CAPACITY UTILIZATION IN ELECTRICITY MARKET
BEHAVIOR: AN EXPERIMENTAL ANALYSIS
Jaime Andrés Castaneda Acevedo, MSc (c)
Universidad Nacional de Colombia, Medellin, Colombia
Centro de Complejidad - CeiBA
Carrera 82 A No. 21 - 159
Phone/fax: +57 (4) 3430773 / +57 (4) 3430773
jacasta2@ unalmed.edu.co
Santiago Arango Aramburo, PhD
Universidad Nacional de Colombia, Medellin, Colombia
Centro de Complejidad - CeiBA
Carrera 80 No. 65 - 223, oficina M8A -211, Escuela de Sistemas
Phone/fax: +57 (4) 4255371 / +57 (4) 2341002
saarango@ unalmed.edu.co
ABSTRACT
This paper describes a laboratory experiment of electricity markets to study the effect of
variable capacity utilization over market dynamics. Previous experiments have left out a
potential source of cyclical behavior by assuming full capacity utilization. We run 12
experimental markets of the power generation sector, involving two treatments: a first
treatment with fixed (full) capacity utilization where subjects make investment decisions,
and a second treatment where subjects make both investment and capacity utilization
decisions. Visual inspections, basic statistics and simulation tests run with decision rules
estimated from experimental data show that the markets run under full capacity utilization
present a cyclical behavior in market development. Conversely, such tests show a non-
cyclical market development for the markets run under variable capacity utilization,
suggesting that varying capacity utilization favors stability rather than a cyclical behavior.
Keywords: Electricity Market, Capacity Utilization, Decision-Making, Experimental
Economics, System Dynamics.
1, INTRODUCTION
The deregulation of the electricity industry took place in the late 80s. In general, positive
and negative aspects have been observed (Sioshansi & Pfaffenberger, 2006). Several
authors argue about the potentiality of a prejudicial cyclical behavior in the industry (Bunn
& Larsen, 1992 and 1994; Ford, 1999 and 2001; IEA, 1999, 2002 and 2003; Larsen &
Bunn, 1999; Lomi & Larsen, 1999; de Vries & Hakvoort, 2004; Kadoya et al., 2005). Since
the time series of deregulated electricity markets are still short to show evidence of a
regular cyclical behavior (Ford, 1999; IEA, 1999 and 2003; Larsen & Bunn, 1999; de Vries
& Hakvoort, 2004; Olsina et al., 2006; Botterud & Doorman, 2008), the concerns are based
on simulation models (Bunn & Larsen, 1992 and 1994; Ford, 1999 and 2001; Larsen &
Bunn, 1999; Kadoya et al., 2005; Olsina et al., 2006) and experiments (Arango, 2006a and
2006b) of electricity markets.
These studies rely on simplifications that differ from reality. Rather than a disadvantage,
the simplifications prevent the simulation model builder to lose control over her own model
and help her to understand the structure responsible for the model’s behavior (Randers &
Goluke, 2007). This applies for experimenters as well, since the simplicity of the
experiment allows them to have control over the variables, offering the best opportunity to
learn something useful about the question that motivated the research (Friedman & Sunder,
1994; Friedman & Cassar, 2004). However, the assumption of full capacity utilization
assumed on those studies is not a realistic supposition. One could develop a simulation
model incorporating variable capacity utilization or, analogously, design an experiment
allowing subjects to make capacity utilization decisions.
Many commodity industries suffer from persistent cyclical instability. Additionally, some
of them show at least two distinct cycle periods: a short-term cycle in inventories,
production and prices and a long-term cycle in capacity and/or prices (Sterman, 2000;
Randers & Géluke, 2007). The classical economic theory of commodity cycles is the
Cobweb Theorem (Ezekiel, 1938). As argued by Sterman (2000, p. 798), although Cobweb
models do capture the core structure underlying commodity cycles, they are unsuitable for
serious modeling of market dynamics because they do not distinguish between production
capacity and capacity utilization and so cannot explain the multiple oscillatory periods
observed in many industries. Some authors have already used a more realistic approach
than the Cobweb Theorem developing System Dynamics models and have shown a pattern
of interplay between a “4 year” capacity utilization cycle and a “20 year” capacity cycle.
Meadows’ (1970) and Randers & Goluke’s (2007) models support this pattern of behavior
in the context of livestock and oil tankers industries respectively. Moreover, Mass’ (1975)
model supports the same pattern of behavior in a macroeconomic context.
Although useful for understanding the interaction between capacity utilization cycles and
capacity adjustment cycles in several contexts, these models include behavioral
assumptions that we would like to test rather than induce. Under these circumstances,
experimental economics provide a methodological framework to test the rationality of
subjects making isolated investment and capacity utilization decisions in the context of a
deregulated electricity market.
Previous experiments of electricity markets took as starting point the simplest Cobweb
model (Arango, 2006a and 2006b)!. Arango added complexity and realism to the markets
to respond to the critics of experimental economics who argue that real markets are
! Other previous applications of experimental economics in electricity markets have focused mainly in market design
(e.g., Rassenti et al., 2003; Vogstad et al., 2005; Kiesling & Wilson, 2007).
inherently more complex than the markets analyzed in laboratories and so experimental
results are not representative of real economic phenomena (Loewenstein, 1999; Fatas &
Roig, 2004). Arango (2006a) showed cyclical tendencies in prices as market complexity
increased, while the follow-up experiment of Arango (2006b) showed a well-defined
oscillatory behavior in prices. The present experiment can be seen as a continuation of
Arango’s works. The main difference is that we are relaxing Arango’s full capacity
utilization assumption.
We formulate the null hypothesis based on rational choice classic theory (Muth, 1961;
Lucas, 1981) and the standard assumption in neoclassical economics about optimal decision
making. The null hypothesis is convergence to a stable Cournot Nash equilibrium; minor
and seemingly random variations around the equilibrium value will be consistent with this
hypothesis.
The alternative hypothesis is based on the bounded rationality (Simon, 1955 and 1979) and
the use of very simple information-processing rules or heuristics (Tversky & Kahneman,
1974), which are consequence of bounded rationality (Kleinmuntz, 1993). There is
experimental support for bounded rationality theory in dynamic experiments (e.g., Sterman,
1989a and 1989b; Kampmann, 1992; Paich & Sterman, 1993; Diehl & Sterman, 1995;
Duffy & Ochs, 1999; Lei et al., 2001; Moxnes, 2004; Arango, 2006b). While heuristics
could lead to near-to-optimal results for simple problems, the results are likely to
deteriorate with complexity (Kampmann, 1992; Paich & Sterman, 1993; Diehl & Sterman,
1995; Moxnes, 2004; Arango, 2006a).
Regarding cycles, we propose two heuristics that express the intended rationality of agents.
The first one, conceming investment behavior, is inspired on the investment function
formulated in Senge (1980) and the investment dynamics of electricity markets reported in
Stoft (2002). It assumes that agents use a feedback strategy to adjust their capacity towards
a desired capacity. This rule is consistent with the anchoring and adjustment heuristic
(Tverksy & Kahneman, 1974). Previous experimental support for similar heuristics is
presented in dynamic experiments (e.g., Sterman, 1989a and 1989b; Bakken, 1993; Paich &
Sterman, 1993; Diehl & Sterman, 1995; Barlas & Ozevin, 2004; Arango, 2006b). The
strategy tends to underestimate the investment lag, which results in continuous investments
even when there is a lot of capacity in the supply line (capacity still in construction phases),
generating a pronounced raise in capacity when all these investments realize in installed
capacity. This raise results in a dramatic fall in prices with the subsequent under-investment
behavior to raise prices again. In theory, this behavior should produce the long-term
capacity cycle (e.g., Sterman, 1987 and 1989a; Bakken, 1993; Arango, 2006b). The second
one, conceming capacity utilization behavior, is inspired on the capacity utilization
function formulated in Randers & Géluke (2007) in an inventory management problem.
The strategy tends towards full utilization when prices are high and to minor utilization
rates when prices are low. In theory, this behavior should produce the short-term capacity
utilization cycle. There is no previous experimental support for the capacity utilization
heuristic. Thus, we consider the experiment exploratory in this regard.
Section 2 describes the experimental design. The design includes testable hypotheses based
on rational choice and bounded rationality theories. Section 3 presents the experimental
results. Section 4 tests the hypotheses. Finally, section 5 concludes.
2. EXPERIMENTAL DESIGN
2.1. Experimental economic model
We use a computerized experiment of a symmetrical Cournot five player market with linear
demand. The design corresponds to a Cournot market experiment under standard conditions
(Huck, 2004)2, except for the investment and capacity utilization dynamic complexity as we
explain later in the experimental treatments. We use five players in order to ensure a non-
collusive behavior with outcomes expected to be about the Cournot Nash outcome or even
about competitive levels (Huck et al., 2004). We use the same experiment of Arango
(2006b), with a time step of one year, with four years before new production capacity is in
place and capacity lasts for sixteen years. Investment decisions are made yearly. Each
subject decides freely on investments with the exceptions that its capacity must not exceed
20% of the total capacity (reflecting the maximum allowed market share) and that its
investments must not be negative. The market price is determined by a linear inverse
demand function with a non-negativity restriction. Information about the realized price and
own profits is given each period. The market price in period t is:
5
Pp = Max{ 6-043 a0] (1)
i=l”
where qj; is the production of subject i in period t. Production varies according with the
experimental treatments. There are two experimental treatments. Treatment T1 is identical
to Arango’s (2006b) experiment except for the more disaggregated investment and capacity
vintages while T2 introduces variable capacity utilization.
Following, we describe the treatments and the rest of the experimental design.
2.1.1. Treatment T1
We set up our first treatment, T1, equal to Arango (2006b), where subjects have fixed
capacity utilization (i.e., production equals installed capacity). Production equals the sum of
the capacities of all players. Given the investment lags and the vintages of capacity,
production of subject i in period t is:
? Standard conditions (Huck, 2004, p. 106): (i) interaction takes place in fixed groups, (ii) interaction is repeated over a
fixed number of periods, (iii) products are perfect substitutes, (iv) costs are symmetric, (v) there is not communication
between subjects, (vi) subjects have complete information about their own payoff functions, (vii) subjects receive
feedback about the aggregated behavior of the other subjects, and (viii) the experimental instructions use an economic
framework.
‘ (2)
Foo es
Git j-E19 1,]
where xj; is the investment decision made in years j = t-19 toj = t-4. The profit function in
experimental pesos (E$) for subject i in period t is:
my =(P,-c)- ai (3)
where c are the marginal costs, which include both capital and operational costs and are
equal to 1 E$/Unit.
This treatment links the present work with the literature and is identical to Huck’s standard
conditions for Cournot markets, except for the longer lag in investment and the more
disaggregated investment and capacity vintages showing explicitly information of the
investment that is about to realize in capacity and the capacity that is about to depreciate in
a given period. Thus, subjects receive information about: (i) their total investments,
aggregate over three vintages, (ii) their capacities, aggregate over sixteen vintages, (iii)
their productions, (iv) aggregate production of the other players, and (v) production of the
market (see Appendix 1, in Spanish). This change in the information presented to subjects
favors model transparency, which in general has a positive effect over subjects’
performance (Rouwette et al., 2004). Since T1 is run under such information conditions, T2
has to be run under the same information conditions as well and not under the conditions
used in Arango (2006b). If we do not do it in such a way, the variations in the results of T1
with respect to the results of T2 could be due either to model transparency or to the variable
capacity utilization (or both) and we might not know precisely which of them is the
responsible for the variations. However, it is not an objective of this work to see if the
transparency will have a positive effect over subjects’ performance. If this was the case, we
would have to compare the results we obtain in T1 against the results reported in Arango
(2006b).
2.1.2. Treatment T2
Different from T1, the second treatment, T2, does not assume full capacity utilization since
investors may adopt a strategic bidding behavior (Arango, 2006a and 2006b). In this
treatment subjects have the possibility to make capacity utilization decisions in a yearly
basis like the investment decisions. Given the time step that we are using, the shorter delay
that we can use for capacity utilization decisions is one year. While it might look like a long
lag, in real life situations not only do decision makers have to adjust the utilization but also
have to assess the current status of several variables in order to make the wisest decisions,
activity that in the case of corporate and economic environments may take up to a year
(Sterman, 2000, p. 636) . Thus, it takes one year before a utilization decision realizes.
Most observers expect that competition increases capacity utilization rates in electric
generation just as it has done in every other deregulated industry and it is conceivable that
capacity utilization reaches rates above 70%, possible above 80% (Maloney, 2001). Thus,
in this treatment capacity utilization decisions are restricted to values between 70% and
100%. This treatment is also identical to Huck’s standard conditions for Cournot markets,
except for the longer lag in investment and the more disaggregated investment and capacity
vintages as well as for the distinction between production capacity and capacity utilization.
Since it is possible that the installed capacity be not equal to production, information items
(iv) and (v) of T1 become (iv) aggregate capacity and production of the other players and
(v) capacity and production of the market for T2 (see Appendix 1, in Spanish).
Production equals the sum of the capacities of all players multiplied by their respective
capacity utilizations. Given the investment lags, the vintages of capacity and the utilization
lag, production of subject i in period t is:
ted
it = | Pag tid CUitt (
where xi; is the investment decision made in years j = t-19 to j = t-4 and CUjir1 is the
capacity utilization decision of subject i in period t-1. The profit function in experimental
pesos (E$) for subject i in period t is:
=(-B}aiy-a ‘Sx (5)
Tht t it j=f19 i,j
where B and o are the operational and capital costs respectively. As we just noticed, this
extension of T1 implies a change in the cost function since now we have both capital and
operational costs. The cost function for T1 is’:
c =C +g (6)
where C are the marginal costs which include both capital and operational costs and are
equal to 1 E$/Unit, and q; is the electricity production of subject i.
The cost function for T2 is:
c = Bq, +a-Cl; (7)
where gi and IC; are the electricity production and the installed capacity of subject i
respectively. As we mentioned previously, B and a are the operational and capital costs
respectively.
5 The cost function for T1 is the same cost functions used in Arango (2006a and 2006b).
To link T2 with T1, the Cournot Nash equilibrium must be the same. This implies that the
values of the capital (a) and operational (B) costs must be chosen in order to hold the
expression that provides the first-order condition for the production, which is derived in
Appendix 2.
We use a time horizon of 70 years which should be large enough to allow leaming and
eventual convergence towards some equilibrium.
The model underlying the experimental economic model is represented by System
Dynamics methodology as shown in Figure 1. Notice that there are not feedback structures
feeding the investment decisions for both T1 and T2, while for T2 there are not feedback
structures feeding the capacity utilization decisions as well, i.e., there are not behavioral
assumptions since we want to test the rationality of those decisions rather than induce it.
— a cus te?)
Tl
Figure 1. Stock and flow diagram of the experimental markets.
2.2. Experimental procedure
The experiment follows the standard framework used in experimental economics (Friedman
& Sunder, 1994; Friedman & Cassar, 2004). All subjects were recruited from the same
population last year students in the undergraduate programs of Industrial Engineering,
Management Engineering and Economics at the Universidad Nacional de Colombia,
Medellin, Colombia in spring of 2009. There were 12 markets, 6 for each treatment. No
subject had previous experience in any related experiment. Subjects were told they could
eam between Col$10.000 and Col$50.000 (US$5 - US$25 at that time) in about one and a
half hour, values that in general are greater than the opportunity cost of subjects. They
knew that rewards were contingent on performance, which was measured in cumulative
profits.
Upon arrival, subjects were seated behind computers. Groups were formed in a random
way, such that subjects could not identify rivals in the market. Instructions (see Appendix
3, in Spanish) were distributed and they were read aloud by the experimenter. Subjects
were allowed to ask questions and test the computer interface. All the experiment
parameters were common knowledge to all subjects, including the symmetry across firms.
The initial condition was a total industry production of 55 Units and individual productions
of 11 Units (which implies a utilization of 1 or 100% for T2). Thus, the price started at 0.5
E$/Unit. These initial values were identical across groups.
Each simulated year, subjects were asked to make investment decisions in both treatments.
In addition, subjects were asked to make capacity utilization decisions in T2. The
experiment was run in a computer network using the simulation software Powersim
Constructor version 2.51. The software ran automatically and kept record of all variables
including subject's decisions. Still subjects were asked to write their decisions in a sheet of
paper to keep a memory of past decisions and to provide a backup of the experiment. At the
end of the session, subjects were asked to answer in written a question about the strategy
they had followed during the experiment and an additional question about difficulties they
might have experienced during the experiment. The software interfaces are presented in
Appendix 1 (in Spanish) and the experiment is available upon request.
2.3. Testable hypotheses
2.3.1. Rational choice hypothesis: Cournot Nash equilibrium
The null hypothesis is based on rational choice classic theory (Muth, 1961; Lucas, 1981).
Under this hypothesis, the economic model has a unique Cournot Nash equilibrium. Table
1 shows the numbers characterizing the Cournot Nash equilibrium. Previous experiments
have shown some biases (e.g., Arango, 2006a and 2006b). To judge our results in this
regard, the table also presents the equilibrium values for perfect competition and joint
maximization. Minor and random fluctuations around the Coumot Nash equilibrium are
consistent with this hypothesis.
Table 1. Experimental markets equilibriums’.
Individual investment Market production Price
(Units) (Units) (Es/Unit)
Perfect competition 0.63 50.0 1.00
Cournot Nash 0.52 41.7 1.83
Joint maximization 0.31 25.0 3.50.
* For T2 all equilibrium points are reached investing the amount specified in the table and making full capacity utilization
decisions, i.e, CU =1 (100%) for all individuals.
Neoclassical economic theory suggests no cyclical behavior but stability. Any predictable
cyclical tendency would lead to countercyclical investments and stabilization. In fact, if the
economist can show that there is a negative feedback loop, there would be equilibrium and
cyclical tendencies will be prevented by a countercyclical behavior (Stoft, 2002).
Accordingly, economic theory normally attributes cyclical behavior to external shocks,
particularly in commodity markets (Deaton & Laroque, 1992, 1996 and 2003; Deaton,
1999; Cashin et al., 2002). We consider random shocks generated within a market to be
consistent with standard economic theory. Previous experimental Coumot markets have
found that outputs and prices are not exactly equal to the Cournot Nash equilibrium but
close, typically closer than one standard deviation of the observed price fluctuations (Huck,
2004). To summarize, we present the next formal hypotheses:
Hypothesis 1: average prices are equal to Cournot Nash equilibrium predictions.
Hypothesis 2: market prices do not show cyclical behavior, while random variations may
occur.
2.3.2. Bounded rationality hypothesis: heuristics and cycles
The alternative hypothesis is based on bounded rationality theory (Simon, 1955 and 1979).
We propose that people use investment and capacity utilization heuristics.
The investment heuristic is inspired on the investment function formulated in Senge (1980)
and the investment dynamics of electricity markets reported in Stoft (2002). This heuristic
is similar to Arango’s (2006a and 2006b) formulations and is consistent with the anchoring
and adjustment heuristic (Tversky & Kahneman, 1974). The function assumes that people
use a feedback strategy to adjust their capacity towards a desired capacity. The investment
function is:
Ge c ci -c;)
X, = Max| ir? Ss Dt +O -\Cy -C,} 0 (8)
where the Max function precludes negative investments, capacity C; divided by the lifetime
LT denotes a normal level of investments to replace depreciated capacity, o determines
how quickly the supply line (capacity in construction) SL: is adjusted towards the desired
supply line C*yID, where ID corresponds to the investment delay. Finally, a determines
how fast capacity is adjusted towards the desired capacity C”;. The desired capacity is:
e
c* -vn-(4 =p ,0
t pe t
which represents a linear function of actual price P;. This is the same formulation used in
Arango (2006a and 2006b) with the exception that since we do not have information about
subjects’ long run price expectations, we assume that the adjustment is based on the actual
price P;. When P, equals the equilibrium price P®, desired capacity C*; equals equilibrium
production q°. The parameter a is restricted to a < q° to avoid negative slopes.
(9)
The capacity utilization heuristic is inspired on the capacity utilization function formulated
in Randers & Géluke (2007) in an inventory management problem. This heuristic assumes
that subjects adjust his capacity utilization towards a desired capacity utilization. Such
adjustment is given by the following expression
cu dust — au (cut -cu,} (10)
where Oy. determines how quickly the capacity utilization CU; is adjusted towards the
desired capacity utilization CU’, which is also consistent with the anchoring and
adjustment heuristic. Since we do not have information about subjects’ short run price
expectations, the desired capacity utilization is a function of the actual price P,. and is
inspired on the tabular function formulated in Randers & Géluke (2007). Figure 2 shows
the desired capacity utilization function.
Figure 2. Desired capacity utilization function.
As we can observe in Figure 2, a desired full utilization realizes with prices closer to joint
maximization levels than to the Cournot Nash equilibrium. This function is more realistic
than a formulation that assumes a desired full utilization at the Cournot Nash equilibrium in
the sense that there is a concern about price manipulation since in a deregulated
environment theory suggests that generation owners could reduce output to raise the price
(Montero & Sanchez, 2001; de Vries & Hakvoort, 2004; Puller, 2007). This function
restricts the desired capacity utilization to values between 70% and 100% to hold
consistency with the experimental conditions.
Initial conditions are the same as in the experiment. We choose a = 38 as in Arango
(2006b). We use two sets of parameters and perform some sensitivity tests. Set 1 has og =
0.1 and o = 0.26 and set 2 has a = 0.5 and a = 0.5. For both parameter sets, we choose
Ou = 0.5, which corresponds to a value used by Randers & Goluke (2007) in an analogous
tule for capacity utilization decisions in an inventory management problem. Set 1 refers to
values estimated by Sterman (1989b) in an analogous heuristic for an inventory
management problem and set 2 refers to values studied by Arango (2006a and 2006b),
which represent a more aggressive policy where half of the adjustments take place within
one year.
Figure 3 shows simulated behavior for parameter sets 1 and 2 with full (line 1) and variable
capacity utilization (line 2). As in Arango (2006b), we observe that the heuristic leads to
oscillatory behavior in both cases. Set 1 produces one dominant cycle with an increasing
amplitude over time. Set 2 shows a dominant cycle with a slightly shorter period than the
observed with set 1. We also observe that the variable capacity utilization reduces the
amplitude of the oscillations and does not allow prices to go below competitive levels,
showing this way a more stable price behavior that allows having profits all the time.
Price
0 20 40 60 0 20 40 60
Figure 3. Simulated prices of the experimental market with the heuristics of the literature
with full (line 1) and variable capacity utilization (line 2).
Sensitivity analysis of the hypothesized parameters for both sets shows a tendency towards
price stabilization when oj and o are reduced. Low values of oj in combination with
increasing values of o; lead to stronger instability, which indicates that ignoring the supply
line and focusing primarily in capacity leads to greater oscillations. Behavior is not very
sensitive to reasonable changes in ay.
Sensitivity analysis of the parameters for both sets shows a tendency towards price
stabilization when o, and o% are reduced. Low values of o, in combination with increasing
values of o lead to stronger instability, which indicates that ignoring the supply line and
focusing primarily in capacity leads to greater oscillations. Behavior is not very sensitive to
reasonable changes in o¢u.
The simulations in Figure 3 are deterministic. To study the effects of internally generated
disturbances, we introduce a normally distributed noise u; to investment, u; ~ N(0, S’,) and
to capacity utilization, u, ~ N(0, $,)4, Figure 4 shows simulated behavior for parameter sets
1 and 2 with full and variable capacity utilization, and without (line 1) and with noise (line
2)°. For set 1, we observe one dominant cycle period with some minor disturbances, i.e.,
noise does not affect the underlying mode of behavior observed in deterministic
simulations. For set 2, we also observe cycles, but the mode of behavior is different with
respect to deterministic simulations since we observe a double-cycle behavior: cycles with
relative high amplitudes followed by cycles of lower amplitudes.
4S, is set as the average standard error for regressions of the investment heuristic, while S, is the analogous case for the
capacity utilization heuristic.
5 Given the inherent randomness in the process that introduces noise into the simulations, we run several simulations with
noise. We show a representative simulation of each case.
Time Time
Full capacity utilization Variable capacity utilization
Set 2
Figure 4. Simulated prices of the experimental market with the heuristics of the literature
for parameter sets 1 and 2 with full and variable capacity utilization, and without (line 1)
and with noise (line 2).
To summarize, we present the next formal hypothesis:
Hypothesis 3: market prices show cyclical behavior.
2.4, Methods to test the occurrence of cycles
We run simulation tests with the proposed investment and capacity utilization adjustment
heuristics. The simulations are run with estimated parameters for the linear forms of
equations (8), (9) and (10) (see Appendix 4 for the derivation of the linear form of the
decision rules).
The following simple linear form is an approximation of the aggregated investment
behavior in equations (8) and (9):
Xp =MySLy +m,P, +b (11)
where m2, m; and b are parameters to be estimated.
The following simple linear form is an approximation of the aggregated capacity utilization
adjustment behavior in equation (10) and the tabular function of the desired capacity
utilization in Figure 2:
cu adust _m cu, +mzZ, +b 12°
where m2, m; and b are parameters to be estimated.
Table 2 presents the theoretical values for these parameters, which will serve as references
for comparison with the estimation results derived from the estimation process performed
with the experimental results.
Table 2. Theoretical values of the parameters of the linear forms of the proposed heuristics.
Mm my b
Investment
Theoretical values set 1 -0,10 2,55 -1,02
Theoretical values set 2 -0,50 5,63 -2,50
Capacity utilization adjustment
Theoretical values -0,50 0,16 0,34
3. RESULTS
Figure 5 shows price development for the six markets of both treatments over time. The
analysis could be performed with a focus on prices or capacities. We choose prices since
they are easier to compare with real markets. In T1, prices vary from 0 E$/Unit to values
close to 4 E$/Unit, suggesting a fluctuating price behavior. In T2, prices vary from 0
E$/Unit to values close to 4 E$/Unit, suggesting a fluctuating price behavior as well. In T1,
visual inspection suggests tendencies towards regular price cycles for most of the markets
with exploding oscillations in markets 1 and 2. Although market 4 has no apparent signs of
cycles, it still shows great variations in prices. Regarding T2, visual inspection suggests a
tendency towards regular price cycles in half of the markets (7, 9 and 11). Although the rest
of the markets have no apparent signs of cycles, they still show great variations in prices. In
general, the results for both treatments show no signs of a tendency towards stabilization in
spite of the fact that the experiment was run over 70 periods (years).
® 7 refers to the price, but it is not the actual price. Since the desired capacity utilization function is a tabular function, we
performed a curve fitting process to approximate CU*(P,), which resulted in a non-linear component for P, (see Appendix
4 for details on the derivation of equations (11) and (12)).
Price
Price
Price
Price
Pica
Piice
Price
Price
Price
Price
Piice
Piice
20 40 60
Figure 5. Observed prices for both treatments.
Table 3 shows a summary of price statistics for both treatments. In T1, we observe that all
markets have average prices closer to perfect competition levels than to the Cournot Nash
equilibrium. The average coefficient of variation shows that the average dispersion of
prices is 86%, suggesting a fluctuating price behavior. Moreover, the table shows high one-
lag autocorrelations, on average 0,87, which constitutes an indication of cycles. With
respect to T2, we observe that markets 9, 10, 11 and 12 have average prices closer to the
Coumot Nash equilibrium than to perfect competition levels, while for markets 7 and 8 is
the opposite case, showing that varying capacity utilization allows generators having higher
prices. The table also shows high one-lag autocorrelations for T2, on average 0,78, which
constitutes an indication of cycles as in T1. However, the average coefficient of variation of
T2 suggests a more stable price behavior than in T1.
Table 3. Summary statistics of the observed prices for both treatments’.
Ti
T2
P (E$/Unit) S$ (E$/Unit) cv a P_($/Unit) _S (E$/Unit) cv a
M1 0,79 0,65 0,83 0,89 1,38 0,93 0,67 0,78
M2 1,15 0,92 0,79 0,92 1,21 0,62 0,51 0,68
M3 1,21 0,70 0,57 0,92 1,75 0,88 0,50 0,92
M4 0,75 0,53 0,71 0,69 2,20 0,62 0,28 0,76
M5 1,05 1,09 1,05 0,94 1,55 0,68 0,44 0,84
M6 0,50 0,62 1,24 0,88 1,93 0,38 0,20 0,71
Average 0,91 0,75 0,86 0,87 1,67 0,68 0,43 0,78
* P: mean price; S: standard deviation; CV: coefficient of variation; a: one-lag autocorrelation.
While the initial analyses we conducted in this section suggest a fluctuating behavior in
prices for both T1 and T2, with a tendency towards a higher and a more stable price
behavior in T2 than in T1, they can be misleading given that they correspond to basic tests
and, hence, the conclusions derived from them may be not accurate, especially the
conclusions derived from visual inspections. Thus, next section presents the formal
hypothesis tests.
4, TESTING THE HYPOTHESES
Following, we perform the formal tests of the hypotheses presented in section 2.
4.1. Hypothesis 1
We present the limits for the 95% confidence intervals of the average prices in Table 4. We
observe that hypothesis 1 is rejected for all markets of T1 since none of them has the
average price in an interval that includes the Cournot Nash equilibrium value. Furthermore,
all markets have average prices closer to perfect competition levels than to the Cournot
Nash equilibrium. This bias towards competition was also observed in Arango (2006a and
2006b) and is consistent with previous experiments of Coumot markets (see summary in
Huck, 2004 and Huck et al., 2004). We observe similar results for T2 in the sense that
hypothesis 1 is rejected for all markets, except for market 9. However, this time only
markets 7 and 8 show a bias towards perfect competition levels, while markets 10, 11 and
12 show a bias towards the Cournot Nash equilibrium.
Table 4. Average prices and 95% confidence interval limits for both treatments.
T1 T2
E$/Unit Mi M2 M3 M4 _ M5 M6 | M7 M8 M9 M10 Mil Mi2
Lower bound 063 0,94 1,04 0,62 0,78 0,35] 1,16 1,06 1,55 2,05 1,39 1,84
Average 0,79 1,15 1,21 0,75 1,05 0,50} 1,38 1,21 1,75 2,20 1,55 1,93
Upper bound 0,94 137 1,38 0,87 1,31 0,65 | 160 135 1,96 235 1,72 2,02
Next, we test the hypothesized cyclical behavior by performing regressions on the
investment and capacity utilization heuristics and running simulations with the estimated
tules, comparing those simulations against simulations run with the theoretical
hypothesized behavior.
4.2. Hypotheses 2 and 3
4.2.1, Investment behavior
We explore the aggregated investment behavior for both treatments by performing
regressions of equation (11) with the aggregated experimental results. Table 5 presents the
regressions. In T1, we observe that two out of six markets have significant values for m,
(SL) with a positive average contrary to theoretical values, m; (P) is significant in five out
of six markets with a positive average, and b is always significant with a positive average
contrary to theoretical values (significance at least at 10%). Thus, price drives investments,
which is consistent with the view that decision-making in deregulated environments is
guided by price (or profit) signals (Stoft, 2002; Olsina et al., 2006). Moreover, these results
are also consistent with other experiments on Dynamic Decision-Making in the sense that
the supply line is ignored in the decision-making process, which is a source of instability
(Sterman, 1989a and 1989b; Bakken, 1993; Diehl & Sterman, 1995; Barlas & Ozevin,
2004; Arango, 2006a and 2006b). Regarding T2, m; (SL) is significant in four out of six
markets with a positive average contrary to theoretical values, m, (P) is significant only in
one market with a positive average, and b is significant only in half of the markets with a
positive average contrary to theoretical values (significance at least at 10%). According to
this, supply line drives investments, which is neither consistent with the behavior reported
in the literature (Stoft, 2002; Olsina et al., 2006) nor with the results reported in similar
experiments (e.g., Arango, 2006a and 2006b). We should consider the poor results of the
regressions whenever the average R’ is only 13,60 and it is mostly influenced by one
market with an R? of 32,94.
The difference between T1 and T2 in the results of the regressions may be due to
information availability. The available information is greater in T2 than in T1, which imply
that subjects may have used more information besides price and supply line in the
investment decision-making process. This indicates that subjects may use different mental
models for decision-making according to the information available at the time they make
decisions.
Table 5. Parameter estimates of the aggregated investment behavior for both treatments.
m, (SL) m, (P) Db R
MI -0,07 (0,32) 2,88 (0,00) T,61 (0,00) 29,71
M2 0,12 (0,02) 0,15 (0,58) 1,61 (0,01) 7,90
M3 0,02 (0,74) 1,19 (0,01) 1,19 (0,02) 18,44
Tl M4 -0,01 (0,85) 2,23 (0,00) 1,57 (0,03) 15,37
M5 0,08 (0,10) 1,23 (0,00) 1,08 (0,02) 36,32
M6 0,02 (0,81) 1,44 (0,01) 2,60 (0,00) 13,00
Average 0,03 1,52 1,61 20,12
M7 -0,06 (0,26) 2,86 (0,00) 0,19 (0,80) 32,94
T2 M8 0,14 (0,02) 0,60 (0,22) 1,18 (0,12) 12,87
M9 0,04 (0,56) -0,32 (0,30) 3,28 (0,00) 2,70
M10 0,17 (0,00) 0,22 (0,54) 0,99 (0,22) 15,69
Mil 0,12 (0,03) 0,51 (0,12) 1,34 (0,07) 10,44
M12 0,12 (0,03) -0,001 (0,99) 1,98 (0,00) 6,94
Average 0,09 0,64 1,49 13,60
Theoretical set 1 -0,10 2,55 -1,02
Theoretical set 2" -0,50 5,63 -2,50
* p-values are presented in parentheses.
* Theoretical values from Table 2.
We also explore the individual investment behavior for both treatments. The proposed
investment function for individuals is:
i i i 7
x= mC, +mySLy +m Pt +b (13)
where m3, Mz, m; and b are parameters to be estimated. The index i represents individuals
and the variables conserve the previous names. Table 6 shows the regressions of equation
(13) for all individuals across markets. In T1, we observe 13, 15, 10 and 13 significant
values out of maximum of 30 for m; (Cj), my (SLi), m; (P) and b respectively (significance
at least at 10%). The significant coefficients are not largely consistent with the coefficients
for the aggregated markets in the sense that SL; has more significant values than C; and P.
In addition, the low values of R? call for further research about individual investment
heuristics whenever the average R? is 20,37. Regarding T2, we observe 18, 13, 11 and 21
significant values out of maximum of 30 for m3 (Cj), mz (SLi), mi (P) and b respectively
(significance at least at 10%). While the significant coefficients are not largely consistent
with the coefficients for the aggregated markets, they suggest a similar behavior to the one
reported in analogous experiments in the sense that the supply line is ignored in the
decision-making-process. Although this time the average R’ for individuals is greater than
in T1 (25,40 and 20,37 respectively), it is still low and calls for further research about
individual investment heuristics.
Table 6, Parameter estimates of the individual investment behavior for both treatments’.
ms (C)) m, (SLi) m, (P) b R
pl -0,03 (0,01) 0,20 (0,00) 0,02 (0,76) 0,20 (0,03) 39,83
p2 -0,02 (0,29) 0,12 (0,01) 0,61 (0,00) 0,20 (0,56) 39,18
M1 p3 -0,16 (0,00) -0,16 (0,03) 1,24 (0,01) 2,61 (0,00) 37,60
p4 0,01 (0,67) 0,16 (0,00) 0,18 (0,09) -0,02 (0,91) 18,26
pd -0,13 (0,01) -0,02 (0,78) 0,14 (0,55) 3,21 (0,00) 12,01
pl -0,14 (0,01) -0,06 (0,43) -0,02 (0,94) 3,34 (0,00) 12,48
T1 p2 -0,08 (0,01) 0,06 (0,26) -0,07 (0,19) 1,08 (0,00) 17,17
M2 p3 -0,08 (0,00) 0,08 (0,07) 0,06 (0,15) 1,00 (0,00) 47,08
p4 -0,04 (0,42) 0,15 (0,01) -0,24 (0,34) 0,99 (0,23) 13,35
pd -0,003 (0,97) 0,01 (0,86) -0,12 (0,54) 0,51 (0,33) 1,14
pl 0,06 (0,00) -0,09 (0,27) 0,03 (0,39) -0,05 (0,50) 38,31
M3 p2 -0,06 (0,23) -0,05 (0,47) 0,30 (0,05) 0,78 (0,20) 13,66
p3 -0,03 (0,47) -0,10 (0,19) 0,62 (0,02) 0,94 (0,25) 11,36
7 Note that, unlike the aggregated investment behavior, the individual investment behavior includes capacity for
individuals. This is so because for the aggregated investment behavior price is a function of the capacity, .i.e., one must
use price or capacity but not both, while for the individual investment behavior that is not the case.
p4 -0,01 (0,88) -0,16 (0,02) -0,07 (0,24) 0,89 (0,02) 9,53
po -0,05 (0,12) 0,11 (0,05) -0,09 (0,75) 0,98 (0,11) 13,25
pl -0,10 (0,27) -0,07 (0,38) 0,17 (0,80) 1,81 (0,22) 3,53
p2 -0,02 (0,44) 0,06 (0,38) 0,02 (0,85) 0,99 (0,03) 2,25
M4 sp3 -0,09 (0,01) 0,03 (0,60) 0,91 (0,01) 1,14 (0,06) 24,19
p4 0,02 (0,16) 0,20 (0,00) 0,44 (0,00) -0,25 (0,13) 50,21
po -0,004 (0,78) 0,19 (0,00) 0,11 (0,17) 0,05 (0,68) 21,11
pl -0,07 (0,10) -0,02 (0,80) -0,03 (0,84) 0,62 (0,02) 4,36
p2 0,09 (0,05) -0,12 (0,05) 0,39 (0,00) -0,44 (0,35) 30,25
M5 p3 -0,01 (0,86) 0,01 (0,86) -0,05 (0,73) 0,76 (0,13) 0,24
p4 -0,09 (0,11) -0,01 (0,91) 0,45 (0,10) 1,66 (0,13) 37,99
po -0,05 (0,40) -0,04 (0,54) 0,45 (0,03) 0,87 (0,31) 24,29
pl -0,02 (0,42) 0,12 (0,07) 0,16 (0,53) 0,39 (0,23) 10,27
p2 0,001 (0,95) 0,12 (0,02) 0,10 (0,42) 0,27 (0,25) 8,33
M6 p3 -0,15 (0,04) 0,003 (0,96) 0,03 (0,96) 2,58 (0,03) 32,58
p4 -0,03 (0,06) 0,19 (0,00) 0,02 (0,81) 0,99 (0,00) 29,70
po -0,17 (0,09) -0,18 (0,04) -0,40 (0,45) 3,28 (0,03) 7,59
Average 20,37
pl -0,09 (0,00) -0,01 (0,84) 0,17 (0,00) 0,93 (0,00) 41,77
p2 -0,06 (0,11) -0,05 (0,47) -0,29 (0,20) 1,52 (0,02) 4,37
M7 p3 -0,06 (0,11) -0,11 (0,06) 1,33 (0,00) 0,10 (0,91) 38,39
p4 -0,07 (0,14) -0,04 (0,58) 0,10 (0,56) 2,04 (0,03) 7,14
po -0,24 (0,00) -0,30 (0,00) 1,03 (0,00) 2,49 (0,00) 52,81
pl -0,06 (0,01) 0,21 (0,00) -0,17 (0,37) 1,03 (0,02) 44,43
p2 -0,09 (0,01) 0,03 (0,57) 0,02 (0,92) 1,33 (0,01) 15,01
M8 p3 -0,15 (0,00) -0,06 (0,41) -0,20 (0,50) 3,22 (0,00) 18,21
p4 -0,02 (0,20) -0,03 (0,63) -0,02 (0,78) 0,26 (0,05) 2,70
po -0,21 (0,00) -0,01 (0,85) 0,35 (0,12) 4,48 (0,00) 22,48
pl -0,14 (0,03) -0,12 (0,12) 0,02 (0,90) 2,14 (0,01) 8,08
p2 -0,02 (0,12) 0,19 (0,00) -0,02 (0,78) 0,23 (0,18) 25,58
M9 p3 -0,09 (0,09) -0,13 (0,07) -0,52 (0,01) 3,66 (0,00) 11,78
p4 -0,01 (0,88) 0,02 (0,82) -0,15 (0,64) 0,82 (0,53) 1,15
po -0,07 (0,02) 0,12 (0,02) -0,23 (0,12) 1,78 (0,01) 24,69
T2 pl -0,07 (0,17) -0,01 (0,89) 0,11 (0,44) 0,82 (0,15) 3,84
p2 -0,04 (0,00) -0,02 (0,69) 0,02 (0,07) 0,81 (0,00) 40,93
M10 p3 0,02 (0,50) 0,03 (0,59) 0,31 (0,06) -0,29 (0,67) 6,53
p4 -0,05 (0,00) 0,20 (0,00) 0,08 (0,06) 0,34 (0,04) 74,28
po -0,01 (0,75) 0,17 (0,00) 0,29 (0,40) -0,18 (0,87) 25,59
pl -0,13 (0,00) 0,12 (0,00) -0,51 (0,00) 2,56 (0,00) 60,07
p2 -0,08 (0,00) 0,11 (0,03) -0,36 (0,09) 1,88 (0,00) 27,22
Mill p3 -0,02 (0,60) 0,12 (0,15) -0,03 (0,86) 0,78 (0,22) 3,58
p4 -0,17 (0,01) -0,09 (0,20) 0,06 (0,63) 2,04 (0,00) 11,56
po -0,11 (0,00) 0,02 (0,69) 0,54 (0,01) 0,99 (0,02) 33,36
pl -0,02 (0,04) 0,23 (0,00) -0,07 (0,34) 0,67 (0,00) 42,20
p2 -0,13 (0,01) 0,12 (0,01) -0,09 (0,29) 1,80 (0,00) 35,86
M12 p3 0,002 (0,83) 0,27 (0,00) 0,09 (0,37) -0,10 (0,66) 46,58
p4 -0,14 (0,00) -0,01 (0,85) 0,12 (0,63) 2,95 (0,00) 18,66
po 0,01 (0,59) 0,004 (0,94) 0,18 (0,00) -0,17 (0,22) 13,02
Average 25,40
P-values are presented in parentheses.
4.2.2. Capacity utilization adjustment behavior
Now we explore the aggregated capacity utilization adjustment behavior (this is only for
T2) by performing regressions of equation (12) with the aggregated experimental results.
Table 7 presents the regressions. We observe that the coefficient m, (CU) is always
significant with a positive average equal to the theoretical value, m (Z) is always
significant with a positive average, and b is always significant with a negative average
contrary to theoretical values (significance at least at 10%). Thus, CU and Z (price) drive
the adjustment process. Moreover, their average coefficients indicate consistency with the
hypothesized non-full utilization behavior (Montero & Sanchez, 2001; de Vries &
Hakvoort, 2004; Puller, 2007), similar to the behavior observed during the electricity crisis
in Califomia (Joskow & Kahn, 2002; Puller, 2007).
Table 7. Parameter estimates of the aggregated capacity utilization adjustment behavior’.
m (CU) m, (Z) B R
M7 -0,36 (0,00) 1,49 (0,01) -1,20 (0,05) 28,62
M8 -0,68 (0,00) 2,99 (0,00) -2,40 (0,01) 46,06
M9 -0,48 (0,00) 0,57 (0,08) -0,17 (0,60) 33,99
M10 -0,62 (0,00) 14,34 (0,01) -13,82 (0,01) 43,49
Mil -0,36 (0,00) 2,67 (0,00) -2,35 (0,00) 43,62
M12 -0,53 (0,00) 0,03 (0,01) 0,39 (0,00) 44,26
Average -0,50 3,68 -3,26 40,01
Theoretical 0,50 0,16 0,34
* P-values are presented in parentheses.
* Theoretical values from Table 2.
We also explore the individual capacity utilization adjustment behavior. The proposed
capacity utilization adjustment function for individuals is:
cu aust i_mcul +mz, +b (14)
where m2, m; and b are parameters to be estimated. The index i represents individuals and
the variables conserve the previous names. Table 8 shows the regressions of equation (14)
for all individuals across markets. We observe that the coefficient m2 (CUj) is always
significant, except in one case, while m; (Z) and b have 7 and 6 significant values out of
maximum of 30 respectively (significance at least at 10%). Thus, CU; drives the adjustment
process. According to the signs of the estimates, this implies that the higher the capacity
utilization the lower the adjustment no matter the price, which is not consistent with the
aggregated behavior. Moreover, the poor results of the regressions call for further research
about individual capacity utilization heuristics whenever the average R’ is 29,50.
Table 8. Parameter estimates of the individual capacity utilization adjustment behavior .
m, (CU) m, (2) b R?
pl -0,62 (0,00) 1,96 (0,13) -1,39 (0,27) 31,29
p2 -0,40 (0,00) 0,75 (0,49) -0,42 (0,70) 20,96
M7 p3 -0,33 (0,00) 0,48 (0,60) -0,22 (0,80) 16,50
pt -0,87 (0,00) 2,26 (0,02) -1,56 (0,10) 47,29
ps -0,29 (0,00) -2,50 (0,02) 2,73 (0,01) 21,72
pl -0,46 (0,00) 0,42 (0,81) -0,02 (0,99) 22,62
Ms p2 -0,42 (0,00) -0,20 (0,92) 0,56 (0,77) 21,27
p3 -0,55 (0,00) -1,82 (0,26) 2,24 (0,17) 28,17
p4 -0,43 (0,00) -0,18 (0,91) 0,55 (0,75) 21,56
ps -0,78 (0,00) 2,33 (0,15) -1,57 (0,33) 39,63
pl 0,26 (0,00) 0,85 (0,22) -0,64 (0,35) 14,10
p2 -0,61 (0,00) 1,44 (0,03) -0,83 (0,16) 29,84
M9 ps -0,80 (0,00) 0,09 (0,86) 0,49 (0,33) 40,00
p4 -0,48 (0,00) 2,13 (0,02) -1,69 (0,05) 24,97
ps -0,42 (0,00) 0,03 (0,97) 0,33 (0,64) 21,69
pl -0,66 (0,00) 14,48 (0,22) -13,91 (0,24) 35,30
p2 -0,96 (0,00) 2,15 (0,24) -1,46 (0,42) 47,65
M10 —p3 -0,73 (0,00) 1,26 (0,92) -0,62 (0,96) 36,94
p4 0,10 (0,07) 3,94 (0,43) -3,85 (0,44) 4,92
ps 0,06 (0,23) 1,76 (0,60) -1,70 (0,61) 2,34
pl -0,20 (0,01) 1,32 (0,23) -1,16 (0,29) 10,48
p2 -0,56 (0,00) 3,31 (0,04) -2,79 (0,07) 29,33
Mil p3 -1,00 (0,00) 0,05 (0,96) 0,67 (0,53) 55,15
p4 -1,04 (0,00) 0,13 (0,88) 0,90 (0,27) 51,49
ps -0,25 (0,00) -0,02 (0,99) 0,25 (0,83) 12,69
pl -0,56 (0,00) 2,93 (0,66) -2,45 (0,71) 28,18
p2 -0,26 (0,00) 7,43 (0,18) -7,18 (0,19) 17,70
M12 p3 -1,06 (0,00) -18,17 (0,02) 18,95 (0,01) 56,10
p4 0,72 (0,00) -13,20 (0,09) 13,78 (0,07) 40,49
ps 1,08 (0,00) 1,60 (0,89) -0,71 (0,95) 54,75
Average 29,50
* p-values are presented in parentheses.
Next, we test the estimated heuristics by running simulation with them and comparing
those simulations against simulations run with the theoretical hypothesized behavior of
sections 2.3 and 2.4.
4.2.3. Behavioral implications of the estimated heuristics
Now, we compare simulations run with the aggregated linear regression model with the
theoretical values from Table 2 against simulations run with the aggregated linear
regression model with the averages of the estimated parameters in Table 5 (T1) and Tables
5 and 7 (T2). For T1, Figure 6 shows similar cycles, except that the simulation with the
averages of the estimated parameters has a longer period and minor amplitude. For T2,
Figure 6 shows similar cycles in capacities and prices for the simulations run with
theoretical values, but it also shows a quite stable behavior in both capacity and price for
the simulations run with the averages of the estimated parameters. This is an indication of
capacity utilization leading to a more stable behavior as suggested in Arango (2006b). A
clearer picture of this can be observed in Figure 7, where simulations run with the averages
of the estimated parameters with full capacity utilization show dampened cycles, while
simulations run with variable capacity utilization (the same simulations in line 3 of Figure 6
for T2) show a more stable behavior.
Price
Price
Time Time
Tl T2
Figure 6. Simulation of the aggregated investment rule for T1 and the aggregated
investment and capacity utilization adjustment rules for T2 with the theoretical values of
investment set 1 (line 1) and set 2 (line 2) and theoretical values of capacity utilization
adjustment (only for T2), and the average estimates from aggregated experimental results
(line 3).
Time Time
Capacity Price
Figure 7. Simulation of the aggregated investment and capacity utilization adjustment rules
for T2 with average estimates from aggregated experimental results with variable (line 1)
and full (line 2) capacity utilization.
We also run simulations with the estimated parameters for individuals in Table 6 (T1) and
Tables 6 and 8 (T2), which can be observed in Figure 8. For T1, the results at individual
level are largely consistent with the results at aggregated level. We observe that markets 1,
4 and 5 show a pattern of behavior similar to the behavior observed in Figure 7 at
aggregated level with the averages of the estimated parameters, while markets 3 and 6 show
dampened cycles. Thus, this test can be use to reject hypothesis 2, but it cannot be used to
discard hypothesis 3. However, the accuracy of the test is reduced by the poor results of the
regressions, where the average R’ are 20,12 and 20,37 at aggregated and individual levels
respectively. Regarding T2, the results at individual level are consistent with the results at
aggregated level as well. We observe a more stable behavior in four out six markets. Thus,
this test can be used to reject hypothesis 3, but it cannot be use to discard hypothesis 2. But
as for T1, the accuracy of the test is reduced by the poor results of the regressions, where
the average R’ for investment are 13,60 and 25,40 and for capacity utilization adjustment
are 40,01 and 29,50 at aggregated and individual levels respectively.
Price
Time Time
Tl T2
Figure 8. Simulation of the individual investment rule for T1 and the individual investment
and capacity utilization adjustment rules for T2 with estimates from individual
experimental results (line number and line number+6 represents the number of the market
forT1 and T2 respectively).
5. CONCLUDING REMARKS
This thesis presented an experimental electricity market to study the effect of variable
capacity utilization over market dynamics. We explored the potential occurrence of cycles
(cycle hypothesis) in electricity markets in two experimental treatments: first we assumed
full capacity utilization (T1) and second we relaxed this assumption allowing subjects to
make capacity utilization decisions (T2). Previous simulation models (e.g., Ford, 2001;
Kadoya et al., 2005; Olsina et al., 2006) and experimental studies (e.g., Arango, 2006b) of
electricity markets have shown cyclical behavior; however, they assume full capacity
utilization, leaving out a potential source of cyclical behavior (Meadows, 1970; Mass,
1975; Sterman, 2000; Randers & Goluke, 2007). Thus, we isolate investment and capacity
utilization decisions to study the rationality in an experimental market
In T1, we found indications of cyclical tendencies in prices in five out of six markets by
visual inspections, basic statistics and simulation tests. All observations are consistent with
the cycle hypothesis, as suggested by behavioral simulation models (Bunn & Larsen, 1992
and 1994; Ford, 1999 and 2001; Larsen & Bunn, 1999; Kadoya et al., 2005; Olsina et al.,
2006) and previous experiments (Arango, 2006a and 2006b) of electricity markets. In
addition, we found, on average, a tendency towards a competitive behavior in prices in all
markets. On the other hand, inT2, we found weaker indications of cyclical tendencies,
where price cycles occurred only in two out of six markets as shown by visual inspections,
basic statistics and simulation tests. In addition, we found, on average, a tendency towards a
Cournot Nash behavior in prices in four out of six markets. Thus, these results indicate that
varying capacity utilization allows having higher prices.
Since the main treatment difference between T1 and T2 is the variable capacity utilization,
it is safe to conclude that varying capacity utilization leads stabilization. This is due to the
shorter delay of capacity utilization decisions, which was only one period, compared
against the delay of investment decisions, which was four periods, i.e., subjects can have
faster reaction and adjustment of production in T2 than in T1. It means that in T2, subjects
had the possibility to influence market prices faster than in T1, where it took four periods to
do so. In case there were periods with surplus capacity, it only took one year to cut
production to help prices to rise. In fact, the average price of T2 (1,67 E$/Unit) is higher
than that of T1 (0,91 E$/Unit). In addition, the lower bound used for capacity utilization
decisions (70% of the installed capacity) did not allow subjects to raise price in dramatic
ways, which could lead to over-investments and to an unstable behavior (Arango, 2006b).
However, varying capacity utilization did not eliminate the possibility of cycles completely,
as showed by the different tests we performed. Hence, our findings should serve as a
motivation for further research of stabilizing policies in deregulated electricity markets
While our experiment represents an advance with respect to similar experiments (e.g.,
Arango, 2006a and 2006b), the poor results of the regressions call for further investigation
about decision-making heuristics at both aggregated and individual levels. In addition,
more formal tests could be conducted to test cyclicality. For example, one could present
autocorrelograms and autospectra, which are well-known statistical tests to look for
evidence of cycles. Finally, our experiment still has assumptions that differ from reality.
Further works should explore the analysis of those assumptions. For example, further
experiments may explore decision-making under demand growth, bankruptcy, financing,
hydrological uncertainty, etc.
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Appendix 1. Software interfaces (in Spanish).
Informactén general de este afto
Su proiuccin Unde)
| Prades dl esto de wondores (Undaes)
Product tal (Unidas)
Precio Shida)
Costo de pofueciin nao E5Unida)
argon de ganrca Eni)
T1 software interface.
Decision
Inversion en nueva capacidd (Unidades) [2
‘Su desempeo (ES)
Ganancias este aio
Edad de su capacidad (Unidades)
Irs de 1 ao na
Instn de 2 ato Hen
Ines 6 3 tos HAN
Capacidad total en constuccin [NAN
‘af WAN
2s HAN
Saos na
4atos Na
Eats ne
aoe HAN
Taos Na
Balas nav
Sats NaN
0st We
‘Nes HAN
eis NAN
‘thats na
dates Na
es ne
teers WAN
Capacidad ttl insalada Na
Ganancias acumuladas desde el inicio
Informacion general de este afio
‘Su capac (Unidas)
Capacided del sto de adores (Uniades)
Capac etal (Unidades)
8u prodecin (nates
Praducctn del esto de ugaares(Uidados)
Producin total Unidades)
reco (ina)
Ingesos 5)
Costs totals (8)
T2 software interface.
Edad de su capacidad (Unidades) Decisiones.
seine wa] || icon en tcp tieey [=]
wesin do wa] | [eeseemaesmnncers [er |
Copied olen consi [A
‘Su desempenio (ES)
as wm
zat wu] | | oman ete ate aw]
sats wi] | few
2a we
— wa
st eH
— wa
Coptwatteaios [Tun
Appendix 2, Cournot Nash equilibrium derivation.
According to the Cournot Nash model, an oligopolistic market is in equilibrium if each
company produces the same expected production of the other companies in the market,
under conditions of profit maximization. The profit function for each company is:
Th =(P-C)-q (15)
where P is the market price, C corresponds to the marginal costs, which include both
capital and operational costs, and qi is the production for subject i.
The electricity price is given to equilibrate supply and demand. Supply is the sum of the
production of the five subjects. Demand is price sensitive and is given by the following
expression:
P=A-B-S (16)
with A = 6 and B = 0.1. S corresponds to the sum of the production of the five subjects, i.e.,
total electricity supply.
In summary, with high production rates, the price will be low. Respectively, with low
production rates, the price will be high. There is no economic growth, which means that
demand only changes because of changes in the price.
According to the Cournot Nash model:
$ =54, (17)
Replacing (17) in (16):
P=A-5-B-q, (18)
Each subject assumes that the rest of the subjects will produce the same quantities than him.
The quantity is the result of a profit maximization exercise assuming that others’
production is constant, and in equilibrium the quantity is not time dependent. The following
expression gives us the first-order condition for the production q; (Martin, 2002):
pag oP dc(q; )
1 te =0 19
aq dS dg; (19)
Taking the cost function from T1 the first-order condition becomes:
OIL
<i =p_B-q, -C =0 (20)
Fj
Replacing (18) in (20):
CI:
SL a WGih gp Bog -Cm0 (21)
0g;
We know A = 6, B = 0.1 and C = 1. Replacing these values in (21) we obtain that the
equilibrium production for the Cournot Nash model is:
qi = 8.33 Units
Replacing this value in (18) we obtain the equilibrium price for the Cournot Nash model:
P = 1.83 E$/Unit
To link T2 with T1 the Cournot Nash equilibrium must be the same. Given that in T2 we
have variable capacity utilization, the production for each subject is given by:
q, =1C; -CU; (22)
where IC; and CU; are the installed capacity and the capacity utilization of subject i
respectively. Isolating the installed capacity and replacing in the cost function showed in
equation (7) in section 2.1.2, we obtain the following total cost function for each subject:
G
GB tee (23)
Taking this cost function, the first-order condition becomes:
Om Ole
=P -B:45-[ Bef |x0 (24)
Replacing (18) in (24):
OT a
—1=A-5-B-q, -B-q, -| B+—— |=0 25
2; g, -B-q; [> <8-| (25)
In T1 we work under a full utilization assumption, i.e., CU; = 1 (100%). With this value,
the expression in parentheses becomes B + Isolating this expression, replacing A and B
by the known values and replacing q; by the Cournot Nash equilibrium in order to link T2
with T1 and therefore with Arango (2006a and 2006b), we obtain the following expression:
B+a=1 (26)
Thus, parameters B and a must be chosen in such a way that they hold the expression
shown in (26).
Appendix 3. Experimental instructions (in Spanish).
T1 instructions
INSTRUCCIONES
ADVERTENCIA: NO TOQUE EL COMPUTADOR HASTA QUE SE LE AVISE
INTRODUCCION
Bienvenidos. Este es un experimento de toma de decisiones y el caso es un mercado
eléctrico desregulado, apoyado por la Vicerrectoria Nacional de Investigacién de la
Universidad Nacional de Colombia. Las instrucciones son simples y si las sigue
cuidadosamente y toma buenas decisiones usted podria ganar una suma de dinero
considerable, el cual sera entregado en efectivo al final del experimento Usted va a jugar el
rol de un productor de electricidad que vende en un mercado. Cada periodo usted tomara
decisiones de inversion que afectaran su produccién futura. Su objetivo es maximizar las
ganancias a lo largo de todos los periodos del experimento. Entre mayores sean sus
ganancias acumuladas, mayor sera su pago.
ESTRUCTURA DEL MERCADO
Usted es uno entre cinco productores de electricidad. Usted no sabe quiénes son los otros
jugadores en el mercado y como se desempefian individualmente. Sus ganancias son
estimadas como:
Ganancias = Produccion: (Precio - Costos)
m= 45 (P,-¢)
Donde q: corresponde a su produccion en el tiempo t, P; al precio de la electricidad en el
tiempo t y C a los costos tanto de operacion como de capital, que son constantes y
equivalen a 1 E$/Unidad. Su produccion no puede ser negativa y siempre debe estar por
debajo de 20 unidades, que es un limite superior que garantiza un minimo de competencia.
El precio de la electricidad es fijado para equilibrar el suministro total y la demanda. El
suministro total es la suma de la produccion de los cinco jugadores, y la demanda es
sensitiva al precio asi:
P =6-0.1-Q , donde Q es el suministro total (véase la figura Curva de demanda abajo).
Para resumir, entre mayor sea la produccion total de electricidad, menor es el precio.
Respectivamente, entre menor sea la produccion total de electricidad, mayor es el precio.
No hay crecimiento econdmico, lo que significa que la demanda solo cambia debido a
cambios del precio.
ES/unit
Units
Curva de demanda.
PRODUCCION
Su produccion sera siempre igual a su capacidad de produccion, lo que significa que usted
no puede reducir su utilizacién de capacidad. Cada afio usted toma decisiones de inversion
en capacidad nueva (usted puede decidir 0 Unidades). Caracteristicas importantes de los
generadores de electricidad son:
Retraso en la construccidn = 4 afios.
Tiempo de vida de la capacidad instalada = 16 anos.
Esto significa que si usted decide invertir en una capacidad adicional de 0.8 Unidades en el
aho 6, esta capacidad estara bajo construccion por 4 aos y afadira 0.8 Unidades a su
capacidad en el ano 10. Esta capacidad adicional durara hasta el ano 26 inclusive.
CONDICION INICIAL
Cuando el experimento comience los administradores anteriores de la firma han invertido
una cantidad constante de 11 Unidades/vida util = 0.69 Unidades/aio por un largo
tiempo. Consecuentemente, usted comienza con una capacidad de produccion de 11
Unidades y una tasa de depreciacion de 0.69 Unidades/aiio. Todas las firmas son
idénticas, tienen los mismos costos y la misma capacidad inicial. El mercado comienza con
una capacidad total inicial de 11 Unidades:5 firmas = 55 Unidades; para un produccién
total de 55 Unidades, el precio es 0.5 E$/Unidad. Esto significa que inicialmente todos
estan operando con precios mas bajos que sus costos.
PAGO
Usted recibira un pago de acuerdo a su desempefio. Su desempefio es medido por sus
ganancias acumuladas. Entre mayores sean las ganancias acumuladas, mayor sera el
pago. El pago estara entre C ol$ 10.000 y C ol$ 50.000.
CORRIENDO EL EXPERIMENTO ;
Sea cuidadoso, no presione “Accept Decisions” A MENOS QUE ESTE SEGURO. Luego
de presionar “Accept Decisions” su decision no puede ser cambiada.
1. Mire la informacion disponible de la firma y el mercado y tome decisiones de
inversion.
2. Escriba sus decisiones en la hoja que le fue entregada (sus decisiones deben estar
anotadas en la hoja pues ésta es su recibo para el pago) y presione “Accept
Decisions”.
3. Espere hasta que todos los participantes en el mercado hayan tomado sus
decisiones.
La ventana con el botén “Accept Decisions” aparece de nuevo, el juego ha avanzado al
siguiente afio. La informacion es actualizada y es tiempo de tomar decisiones nuevamente.
La simulacion correra por un numero indefinido de afios. Cuando el experimentador pare el
juego usted debe escribir sus ganancias acumuladas en la hoja y preguntar por su pago. Los
pagos se haran en privado.
NOTA
De acuerdo al proposito del experimento se requiere no compartir ningun tipo de
informacion (verbal, escrita, gestos, etc.). Por favor, respete estas reglas pues éstas son
importantes para el valor cientifico del experimento. Romper las reglas implica que el
grupo involucrado es anulado y sus participantes no reciben pago.
Gracias por unirse a este experimento y haga su mejor esfuerzo!!!
T2 instructions
INSTRUCCIONES
ADVERTENCIA: NO TOQUE EL COMPUTADOR HASTA QUE SE LE AVISE
INTRODUCCION
Bienvenidos. Este es un experimento de toma de decisiones y el caso es un mercado
eléctrico desregulado, apoyado por la Vicerrectoria Nacional de Investigacién de la
Universidad Nacional de Colombia. Las instrucciones son simples y si las sigue
cuidadosamente y toma buenas decisiones usted podria ganar una suma de dinero
considerable, el cual sera entregado en efectivo al final del experimento. Usted va a jugar el
rol de un productor de electricidad que vende en un mercado. Cada periodo usted tomara
decisiones de inversion que afectaran su capacidad instalada futura, ademas de decisiones
de utilizacién de capacidad que afectarén su produccién. Su objetivo es maximizar las
ganancias a lo largo de todos los periodos del experimento. Entre mayores sean sus
ganancias acumuladas, mayor sera su pago.
ESTRUCTURA DEL MERCADO
Usted es uno entre cinco productores de electricidad. Usted no sabe quiénes son los otros
jugadores en el mercado y como se desempefian individualmente. Sus ganancias son
estimadas como:
Ganancias = Ingresos - Costo de Produccion - Costo de Capital
m =F, gp —Beqp-o- CL,
Donde q: corresponde a su produccion en el tiempo t, P; al precio de la electricidad en el
tiempo t, CI, a su capacidad instalada en el tiempo t, B a los costos de produccién y aa los
costos de capital (piense en los costos de capital como costos de arrendamiento). Los costos
de produccién equivalen a 0.4 E$/Unidad y los costos de capital a 0.6 E$/Unidad. Su
capacidad instalada no puede ser negativa y siempre debe estar por debajo de 20
unidades, que es un limite superior que garantiza un minimo de competencia. El precio de
la electricidad es fijado para equilibrar el suministro total y la demanda. E] suministro total
es la suma de la produccion de los cinco jugadores, y la demanda es sensitiva al precio ast:
P =6-0.1-Q , donde Q es el suministro total (véase la figura Curva de demanda abajo).
Para resumir, entre mayor sea la produccion total de electricidad, menor es el precio.
Respectivamente, entre menor sea la produccion total de electricidad, mayor es el precio.
No hay crecimiento econdmico, lo que significa que la demanda sdlo cambia debido a
cambios del precio.
E$/unit
Units
Curva de demanda.
PRODUCCION
Su produccion es funcién de la capacidad instalada y la utilizacion de capacidad. Cada afio
usted toma decisiones de inversion en nueva capacidad (usted puede decidir 0 Unidades)
asi como decisiones de utilizacion de capacidad (usted puede decidir utilizar entre el
70% (0.7) y el 100% (1) de su capacidad). Su produccion es la capacidad instalada por la
utilizacion de capacidad. Caracteristicas importantes de los generadores de electricidad son:
Retraso en la construccidn = 4 afios.
Tiempo de vida de la capacidad instalada = 16 anos.
Retraso en la utilizacion = 1 aiio.
Esto significa que si usted decide invertir en una capacidad adicional de 0.8 Unidades en el
ahio 6, esta capacidad estara bajo construccién por 4 afios y afadira 0.8 Unidades a su
capacidad en el ano 10. Esta capacidad adicional durara hasta el ano 26 inclusive. A demas,
si usted decide utilizar el 80% (0.8) de su capacidad en la produccion en el ano 6, esta
decision se hard efectiva en el ano 7. Debe tener en cuenta que esta decision de utilizacién
de capacidad no se hard efectiva con la capacidad instalada del ano 6 sino con la capacidad
instalada del aio 7.
CONDICION INICIAL
Cuando el experimento comience los administradores anteriores de la firma han invertido
una cantidad constante de 11 Unidades/vida util = 0.69 Unidades/aio por un largo
tiempo. Consecuentemente, usted comienza con una capacidad instalada de 11 Unidades.
Adicionalmente, durante el mismo periodo de tiempo han tomado decisiones de utilizacion
de capacidad de 100% (1). De esta manera, usted comienza con una produccion de 11
Unidades y una tasa de depreciacion de 0.69 Unidades/afio. Todas las firmas son
idénticas, tienen los mismos costos y la misma capacidad inicial. El mercado comienza con
una produccion total inicial de 11 Unidades+5 firmas = 55 Unidades; para un produccién
total de 55 Unidades, el precio es 0.5 E$/Unidad. Esto significa que inicialmente todos
estan operando con precios mas bajos que sus costos.
PAGO
Usted recibira un pago de acuerdo a su desempefio. Su desempefio es medido por sus
ganancias acumuladas. Entre mayores sean las ganancias acumuladas, mayor sera el
pago. El pago estara entre Col$ 10.000 y C ol$ 50.000.
CORRIENDO EL EXPERIMENTO ;
Sea cuidadoso, no presione “Accept Decisions” A MENOS QUE ESTE SEGURO. Luego
de presionar “Accept Decisions” su decision no puede ser cambiada.
1. Mire la informacion disponible de la firma y el mercado y tome decisiones de
inversion y de utilizacion de capacidad.
2. Escriba sus decisiones en la hoja que le fue entregada (sus decisiones deben estar
anotadas en la hoja pues ésta es su recibo para el pago) y presione “Accept
Decisions”.
3. Espere hasta que todos los participantes en el mercado hayan tomado sus
decisiones.
La ventana con el boton “Accept Decisions” aparece de nuevo, el juego ha avanzado al
siguiente afio. La informacion es actualizada y es tiempo de tomar decisiones nuevamente.
La simulacion correra por un numero indefinido de afios. Cuando el experimentador pare el
juego usted debe escribir sus ganancias acumuladas en la hoja y preguntar por su pago. Los
pagos se haran en privado.
NOTA
De acuerdo al proposito del experimento se requiere no compartir ningun tipo de
informacion (verbal, escrita, gestos, etc.). Por favor, respete estas reglas pues éstas son
importantes para el valor cientifico del experimento. Romper las reglas implica que el
grupo involucrado es anulado y sus participantes no reciben pago.
Gracias por unirse a este experimento y haga su mejor esfuerzo! ! !
Appendix 4. Derivation of the linear form of the proposed aggregated heuristics.
Investment behavior
We derivate the linear decision rule with the following equations:
*
Cy Ch *
Xt = Max Chay hse Jeet -c,}0
Cy = 60-10P,
e_ e_
C* =Max a+ qa P.,0 ~a+YP., where Y = 2 a
ia pe t t pe
To shorten the presentation, we neglect the index t and take the linear parts. The equations
become:
*
Cc * Cc
x=pp +a, -0}+95 (5-51
C =60-10P
C* =a+YP
Replacing, grouping and simplifying:
*
Cc C
kept, e" -a.C +0 Fp 7 ty SL
60-10P a+YP
=F +0, (a+YP)—a, (60-10P)+a, D7 oy SE
_ 60 10P Mya ay YP
=P LE te, a+a,YP — 604, +100, P+ 1D + 1D a SL
We get the following expression:
x=sit s] LT 1 |*| LT c* 1D
analogous to the expression needed:
jap — 10 ay +100, + “sl 4 }+(theas- 600, + “sl +: which is
Xt = m,SLt + m, Pt +b
The parameter values are:
a= 38
q’ = 41,7
P® = 1,83
LT = 16
ID =4
G& = 0,26 (set 1) and 0,5 (set 2)
= 0,1 (set 1) and 0,5 (set 2)
Finally, the coefficient values are presented in the following table:
Coefficient values of the linear form of the investment heuristic.
Coefficient Set 1 Set 2
m -0,10 -0,50
m, 2,55 5,63
b -1,02 -2,5
Capacity utilization adjustment behavior
We derivate the linear decision rule with the following functions:
djust *
cvs ay fout cu)
cu’,
P
As the desired capacity utilization function is a tabular function, we fit a function to the
curve of the desired capacity utilization. The fitting was done using the Artificial Neural
Network method. The function is:
0,31
1g 2EE-S63R;,
CU; = 067+
The following figure shows the results of the fitting process. It can be observed that the
obtained function is a good approximation for the actual desired capacity utilization
function.
Pp,
Curve fitting for the desired capacity utilization function.
To shorten the presentation, we neglect the index t. Replacing CU’ in CU**"' we obtain the
following expression:
adjust _ 0,31
CU = ceu( 060 + 22-30 on 282-363 -CU
Replacing, grouping and simplifying:
adjust _ 1 _
CU = 0,67a¢y + 0,31a¢y ne 282—363P pen 282 =3,03P OyCU
We get the following expression:
1
sap aap: This
Lee 282 -3,63P
adjust _ _
CU =CU (. Oy a z(031,, a (0674, ), where Z=
expression is analogous to the expression needed:
cu adust = m CU +mZ +b
We have one parameter value: ou = 0,5.
Finally, the coefficient values are presented in the following table:
Coefficient values of the linear form of the capacity utilization adjustment heuristic.
Coefficient Value
mM -0,5
m, 0,16
b 0,34
