On the limits of cooperation in the Arctic to stabilize energy - - PowerPoint PPT Presentation

On the limits of cooperation in the Arctic to stabilize energy supply

Lisa Schulten1 Alberto Vesperoni2

University of Siegen

33rd USAEE/IAEE North American Conference October 25–28, 2015

1schulten@vwl.uni-siegen.de 2alberto.vesperoni@gmail.com

Outline

1 The Arctic 2 Model 3 Results 4 Discussion 5 Conclusions

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The Arctic

Borders in the Arctic

Figure: Source: Durham University, NASA

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Model

Model setup

two countries 1 and 2 endowed with initial stocks x1 > 0, x2 > 0 stock of country i increases by flow ǫi ≥ 0 final stock: yi = xi + ǫi each flow takes value in finite set Ω ⊂ R+ E [yi] characterizes the expected stock of player i ∈ {1, 2} ⇒ E [yi] = xi + E [ǫi] = xi +

• ǫ1∈Ω
• ǫ2∈Ω

ǫip(ǫ1, ǫ2)

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Model

Model setup

payoffs of both players are defined by their security we assume the security of a player is a function of both stocks of strategic goods to capture the rivalry the function si is twice differentiable and fulfills the following basic properties: Anonymity payoffs are a priori symmetric Monotonicity payoff of a country strictly increases in its own stock and strictly decreases in the stock of the other Risk aversion for any given stock of the other, a player always prefers to receive a deterministic flow equal to the expected flow

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Model

Model setup

countries cooperate if the following condition is fulfilled si(xi + E [ǫi] , x¬i + E [ǫ¬i]) > E [si(xi + ǫi, x¬i + ǫ¬i)] (1) probability mass function is assumed to be symmetric p(ǫ1, ǫ2) = p(ǫ2, ǫ1) for any ǫ1, ǫ2 ≥ 0

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Results

Proposition 1

Proposition If payoffs are exhaustive players never cooperate. Exhaustivity the two countries always possess the total of the resources (e.g. share of total earth’s surface) jointly

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Results

Proposition 2

Proposition Players cooperate if x1 = x2 and the joint distribution is perfectly positively correlated. ǫ2 h l ǫ1 h .6 l .4

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Results

Proposition 3

Proposition Players do not cooperate if the joint distribution is perfectly negatively correlated. ǫ2 h l ǫ1 h .5 l .5

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Results

Proposition 4

Proposition Given any uniform and dyadic joint distribution, players cooperate if and

• nly if none of them is hegemonic.

Given k > 0 total resources (e.g. share of total earth’s surface), player i ∈ 1, 2 is said to be hegemonic if si(xi, x¬i) k/2

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Discussion

Cooperation in the Arctic

NATO vs. Russia cooperate to clarify the Arctic resource potential jointly?

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Discussion

Cooperation in the Arctic

NATO vs. Russia cooperate to clarify the Arctic resource potential jointly? no cooperation in case of:

1 exhaustivity 2 perfect negative correlation 3 hegemony

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Discussion

Exhaustivity

after Cold War rise of China, India, Brazil the world became more multipolar → no exhaustivity

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Discussion

Perfect positive/negative correlation

Perfect positive correlation NATO and Russia commit to an agreement to share resources equally. Then all uncertainty is reduced to the total amount of existing resources. The total amount may be high or low, but both get equal shares.

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Discussion

Perfect positive/negative correlation

Perfect positive correlation NATO and Russia commit to an agreement to share resources equally. Then all uncertainty is reduced to the total amount of existing resources. The total amount may be high or low, but both get equal shares. Perfect negative correlation The aggregate amount of resources is known, but not their location and hence it is not clear who owns them. An agreement does not exist between NATO and Russia, so all uncertainty is about who gets them. Is an agreement between NATO and Russia likely?

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Conclusions

Conclusions

theoretical analysis finds the following minimum requirements for cooperation:

1 no exhaustivity 2 x1 = x2 and perfect positive correlation of the joint distribution 3 no hegemony

in the context of the Arctic (1) is fulfilled, but (2) is disputable

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Thank you for your attention!

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Back up

Basic assumptions

Anonymity: s1(y1, y2) = s2(y2, y1) for all y1, y2 ≥ 0 Monotonicity: si(y′

i , y¬i) > si(yi, y¬i) if y′ i > yi and

si(yi, y′

¬i) < si(yi, y¬i) if y′ ¬i > y¬i

Risk aversion: si(xi + E [ǫi] , x¬i) > E [si(xi + ǫi, x¬i)] for all x1, x2 ≥ 0

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Back up

Further restrictions

Independence of normalized payoffs: si(yi, y¬i)/r(y1, y2) = si(y′

i , y′ ¬i)/r(y′ 1, y′ 2) if and only if yi = y′ i

Independence of residual: r(y1, y2) = r(y′

1, y′ 2) if and only if y1 + y2 = y′ 1 + y′ 2

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Back up

Example uniform dyadic joint distribution

ǫ2 δ ǫ1 δ .25 .25 .25 .25

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