Do Strategic Substitutes Make Better Markets? A
Comparison of Bertrand and Cournot Markets as
Trading Institutions
Douglas Davis
October 10, 2008
Thanks to
Bob Reilly, Roger Sherman, Oleg Korenok and Asen Ivanov
Motivation:
This paper examines the relation of strategic complements and
strategic substitutes in a market context.
Some definitions: Suppose we have a strategic context, and that
possible actions (e.g., choices by the players) can be rank-ordered
from lowest to highest.
Actions are strategic complements when high action choices by one
player induces others to also make high action choices.
Actions are strategic substitutes when high action choices by one
player induces others to make low action choices.
To make this concrete, consider the two standard models of oligopoly
interactions.
Cournot Interactions: Sellers pick quantities. Once all quantity choices are
complete, a market clearing price is determined, and all offered units are
sold at the market clearing price.
Bertrand Interactions: Sellers pick prices. Once all price choices are
complete, sales are determined, with the low pricing seller selling the most
units. (A number of variants are possible.)
In a Bertrand Game, actions are strategic complements. High price
choices by rival sellers induce a seller to post a high price, just a
little below that (s)he expects rivals to post.
In a Cournot Game, actions are strategic substitutes. Low quantity
choices by rival sellers induce a seller to post a large quantity, to
take most of the market.
Cournot games are a little institutionally artificial. It is most natural to think
of sellers competing on the basis of price. However, Cournot interactions
have a number of desirable properties that theorists find useful.
-Historically, it was the first model of strategic interdependence.
-The equilibrium price cost markup varies inversely with the number of
sellers.
More recently, however, some economists have argued that Cournot games
might actually be a desirable form of organization. Some of the reasoning
follows from the relation of strategic substitutes and strategic complements.
A series of recent experimental papers suggest that contexts where actions
are strategic substitutes have important properties relative to contexts
where actions are strategic complements.
Heemeijer, Hommes, Sonnemans and Tuinstra (2007) report
that markets where actions are strategic substitutes converge
more quickly and more completely to static Nash (here
competitive) conditions.
Fehr and Tyran (2008) find that contexts where actions are
strategic substitutes respond much more quickly to a fully
announced nominal shock than contexts where actions are
strategic complements.
Potters and Suetens (2008) find that contexts where actions
are strategic substitutes are less susceptible to tacit collusion
than contexts where actions are strategic complements.
Why?
These authors all explain convergence differences in terms of a bounded
rationality argument by Haltiwanger and Waldman (1985, 1989).
Idea: Suppose the rationality of some players is limited in the sense that some
sellers expectations are adaptive (e.g, not forward looking).
In a context where actions are strategic substitutes, rational players have an
incentive to move away from the rational players. A balance of the rational
and boundedly rational action choices drives markets to an equilibrium.
In a context where actions are strategic complements, rational players have
an incentive to copy the actions of the boundedly rational players, resulting in
slow convergence, limited adaptability and, in a repeated context,
susceptibility to tacit collusion.
Startlingly different responses to a fully announced nominal shock observed
by Fehr and Tyran (2008) motivate these authors to go a step further. They
argue that institutions where actions are strategic substitutes
endogenously induce rationality. To see this, consider the best reply
functions of sellers in Bertrand and Cournot games.
pi
Bertrand Game (q =.5)
qi
Cournot Game (q =.5)
45  line
45° line
Best Reply Pre-Shock
Best Reply Pre Shock
A
A
qA
pA
C
B
pB
C
B
Best Reply Post Shock
pC
pi
pA
Best Reply, Post Shock
qB
qC
p-i
Bertrand Game (q =.9)
qi
qA
q -i
Cournot Game (q =.9)
In response to a shock an adaptive player will move from action A to
45  line
45° line
action B, resulting in a group
response of action C.
The
distance
A-C
is
Best Reply Pre-Shock
much larger in a quantity context (on the right) than in a price context (on
the left), which should induce more rapid responses.
Best Reply Pre Shock
c
a
q -i
These implications come as something of a surprise to those familiar
with the behavioral industrial organization literature.
-Although Cournot markets are not explosively unstable, several
investigators have observe the slow and incomplete convergence of
Cournot markets, particularly when compared to Bertrand markets.
-In a meta analysis of experimental results Suetens and Potters
(2007) conclude that Bertrand markets are more susceptible to tacit
collusion than Cournot markets. However, their results are based
primarily on duopoly results. Evidence from thicker markets
(particularly markets with more than 3 sellers) is rather unconvincing.
Importantly, the environments in each of the environments reported
above were very highly stylized.
-In HHST – best responses to action choices were ‘hard wired’ into
seller decisions.
-In Fehr and Tyran and Potters and Suetens, agents made action
choices in a bi-matrix game format, where all factors other than the sign
on the slope of the best reply function are held constant.
Project: Address this curious inconsistency in the literature
between results regarding strategic substitutes and strategic
complements, and Cournot/Bertrand oligopoly performance.
Approach: Rather than hold all things constant except the sign
on the slope of the best reply function, we examine behavior in a
differentiated product oligopoly, where underlying cost and the
demand system are held constant.
A Model.
To see the differences induced by shifting the form of strategic
interactions for a given demand system, consider the following model.
Consider a market with four firms, constant unit costs, c, differentiated
products and a symmetrical demand system for all sellers. For a quantity
setting game, write inverse demand for seller i as
pi  a  qi  3qqi
For a price setting game, write demand as
qi  a~  pi  3pi
These expressions are equivalent when
1  2q

(1  q )(1  3q )
and
Each firm acts to optimize
 i  ( pi  c)qi

q
(1  q )(1  3q )
a) Static Considerations:
In such game, it is easy to show that in the Cournot game, the static
equilibrium price will be higher and the static equilibrium quantity will be
lower than in the comparable Bertrand game (Vives, 1999).
More interesting for us are the best response functions. In the Cournot game, the
best response function is
a c 3qqi
qi 

2
2
In Bertrand game, we have
a~   c 3pi
p 

2
2
b
i

a (1  q )  (1  2q )c 3qpi

2  4q
2  4q
Taking the ratio of the slopes (q to p), observe that as long as 0<q<1, the slope
of the best reply function will be flatter in the Bertrand game than in the Cournot
game
2  4q
2
Further, this difference increases with differentiation.
In the background papers, these slopes were held constant across games.
As we can see, this is impossible for a given demand system.
What does this difference mean? It strengthens the ‘endogeneous rationality
argument of Fehr and Tyran.
pi
Bertrand Game (q =.5)
qi
Cournot Game (q =.5)
45  line
45° line
Best Reply Pre-Shock
Best Reply Pre Shock
A
A
qA
pA
C
B
pB
C
B
Best Reply Post Shock
pC
pA
qC
p-i
Bertrand Game (q =.9)
pi
Best Reply, Post Shock
qB
q -i
qA
Cournot Game (q =.9)
qi
q -i
45  line
45° line
Best Reply Pre-Shock
Best Reply Pre Shock
c
a
qa
a
pa
pb
c
b
pc pa
Best Reply, Post Shock
Best Reply Post Shock
q bT
qb
p -i
qc
q cT
qa
b
q -i
q -i
Just compare adaptive expectation differences across markets in the upper
panel (q=.5) and the lower panel (q=.9).
This result suggests our first two conjectures, regarding stability and
convergence. First, recalling HHST and Fehr and Tyran
Conjecture 1: Convergence levels and speeds are higher in Cournot
markets than in comparable Bertrand markets
Second, to the extent the ‘endogenous rationality argument is
pertinent, we have a second conjecture.
Conjecture 2: The difference in convergence levels and speeds across
Bertrand and Cournot markets is larger when products are close
substitutes (q=.9) than when they are more differentitated (q=.5)
Potentially countering this effect are the costs of a given deviation. Consider
for example, the costs of a small deviation from the best reply in Cournot and
Bertrand markets.
 c   qi2
In the Cournot market,
In contrast, in the Bertrand market
 b  pi2
 
1  2q
pi2
(1  q )(1  3q )
% of Nash Equilibrium Earnings
Notice that these deviations are always larger in the Bertrand markets, and
become increasingly so as differentiation increases.
8%
Bertrand Market
6%
4%
2%
Cournot Market
0%
0
0.5
0.9
1
Not only may this affect
convergence speeds in Bertrand
markets, it may affect incentives
to tacitly collude, because the
profit losses of deviations from the
best reply reflect the costs of both
signaling and responding to
signals.
Some Dynamic Considerations.
Economists typically evaluate incentives to tacitly collude in terms of the
‘Friedman Coefficient’
 D   JPM
=
 D  N
Lower values suggest that a tacit collusion is more easily sustained.
Notice that for a given demand system, these values are higher for
Bertrand games than Cournot games, with the difference increasing as
product differentiation falls (q rises).
Observations:

1
1) Suetens and Potters (2007)
suggest that institutional effects
dominate the effects of tacit
incentives to collude.
Bertrand Market
0.8
0.6
Cournot Market
0.4
0.2
0
0
0.5
0.9
1
q
2) In a Price setting game Davis
(2007) finds that tacit collusion
does move inversely with .
However,  is a coincident
explainer of tacit collusion.
These observations suggest two additional behavioral conjectures. The first
regards an extension of Potters and Suetens to the current context.
Conjecture 3. Tacit collusion, measured as the mean deviation
from the static Nash equilibrium price is higher in Bertrand markets
than in Cournot markets.
A second conjecture regards the collusion damping effects of
increased signalling costs in the Bertrand markets.
Conjecture 4, Increasing the rate of substitutability from q=.5 to q=.9
reduces the incidence of tacit collusion in Bertrand games relative to
Cournot games.
Experiment Design.
To test these four conjectures, we conducted the following experiment.
-24 sessions. Each session consisted of two 40 period sequences.
-Sessions are combinations of two treatment variables, the institution (‘C’
Cournot or ‘B’ Bertrand) and, given the impact of product differentiation on
predictions, the degree of substitutability (‘L’ q=.5 and ‘H’ q=.9). We refer to
treatments as combinations of these variables (e.g, ‘BL’ is the bertrand
markets with q=.5)
-The experiment is conducted in a simple 2x2 design, with 6 markets in each
cell.
Experiment Procedures
-Participants were 96 undergraduate students enrolled in business
and economics courses in the Spring semester of 2008. No person
participated in more than one market.
-In each period, sellers make a simultaneous action choice (price or
quantity) as well as a forecast of the average of their rivals’ action choices.
After all action choices were complete, sellers see their own sales and
earnings, as well the average of rivals’ action choices. Each period lasted up
to 90 seconds.
-To assist players, they were given a profit calculator, that showed the profit
consequences of own choices, given the presumed average actions of
rivals.
-At the end of the first sequence, the session is paused, and both supply
and demand are shifted downward. To keep earnings constant (and make
the shift nominal) the U.S. currency/Lab exchange rate is quadrupled.
-Participant earnings for the 70 minute sessions ranged from $13 to $40 and
averaged $23.75.
Results. Mean transaction prices provide an overview of results
_
P-PNE
$20
$15
$10
$5
$0
-$5 0
-$10
-$15
-$20
_
P-PNE
$20
$15
$10
$5
$0
-$5 0
-$10
-$15
-$20
BL
_
P-PNE
Nominal Shock
.
80 Period
40
BH
_
P-PNE
Nominal Shock
.
40
$20
$15
$10
$5
$0
-$5 0
-$10
-$15
-$20
80 Period
$20
$15
$10
$5
$0
-$5 0
-$10
-$15
-$20
CL
Nominal Shock
.
80 Period
40
0.564601
-0.21091
So: We observe no significant deviations in NE d
CH
Nominal Shock
pds. 1-10
pds 11-20
pds. 21-30
pds. 31-40
.
40
80 Period
Observe that the relative stability of the Bertrand markets contrasts
sharply with that in the Cournot markets.
-Observe also that the only obvious evidence of tacit collusion
comes in the BL treatment.
pds. 41-60
pds. 61-80
pds. 81-100
pds.101-120
To evaluate convergence levels, we follow Chen and Gazzale (2004) and
examine the percentage of decisions within =5% of the static NE action
choice.
Table 2 - Level of Convergence in the Last 20 periods
Percentage of players within 5% of Nash Equilibrium
Permutation Tests
Initial Sequence
(1)
Treatment
BH
BL
CH
CL
i
0.91
0.89
0.33
0.48
ii
0.88
0.70
0.18
0.24
Treatment
BH
BL
CH
CL
i
0.84
0.16
0.11
0.28
ii
0.96
0.88
0.03
0.08
(2)
Markets
iii
iv
0.75 0.93
0.60 0.04
0.16 0.58
0.09 0.13
(3)
Overall
v
0.81
0.65
0.14
0.24
Markets
iii
iv
0.76 0.98
0.71 0.29
0.10 0.15
0.03 0.06
Post-Shock Sequence
Overall
v
vi
0.66 0.91
0.85
0.21 0.01
0.38
0.09 0.00
0.08
0.38 0.00
0.14
vi
0.98
0.46
0.21
0.13
0.88
0.56
0.26
0.21
(4)
H1
CL ≠BL
BH≠ CH
H1
CL≠ BL
BH ≠CH
(5)
p- value
0.08*
0.00***
p- value
0.57
0.00***
To gain more
insight into
convergence
levels and to
evaluate
convergence
speeds, we
analyze a
linear
probability
model.
Table 3. Convergence Levels and Speed: Linear Probability Models with Clustering at
the Market Level
Dependent Variable: Percentage of plays within 5% of the NE
Independent Variable
Constant
DBL
DCH
DCL
ln (period)
Initial Sequence
(1)
(2)
0.47***
(0.09)
-0.28***
(0.09)
-0.55***
(0.07)
-0.58***
(0.06)
0.10***
(0.02)
DBL ln(period)
DCH ln(period)
DCL ln(period)
Observations
Number of Groups
Adjusted R2
F(3,23)
960
24
0.50
39.99
DBL=DCL
- DCH=DBL - DCL
DBL ln(period)=DCL ln(period)
- DCH ln(period)=
DBL ln(period)- DCL ln(period)
13.32***
65.23***
0.27***
(0.02)
-0.10***
(0.03)
-0.19***
(0.02)
-0.20***
(0.02)
960
24
0.78
86.09
Post shock Sequence
(3)
(4)
***
0.60
(0.09)
-0.45***
(0.11)
-0.72***
(0.06)
-0.64***
(0.07)
0.06***
0.27***
(0.02)
(0.02)
-0.15***
(0.04)
-0.24***
(0.02)
-0.22***
(0.02)
960
960
24
24
0.58
0.74
52.18
70.90
3.40*
58.22***
11.66***
3.42*
61.11***
55.46***
Notes: Robust standard errors in parentheses are adjusted for clustering at the market level.
Significant at * 10 percent level; ** 5 percent level, *** 1 percent level. Dy is the dummy variable
for treatment y. The excluded dummy is DBH. The bottom panel presents null hypotheses and
Wald 2(1) test statistics.
This analysis suggests an initial pair of findings, regarding
convergence.
Finding 1. Neither convergence levels nor convergence speeds
are significantly higher in Cournot markets than in comparable
Bertrand markets. In fact, in most instances, the opposite is true.
Finding 2. Increasing differentiation improves convergence
levels and speeds in Bertrand markets relative to Cournot
markets.
Notes:
-Finding 1 runs exactly counter to both HHST and Fehr and Tyran.
-Finding 2 runs flatly against the ‘endogenous rationality’ argument of
Fehr and Tyran. We’ll consider reasons for this momentarily. First,
however, consider tacit collusion.
Tacit Collusion. Following Potters and Suetens (2008) we analyze tacit
collusion in terms of a cooperativeness index
average choice kt  choice Nash
kt 
choice JPM  choice Nash
Table 4 – Degree of Cooperation -Last 20 periods
k
treatment
BH
BL
CH
CL
Initial Sequence
(2)
Markets
i
ii
iii
iv
v
vi
-0.03 0.00 -0.02 0.02 -0.02 0.02
0.03 -0.06 -0.02 0.34 0.00 0.03
0.02 0.05 -0.13 -0.01 -0.05 0.10
0.04 0.03 -0.28 -0.13 -0.08 0.49
BH
BL
CH
CL
i
-0.01
0.23
0.07
-0.25
(1)
Treatment
Post-Shock Sequence
ii
iii
iv
v
vi
-0.01 -0.04 0.02 0.00 0.02
-0.03 -0.08 -0.16 0.24 0.58
-0.05 0.00 -0.06 0.04 -0.13
-0.33 -0.69 0.02 -0.09 -1.56
average choice kt  choice Nsah
 choice JPM  choice Nash
t  y  20
Permutation Tests
(3)
Overall
(4)
H1
(5)
p
-0.01
0.05
0.00
0.01
BL≠CL
BH≠CH
1.00
1.00
0.00
0.13
-0.02
-0.48
BL≠CL
BH≠CH
0.08*
1.00
y
Notes: k 
20
.where y= the final period for a sequence k (e.g.,
period 40 or period 80). Bolded entries highlight instances where k>.20
Mean
cooperation
rates are not
significant
higher in BH
markets than
in CH mkts.
BL markets are
more
cooperative
(less
uncooperative)
than CL
markets.
This yields two additional results, each of which pertains to tacit
collusion
Finding 3. Tacit collusion is not uniformly more pervasive in Bertrand
Markets than in Cournot Markets. When q=.9 the effects of tacit
collusion are no more pronounced in Bertrand markets than in
Cournot markets.
Finding 4. Reducing substitutability from q=.9 to q=.5 increases the
incidence of tacit collusion in Bertrand markets relative to Cournot
markets.
Tacit Collusion and Institutions. There is little organized activity in
any of the markets. Sellers, however, do engage in signaling activity. Consider
the signals sent.
(1)
Treatment
i
ii
Table 5. Signaling Activity
(2)
Market
iii
iv
(3)
Overall
v
vi
7/ 0
0/ 0
0/ 0
0/ 11
Initial Sequence
9/ 0
4/ 0
6/ 14
2/ 26
0/ 0
0/ 0
0/ 0
0/ 11
7/ 0
4/ 12
0/ 0
0/ 11
4/ 0
2/ 21
0/ 0
0/ 0
37/ 0
3/ 73
0/ 11
0/ 33
11/ 0
0/ 0
1/ 0
0/ 0
Post Shock Sequence
11/ 0
5/ 0
2/ 0
0/ 13
1/ 0
2/ 0
3/ 0
2/ 0
15/ 0
5/ 11
0/ 0
0/ 0
5/ 0
3/ 31
0/ 0
0/ 0
52/ 0
10/ 88
4/ 13
5/ 0
Spikes / Surges*
BH
BL
CH
CL
BH
BL
CH
CL
6/ 0
1/ 0
0/ 11
0/ 0
10/ 0
0/ 33
0/ 13
0/ 0
* Notes: ‘Spikes’ are quantity postings of zero, or a price postings that yield sales of zero.
‘Surges’ are consecutive periods of quantity postings below, or price postings above the best
reply by a margin sufficient to miss the forecasting prize (10 minimum). Bolded entries highlight
instances where the cooperative index >.20.
Data are only suggestive, but signaling levels are higher in Bertrand
markets than in Cournot markets. High prices appear to be driven by
‘surges’ rather than ‘spikes’.
6. Bounded Rationality and Market Convergence.
Why don’t
Cournot markets converge more quickly than Bertrand markets? We consider this
question in terms of response to the nominal shock.
q=.5
Consider first how
sellers update
expectations
Frequency
50%
40%
BL
CL
30%
20%
10%
0%
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10 >10.5
Range Midpoint- $ (Bertrand) or Units (Cournot)
q.9
Frequency
50%
40%
BH
CH
30%
20%
10%
0%
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Range Midpoint - $ (Bertrand) or Units (Cournot)
Cournot sellers (hollow bars) do not update expectations more
quickly than Bertrand sellers (solid bars).
7
8
9
10 >10.5
More problematic: Cournot sellers do not appear to best respond to their
forecasts.
pi
qi
50
BL
50
40
Best Response
30
q i given q -if
40
p i given p -if
'Surge' Prices
CL
30
20
20
10
10
Best Response to q -if
0
0
10
20
pi
30
40
50 p -if
40
10
20
30
40
50 q -if
CH
q i given q -if
40
Price 'Spike'
Best Response
p i given p -if
30
0
qi
50
BH
50
0
30
20
20
10
10
0
0
Best Response to q -if
0
10
20
30
40
50 p -if
0
10
20
Quantity 'Spike'
Figure 6a. Price (Quantity) Choices given forecasts, periods 41-46.
30
40
50 q -if
Time does not eliminate this problem. Consider the final 20 periods
post-shock.
pi
qi
50
Bl
50
CL
Price 'Spikes'
40
p i given p -if Best Response
'Surge' Prices
q i given q -if
40
30
30
20
20
10
10
0
0
Best Response to q -if
0
10
20
pi
30
40
50 p -if
40
10
20
qi
50
BH
50
0
30
40
50 q -if
40
50 q -if
CH
40
Price 'Spikes'
Best Response
30
30
q i given q -if
p i given p -if
20
20
10
10
0
0
Best Response to q -if
0
10
20
30
40
50 p -if
0
10
20
30
This would seem to suggest that it is the Bertrand Institution rather than the
Cournot institution that fosters rationality.
Treatment
Table 6. Some Adjustment Rules
Absolute Proximity
Relative Proximity
(1)
(2)
(3)
(4)
(5)
Best Reply
Inertia
Forecast Best Reply
Inertia
(6)
Forecast
First 5 periods post shock (Periods 41-46)
BH
0.38
0.32
0.36
BL
0.13
0.17
0.10
CH
0.03
0.18
0.17
CL
0.03
0.17
0.11
0.45
0.30
0.32
0.29
0.29
0.37
0.41
0.37
0.27
0.33
0.27
0.34
Last 40 periods (Periods 41-80)
BH
0.56
0.55
BL
0.20
0.40
CH
0.10
0.30
CL
0.11
0.29
0.30
0.21
0.29
0.22
0.30
0.31
0.28
0.30
0.40
0.48
0.43
0.48
0.46
0.27
0.16
0.10
Bertrand sellers are absolutely closer to BR than Cournot sellers
But, we suspect that the pertinent rationality bound here regards action responses.
In addition to making best replies, sellers use rules of thumb, such as the own
action choice of the preceding period (‘inertia’) or the anticipated actions of rivals
(‘herding’) as anchors. Notice that in relative terms these choice frequencies are
quite similar for all sellers.
Interestingly, the relative incidence of these rules is remarkably similar
across treatments. Observe also that few individuals select a ‘pure’ rule.
Incidence
CL
Incidence
100%
100%
80%
80%
60%
60%
40%
40%
20%
20%
0%
0%
Participants
Incidence
Participants
CH
Incidence
100%
100%
80%
80%
60%
60%
40%
40%
20%
20%
0%
Best Reply Deviation
BL
BH
v
0%
Participants
Forecast Deviation
Inertia Deviation
Best Reply Deviation
Participants
Forecast Deviation
Inertia Deviation
Institutions interact with the use of these anchors in that the distance between
these anchors varies substantially. To see this, consider again figure 1.
pi
Bertrand Game (q =.5)
qi
Cournot Game (q =.5)
45  line
45° line
Best Reply Pre-Shock
Best Reply Pre Shock
A
A
qA
pA
C
B
pB
C
B
Best Reply Post Shock
pC
pA
qC
p-i
Bertrand Game (q =.9)
pi
Best Reply, Post Shock
qB
q -i
qA
Cournot Game (q =.9)
qi
q -i
45  line
45° line
Best Reply Pre-Shock
Best Reply Pre Shock
c
a
qa
a
pa
pb
c
b
pc pa
Best Reply, Post Shock
Best Reply Post Shock
q bT
qb
p -i
qc
q cT
qa
b
q -i
q -i
The distance
between an
‘inertia’
choice, for
example, and
an adaptive
best reply is
much smaller
in Bertrand
markets than
in Cournot
markets.
A simple simulation represents one method that might support the plausibility of a
conjecture that the increased differences between rules of thumb and best replies
in the Cournot game explains the observed relative instablity of Cournot markets.
Suppose that sellers use a mechanical rule. They anchor action choices on best
reply, inertia and herding with equal probabilities. That is,
BR ( a ft )(1   ) Pr(1 / 3)
at  a ft (1   )
Pr(1 / 3)
at 1 (1   )
Pr(1 / 3)
Initial choices are randomly selected over the action space range. In
a subsequent periods, sellers reduce the markup of price over cost,
or their quantity by half until they hit the market once. Then they
follow the above rule.
S im u la te d A b so lu te D e v ia tio n s
(n = 5 ,0 0 0 )
|P -P N E |
Shock
$12
$8
CH
CL
$4
$0
0
BL
BH
40
80
P e rio d
O b se rv e d A b so lu te D e v ia tio n s- M A (5 )
|P -P N E |
N o m in a l S h o c k
CH
$12
Observe:
Simulated absolute
mean transaction
price deviations
look pretty similar
to observed results
(smoothed for
purposes of
presentation to a
MA(5) process).
CL
$8
v
BL
$4
$0
0
40
80
BH
P e rio d
O b se rv e d A b so lu te D e v ia tio n s, A d ju ste d fo r
T a c it C o llu sio n a n d 'C o n fu sio n ' - M A (5 )
|P -P N E |
N o m in a l S h o c k
CH
$12
CL
$8
v
BL
$4
$0
0
40
BH
80
P e rio d
Results are
particularly close if
‘cooperative’
sessions are
excluded.
Conclusions
Our Cournot markets neither converge more quickly or completely,
nor are they uniformly more susceptible to tacit collusion than
Bertrand markets
Importance
- For IO this calls into question the relative preferability of Cournot
markets. The answer turns on whether the pertinent rationality bound
regarding updating expectations, or submitting best responses.
-More generally, suggests a caution about making broad inferences
about performance in natural contexts from highly stylized
experiments. This is particularly true when the motivation driving the
result is a form of bounded rationality.
-In moving from a simple context to a relatively more complicated
one, other rationality limitations may arise, and may exert dominating
effects.