Game theory focus group

E&P Games

Bart J.A. Willigers, Palantir Economic Solutions Ltd.

Reidar Bratvold & Kjell Hausken, University of Stavanger, Norway

Agenda
• Introduction Game theory

• Three games

– Oil price setting

– Investing in one field or the next

– Choosing a regional hub

• Decision analysis and game theory

• Conclusions

“Slave”

“Master”


Game theory
• Players in a relationship have different objectives and influencing powers

• The optimal choice for any individual player might not be optimal for its fellow
players

• The preferred outcomes might not be achievable because of the power of other
participants


How many SPE papers have been written on game theory?

a) more then 1,000

b) between 500 and 1,000

c) between 100 and 500

d) between 50 and 100

e) less than 50


• Some SPE statistics….. • How many SPE game theory papers?

– Total papers: 50,000 a) more then 1,000

– Risk papers: 6,338 b) between 500 and 1,000

– Real option valuation papers: 803 c) between 100 and 500

• Game theory d) between 50 and 100

e) less than 50
– Two Nobel prizes

– 27,000 Amazon hits


One paper has been written….
• W. C. Kimbrell (2008)The Consideration and Applicability of Game Theory to
Reserve Valuation. SPE 115541

• 0.002% of the SPE library focuses on Game theory!


Game 1: Oil price setting

• OPEC countries aim to maximise their oil revenues by
setting production targets


Example 1: Oil price setting
• A country can either produce 10 or 20 bll

• Increased production will lower oil price

160
140
120
100
Oil price

80
60
40
20
0
15 20 25 30 35 40 45
Oil produced


Large producing country B

Low production High production
Large Low
producing production
country A
High
production



Large Low 140$*10bll
producing production 140$*10bll
country A
High
production



Large Low 140$*10bll 75$*20bll
producing production 140$*10bll 75$*10bll
country A
High 75$*10bll 40$*20bll
production 75$*20bll 40$*20bll



Large Low 1400$ 1500$
producing production 1400$ 750$
country A
High 750$ 800$
production 1500$ 800$



Large Low
producing production 1400$
country A
High
production 1500$



Large Low
country A
High



Large Low 1400$ 1500$
country A
High
production



Large Low 1400$ 1500$
country A
High 750$ 800$
production


Small producing country C

Large Low 140$*1bll 140$*2bll
producing production 140$*20bll 140$*20bll
country A
High 40$*1bll 40$*2bll
production 40$*40bll 40$*40bll


Large producing country A

Large Low 140$ 280$
country B
High 40$ 80$


The real-life game
• High oil price rises in the 1970s caused a global recession. This reduced oil
consumption for a long period

• Small Producers like Algeria, Nigeria and Libya frequently cheat and exploit the
high prices. Saudi Arabia has a strong incentive not to cheat in order to keep
prices high


• Nash equilibrium: none of the players can profit from changing strategy

• Cournot game: Market equilibrium


Game 2: Investing in a hub or satellite field
• Two E&P players

– have an equity stake in two hydrocarbon fields

– are considering investment in one of the fields

• One field is also a regional hub


Invest in hub
Total for Total for
Hub Satellite player project
Player A 334
Player B 3,002

Invest in satellite
Total for Total for
Player A 258
Player B 2,323


Invest in hub
Total for Total for
Player A 334 1,196
Player B 3,002 133

Invest in satellite
Total for Total for
Player A 258 1,341
Player B 2,323 149


Invest in hub
Total for Total for
Player A 334 1,196 1,530 4,664
Player B 3,002 133 3,134

Invest in satellite
Total for Total for
Player A 258 1,341 1,599 4,072
Player B 2,323 149 2,472


Invest in hub
Total for Total for
Player A 4,664
Player B

Invest in satellite
Total for Total for
Player A 4,072
Player B


Invest in hub
Total for Total for
Player A 4,664
Player B 3,134

Invest in satellite
Total for Total for
Player A 4,072
Player B 2,472


Invest in hub
Total for Total for
Player A 1,530 4,664
Player B

Invest in satellite
Total for Total for
Player A 1,599 4,072
Player B


Game findings
• The preference of a player does not necessarily lead to an optimal overall
project outcome

• Real life additional complexities:

– Investment in host might delay it’s COP

– Information asymmetry


Game 3: Where to build a regional processing facility
• Three E&P players

– equity stakes in three hydrocarbon fields

– when and what regional hub to build

• The reserves of the fields are uncertain

• The facility capex and opex varies for each option


Which Size 1st Which
field? discovery
Build hub?
hub?
First drilling campaign

Which Size 2nd Which
field? discovery
Build hub?
hub?
Second drilling campaign

Size 3th
Build hub?
Which Third drilling campaign
discovery hub?

Production Cost

Value


Hub
Player 1 2 3
Value matrix a
b
c
Total

Player 1 2 3
Loss matrix a
b
c


Hub
Player 1 2 3
Value matrix a 112.5 102.5 97.0
b
c
Total

Player 1 2 3
Loss matrix a
b
c


Hub
Player 1 2 3
Value matrix a 112.5 102.5 97.0
b 153.0 143.0 112.0
c 178.8 208.8 100.0
Total 444.3 454.3 309.0

Hub
Player 1 2 3
Loss matrix a
b
c


Hub
Player 1 2 3
Value matrix a 112.5 102.5 97.0
b
c
Total

Hub
Player 1 2 3
Loss matrix a
b
c


Hub
Player 1 2 3
Value matrix a 112.5 102.5 97.0
b 153.0 143.0 112.0
c
Total

Hub
Player 1 2 3
Loss matrix a
b
c


Hub
Player 1 2 3
Value matrix a 112.5 102.5 97.0
b 153.0 143.0 112.0
c 178.8 208.8 100.0
Total 444.3 454.3 309.0

Hub
Player 1 2 3
Loss matrix a 10.0
b 10.0
c 0.0


Hub
Player 1 2 3
Value matrix a 112.5 102.5 97.0
b 153.0 143.0 112.0
c 178.8 208.8 100.0
Total 444.3 454.3 309.0

Hub
Player 1 2 3
Loss matrix a 0.0 10.0 15.5
b 0.0 10.0 41.0
c 30.0 0.0 108.8


120

100
Win-Lose
80
Win-Win

Loss player B
60

40
Lose-Lose
20
Lose-Win
0
0 20 40 60 80 100 120

45 Loss player A

40 Hub 1 Hub 2 Hub 3
35
30
Loss player B

25
20
15
10
5
0
0 20 40 60 80 100 120
Loss player A
Hub 1 Hub 2 Hub 3


Game findings
• Recognition of allies and rivals

• A player can suffer from additional information

– Preferences are aligned on the basis of expected values

– Conflicting preferences arise when uncertainty is resolved


Agenda
• Introduction Game theory

• Three games

• Oil price setting

• Investing in one field or the next

• Choosing a regional hub

• Decision analysis and game theory

• Conclusions

Ronald Howard
Formulated “decision analysis”

John von Neumann
Minimising Maximum loss (MinMax Theorem)
Backward induction
First formal treatment Game theory

Oskar Morgenstern
First formal treatment Game theory


Game theory Decision analysis

Player A – Decision analysis Uncertainties

Player C – Decision analysis Options

Player B – Decision analysis Players


A game-theoretic framework is relevant if:
1. Multiple players, each of which maximises an objective

2. At least one player can chose between alternatives

3. The payoff to each player depends on the combinations of strategies chosen
by all players


Game theory and E&P economic analysis
• Fellow players can make or break the project for an individual player

• The impact of competing players has been largely ignored

• Modelling complexity: multiple players and uncertainty

Game theory focus group

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