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 ...
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).
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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.
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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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