highest acceptable
bid and bid close but below that amount to earn
as much margin as possible.
The remaining rounds usually (but not always)
result in the dramatic exercise of market power.
Participants now have a solid grasp of how to
bid and how others will bid. The exercise of market
power usually results when one or more portfolio
owners figure out that demand has reached a level
such that some portion of each portfolio is needed
to have sufficient supply. At this point, the
clearing price can rise markedly as one or more
portfolio owners bid very high prices – knowing
that at least some of their high-priced generation
is required. This effect is limited somewhat by
the presence of price-responsive load (i.e., load
that will not consume if prices reach above a
certain level). Price-responsive load can be used
to complicate later rounds and add a new dimension
to the participants’ analyses. Depending on how
much information participants are provided about
the amount of load reduction, the price at which
such reduction will occur and the probability
of it occurring may influence how aggressively
participants bid in the final round.
Many authors have recognized the importance of
using spreadsheet simulations for solving various
MS/OR problems (e.g., Bodily, 1986;
Leon et al., 1995;
Seal et al., 2000).
Hence, we propose extending the use of this simulation
to introductory MS/OR undergraduate and graduate
courses. The simulation could be used as part
of an interactive lecture or in a group exercise.
The simulation can be used to support learning
objectives in model use. It provides an interactive
tool to enhance instruction in the importance
of distinguishing between fixed and variable costs,
some auction basics (including why and how changes
in auction rules result in changes in bidding
strategy), decision making under uncertainty,
and strategic thinking. Unlike instructional tools
that emphasize only one aspect of MS/OR, this
auction model integrates several key ideas and
requires students to move among these concepts
as they formulate their bidding strategies. The
simulation also permits group interaction and
learning among students, which is more representative
of what will confront students in non-academic
settings.
This simulation helps meet the learning objective
of having students gain an understanding of the
following specific aspects of markets and auctions.
- In a single clearing price auction in a perfectly
competitive market,
- the profit-maximizing bidding strategy for
each generation unit is to bid its variable
(marginal) costs;
- bidders do not need to know the cost structure
of their competitors to determine their bid;
and
- the market-clearing price will be the variable
costs of the highest-cost bidder selected
to satisfy demand.
- The details of how auctions work can fundamentally
change bidding strategies, as evidenced by the
difference in strategies between the two types
of auctions presented in this simulation.
- In a paid your bid auction, a reasonable bidding
strategy is to forecast the highest accepted
bid and to bid that amount (or slightly less
depending on one’s risk preference).
- The ability to exercise market power increases
with ownership concentration, demand, and the
ability of competitors to anticipate and implicitly
collude based on the experience of multiple
bidding rounds – but price-responsive demand
can mitigate market power.
Depending on the interest of the instructor and
students, the learning objective can be approached
from several different perspectives. Students
can be asked to use the model in a pure business
context and play the role of profit-maximizing
companies. Students can also use the simulation
to study the implication of two different auction
designs or different market structures (i.e.,
concentration and type of ownership) on market
power in electricity markets. In this case, the
simulation can be used either to conduct systematic
experiments to draw conclusions (e.g., along the
lines, but less sophisticated than, Weiss, 2002)
or as an analytical tool that allows students
to test various assumptions and bidding strategies.
We have described the use of the simulation as
part of an interactive lecture. The simulation
can also be used outside the classroom, for example,
as a group project or homework assignment. As
a homework assignment, students could be asked
either to create a spreadsheet simulation or be
provided the spreadsheet and use it to answer
questions regarding how they anticipate market
participants might bid in different situations.
After playing the game, the students, either as
individuals or groups, could write up or present
their conclusions, including the students who
were the market maker.
It is important to note that the simulation is
not intended to cover auction theory in detail
or to provide a comprehensive model of electricity
markets. For example, transmission congestion
and the need for reserve capacity significantly
complicate real electricity markets. In addition,
auction applications in the electric power industry
are not limited to electric energy markets; auctions
are also used to allocate transmission capacity.
Students should be made aware of the simulation’s
limitations by being asked to assess the spreadsheet’s
weaknesses, which should help reinforce the MS/OR
reasoning and the instructor’s key learning objectives.
The instructor first needs to determine the number
of teams and then assign to each team specific
generation units. All 28 generation units should
be assigned. Using the generation handout file,
Electricity Auction Generation Units, print out
each worksheet and assign each worksheet to a
team. To provide each team with a variety of generation
units (baseload, intermediate, and peaking), we
suggest that the instructor sequentially assign
the units to each team. For instance, if there
are six teams, Unit 1 is assigned to Team 1, Unit
2 is assigned to Team 2, …, Unit 7 is assigned
to Team 1, Unit 8 is assigned to Team 2, and so
on until all units have been assigned.
We also suggest that the instructor write the
unit number on the back of each of the generation
unit bid sheets assigned or print out each team’s
bid sheets on different color paper. This will
facilitate the distribution of the bid sheets
from the market administrator (usually the instructor)
to each team after each round of bidding.
Each student should also be given a copy of the
Instruction for Students, Electricity Auction
Instructions, to read before the simulation, preferably
at least several days ahead of time. We recommend
that the instructor review with students the Summary
of Key Instructions provided at the bottom of
the Instruction for Students immediately prior
to the simulation.
To expedite the processing of bids, the instructor
may want to appoint a student to assist in the
market-making functions. This student can aid
in collecting the bid sheets, arranging them in
sequential order to facilitate data entry, reading
the entries to the instructor who inputs them
into the spreadsheet, and redistributing the bids
sheets to the appropriate teams.
Teams should be given at least 15 minutes to
prepare their bids for the first round. This can
be done either during the class time in which
the simulation takes place, or teams could be
required to meet beforehand to prepare their bids
for the first round. Even if teams are responsible
for preparing their bids ahead of time, the instructor
may want to provide some class time during the
simulation to provide clarifying instructions
and allow the teams to finalize their bids. We
recommend that the instructor not provide any
bidding suggestions during the first round. It
is important for teams to struggle with how to
formulate their bids.
After the first-round bids have been collected,
the market administrator should enter the bids,
clear the market, and present the results using
the Results tab in the simulation spreadsheet.
We recommend hooking the computer used by the
market administrator to an LCD projector to display
the results. Remember when entering the bids to
turn off the LCD display so that the teams cannot
see the bids of the other teams.
We recommend running the first three rounds without
any class discussion of the results. It takes
two to three rounds for the teams to get the mechanics
down, understand the information on their bid
sheets, and understand the results. When presenting
the results of each round, some students will
want to discuss bidding strategies or seek confirmation
on their approach. We recommend avoiding these
discussions at this point of the simulation so
that teams are required to work through these
issues.
If the instructor plans to use Round 3b, the
paid your bid round, the students should be told
prior to Round 3 to submit two sets of bids per
unit and reminded of the differences in auction
rules between Round 3a and 3b. After Round 3,
the instructor should engage in a short discussion
comparing the bidding strategies between Round
3a and 3b.
Rounds 4 through 6 can proceed at a quicker pace
than the first three rounds. Our experience is
that after three rounds, the teams understand
the mechanics and basic strategies and have internalized
a process to prepare their bids. Not only can
they prepare their bids more quickly, but they
start to think strategically about them. The instructor
may want to encourage teams to develop a rough
estimate of the total supply curve as a means
of focusing team discussions. In the final round,
the instructor may want to permit teams to collude
by sharing their confidential information and
prepare bids jointly. This adds an additional
dimension to the simulation and increases the
energy level of the participants.
It is up to the instructor to determine the total
number of rounds and the tradeoff between the
length of the final discussion and the number
of rounds played. We recommend leaving 15 minutes
or so to debrief after the exercise. This allows
each team to summarize their strategies to the
group, contrast their approaches, and digest what
they have learned. We typically summarize the
game with the following points, along with the
reasoning behind them:
- Never bid below a unit’s marginal cost;
- The single-clearing price auction during periods
of low demand and substantial competition provides
a strong incentive to bid a unit’s marginal
cost;
- The paid your bid auction requires estimating
bid of the highest unit that is selected to
be dispatched and then bidding the higher of
that estimate and a unit’s marginal cost;
- As demand increases, the ability to exercise
market power, that is, the ability to raise
prices above their competitive levels by bidding
above marginal costs, increases; and
- Much of the recovery of fixed costs occurs
during periods of high demand and not equally
across all hours.
The importance of spreadsheet modeling in MS/OR
practice and as a pedagogical method is a given.
The simulation presented provides a hands-on introduction
to auction design, which is an important area
within MS/OR research and in practical applications
such as supply chain management. It also provides
an application in one of the largest industries
in a modern economy – one that is undergoing rapid
and fundamental change in many countries. This
simulation requires students to integrate several
skills that they develop in their introductory
MS/OR course and to work in a team environment.
Students enjoy, and we think learn, from the interactive
exercise and the immediate feedback of learning
the consequences of their bidding strategies.
The authors would like to thank the editor, associate
editor, and three anonymous reviewers for their
comments. In addition, the authors would like
to thank the many players of this game for their
participation and input.
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To
reference this paper, please use:
Farr, J. and F.A. Felder (2003), "An Introduction to Electricity Market Auctions Using a Spreadsheet," INFORMS Transactions on Education, Vol. 4, No 1,
http://ite.pubs.informs.org/Vol4No1/FarrFelder/
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Volume 4, Number 1, September 2003
