Game Theory Problem Set #3: OPEC Strategy Memo
Latin Gambits: Matias Bebin / Rodrigo Donoso / Paul Kisiliuk / Andres Pachano / Iñaki Ruiz
Problem Set #3: OPEC Strategy Memo
To begin our analysis we decided to look for the two possible extreme solutions, namely, a fully
collusive one, where all OPEC countries would act fully coordinated forming a monopoly (not a
perfect one as a consequence of the rest of the world (“ROW”) presence), and a fully competitive
one, where no coordination whatsoever would occur. The overall analysis was mainly based on
Cournot’s model.
For the fully collusive outcome we considered all OPEC countries as one producer and therefore
obtained the following marginal cost curve:
OPEC (Colluded) Marginal Cost Courve
Marginal Cost $
25
20
15
10
y = 0.0004x + 3.0921
R² = 0.8814
5
‐
2,500
12,500
22,500
32,500
Barrels Produced
42,500
In order to find the optimal production level we found the point at which the monopolized
OPEC’s marginal revenues would equal their marginal costs. The solution demands an
intermediate step, where the quantity to be produced by OPEC is subject to the quantity
produced by ROW and vice versa. The only difference between OPEC and ROW’s decision
processes is in that OPEC consider its marginal revenue at the time of defining its quantity and
ROW, as a price taker, consider the overall demand (that is, OPEC solves finding the intersection
between marginal cost and marginal revenue and ROW solves finding the intersection between
world demand and marginal cost).
The high and low demand curves and their corresponding ROW marginal cost curves used
through the entire analysis where the following:
Feb-2012
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Game Theory Problem Set #3: OPEC Strategy Memo
Latin Gambits: Matias Bebin / Rodrigo Donoso / Paul Kisiliuk / Andres Pachano / Iñaki Ruiz
World Demand (Low Period)
ROW Marginal Cost (Low Period)
y = ‐0.005x + 448.98
R² = 0.9746
150.00
100.00
50.00
200.00
150.00
Price $
Price $
200.00
100.00
50.00
‐
60,000
65,000
70,000 75,000
Barrels ‐
43,000 44,000 45,000 46,000 47,000 48,000
Barrels
80,000
World Demand (High Period)
150
ROW Marginal Cost (High Period)
200
y = ‐0.0045x + 440.96
R² = 0.9676
150
Price $
Price $
200
y = 0.0197x ‐ 786.03
R² = 0.974
100
100
y = 0.0195x ‐ 775.6
R² = 0.9862
50
50
‐
60,000 65,000 70,000 75,000 80,000 85,000
Barrels ‐
43,000 44,000 45,000 46,000 47,000 48,000 49,000
Barrels
As a result the fully collusive outcome obtained for both the low and high demand periods were
an expected price of $115.77 and $123.21 respectively. This equilibrium is obtained when
colluded OPEC decides to produce 20,866 and 24,517 barrels for the low and high demand
periods respectively. Since these results would imply that some of the countries shouldn’t
produce in low demand periods and others shouldn’t produce at all, we believe that such an
outcome is impossible for the game under analysis.
The following table summarizes the production quantities by country and their corresponding
expected profits. This profits represent the highest achievable expected profit for OPEC overall.
FULLY COLLUSIVE
UAE
Nigeria
Saudi
Iran
Kuwait
Iraq
Venezuela
Total
Feb-2012
Marginal Cost
5
7
9
10
13
16
20
Low Demand Prod.
High Demand Prod.
Total Exp.Profits $
3,000
3,000
3,379,171,075
2,700
2,700
2,988,333,977
12,000
12,000
13,046,284,383
3,166
4,600
4,803,781,946
2,217
1,134,611,124
20,866
24,517
25,352,182,505
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Game Theory Problem Set #3: OPEC Strategy Memo
Latin Gambits: Matias Bebin / Rodrigo Donoso / Paul Kisiliuk / Andres Pachano / Iñaki Ruiz
For the case of a fully competitive scenario, we solved using Cournot’s model, where each
OPEC country choose a quantity to produce based on what the rest of the countries and the world
produce. In order to solve this problem, we started solving country by country, from the smallest
to the biggest assuming that the rest of the countries would produce at maximum capacity and
that ROW would respond as price taker (just like in the previous case).
This process resulted in that for most countries, in both periods (Low and High) their optimal
production (where their marginal revenue would equal their marginal cost) was well above their
production capacity. According to our calculations, this was true for all but one country. Saudi
Arabia faced an optimal production level of 11,509 barrels for the Low demand period, which is
slightly below their maximum capacity of 12,000 barrels.
Running the calculations again, now assuming that Saudi Arabia only produces 11,509 barrels on
low demand periods, the rest of the OPEC countries still faced optimal levels above their
maximum capacity for both demand periods.
The following table summarizes the production quantities by country and their corresponding
expected profits under a competitive scenario. This profits represent the lowest rationally
achievable expected profit for OPEC overall.
NO COOPERATION
UAE
Nigeria
Saudi
Iran
Kuwait
Iraq
Venezuela
Total
Marginal Cost
5
7
9
10
13
16
20
Low Demand Prod.
High Demand Prod.
Total Exp.Profits $
3,000
3,000
2,149,907,579
2,700
2,700
1,881,996,831
11,509
12,000
7,981,377,340
4,600
4,600
3,071,124,994
3,300
3,300
2,106,178,382
3,700
3,700
2,252,692,751
4,400
4,400
2,506,397,896
33,209
33,700
21,949,675,773
In order to define a maximum price to bid on the OPEC countries auction we decided that we
would be willing to pay an amount equal to the expected profits of the fully competitive outcome
minus the value of the least valuable country (Nigeria) plus its minimum bid value (M$ 100).
Feb-2012
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Game Theory Problem Set #3: OPEC Strategy Memo
Latin Gambits: Matias Bebin / Rodrigo Donoso / Paul Kisiliuk / Andres Pachano / Iñaki Ruiz
The following table summarizes the maximum bidding values obtained for each country and the
value paid for Saudi Arabia:
BID VALUES
UAE/Kuwait
Nigeria
Saudi
Iran
Iraq
Venezuela
Max Bid Value
2,474,089,131
100,000,000
6,199,380,509
1,289,128,164
470,695,920.33
724,401,066
Value Paid
6,000,000
-
As the largest producer, we were expected to lead the negotiations by our fellow collusive
comrades; however, we decided to let them do the talk in order to assess their true willingness to
achieve a collusive outcome.
The first problem that we all faced was that the best outcome would imply that some countries
wouldn’t produce. As a solution to this problem we decided to propose a system where
agreements would be reached in terms of production quotas as a percentage of total production
capacity.
Although we knew that each country would have a different quota that would maximize their
profit, we also knew that our quota, as well as the rest’s was fairly close to the quota that
maximized the overall revenues (74%/Low, 86%/High), therefore we immediately accepted this
terms when proposed by one of the countries.
The graph below shows the marginal revenue for OPEC overall at different levels of
productions, as percentage of total capacity. The graph also shows the marginal profit for Saudi
Arabia, within the same ranges:
Feb-2012
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Game Theory Problem Set #3: OPEC Strategy Memo
Latin Gambits: Matias Bebin / Rodrigo Donoso / Paul Kisiliuk / Andres Pachano / Iñaki Ruiz
60,000
Maximization Low Demand Period
40,000
$ Th.
20,000
‐
(20,000)
(40,000)
(60,000)
$ Th.
OPEC Marginal Revenue
70,000
60,000
50,000
40,000
30,000
20,000
10,000
‐
(10,000)
(20,000)
(30,000)
Saudi's Marginal Profit
Maximization High Demand Period
OPEC Marginal Revenue
Saudi's Marginal Profit
Afterwards, another problem we faced was that we had been the only country that had used
Cournot and considered ROW in the analysis with a dynamical approach, where even thought
they would act as price takers, their actions would affect the price. As a result, the expected
prices that our brothers expected were well above the ones we managed. Explaining them that
expected prices should be lower than what they expected was somehow difficult, as trust issues
where raised immediately (influenced by some previous actions undertook by the Latin Gambits
on past experiments…), as if our intention would be to mask an increased production by our
argument of lower expected collusive prices.
Fortunately we were able to prove that the expected prices should be lower and reached an
agreement to produce 74% in low demand (odd) period and 86% in high demand (even) periods.
We think that this outcome, if complied, would be beneficial to us in absolute as well as in
relative terms. Being the largest producer we have the most to win.
Feb-2012
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Game Theory Problem Set #3: OPEC Strategy Memo
Latin Gambits: Matias Bebin / Rodrigo Donoso / Paul Kisiliuk / Andres Pachano / Iñaki Ruiz
The table below shows the expected profits should OPEC comply with the agreed productions.
Saudi Arabia would make an expected profit of almost $3 Bn. above the auctioned value of $ 6
Bn.
REVENUE MAXIMIZING
UAE
Nigeria
Saudi
Iran
Kuwait
Iraq
Venezuela
Total
Marginal Cost
5
7
9
10
13
16
20
Low Demand Prod.
High Demand Prod.
Total Exp.Profits $
2,220
2,580
2,317,629,093
1,998
2,322
2,043,724,591
8,880
10,320
8,895,924,437
3,404
3,956
3,374,205,974
2,442
2,838
2,343,366,438
2,738
3,182
2,540,786,469
3,256
3,784
2,884,125,425
24,938
28,982
24,399,762,426
Until round 2, Saudi Arabia complied with the agreed production; furthermore, we tend to think
that every other OPEC country complied with the agreed quotas, however, UAE/Kuwait, felt that
the price wasn’t high enough and accused the rest of the countries for not complying with the
agreement and unilaterally decided to increase its production to 100% on period 3. In response to
it, Saudi Arabia increased its production 100% on round 4.
On an effort to reach a new agreement, and in order to increase clarity and reduce the possibility
of defection, Saudi Arabia proposed to limit production only on low demand periods to 74% and
maintain 100% production on high demand periods. As shown in the table below, the effect of
this change should have a reduced impact on profits while we hoped it to clear the path for trust
in the fore coming periods.
REVENUE MAXIMIZING
UAE
Nigeria
Saudi
Iran
Kuwait
Iraq
Venezuela
Total
Marginal Cost
5
7
9
10
13
16
20
Low Demand Prod.
High Demand Prod.
Total Exp.Profits $
2,220
2,700
2,313,492,086
1,998
2,430
2,039,007,685
8,880
10,800
8,870,544,408
3,404
4,140
3,363,630,563
2,442
2,970
2,333,958,130
2,738
3,330
2,528,195,361
3,256
3,960
2,865,913,816
24,938
30,330
24,314,742,049
Overall we have decided to adhere to the agreements for the impact on trust we think that would
have failing to do so. We believe that peer pressure and face to face contact can play a relevant
role in the game’s outcome, more than the threat of potential punishment in terms of increasing
production.
Feb-2012
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Game Theory Problem Set #3: OPEC Strategy Memo
Latin Gambits: Matias Bebin / Rodrigo Donoso / Paul Kisiliuk / Andres Pachano / Iñaki Ruiz
If I would be to advice someone in our position, I would probably recommend him to push from
the beginning the last strategy we tried to apply, providing a simpler agreement that is harder to
fail on. Furthermore, I would recommend them to provide a clear range of acceptable outcomes
in prices to facilitate detection and foster credibility. For example, the graph bellow shows the
minimum price that result from a 97.5% confidence interval at different production quotas. That
way everyone would be clear of what represents a failure and what not, and therefore, situations
like the one presented by UAE/Kuwait could be avoided.
140.0
Minimun Acceptable Price (Low Demand Period)
120.0
100.0
$
80.0
60.0
40.0
20.0
‐
$
Price
160.0
140.0
120.0
100.0
80.0
60.0
40.0
20.0
‐
Minimun Acceptable Price (High Demand Period)
Price
Feb-2012
Low 95% Price
Low 95% Price
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