On the limits of cooperation in the Arctic to stabilize energy supply Lisa Schulten 1 Alberto Vesperoni 2 University of Siegen 33 rd USAEE/IAEE North American Conference October 25–28, 2015 1 schulten@vwl.uni-siegen.de 2 alberto.vesperoni@gmail.com
Outline 1 The Arctic 2 Model 3 Results 4 Discussion 5 Conclusions Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 2 / 16
The Arctic Borders in the Arctic Figure: Source: Durham University, NASA Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 3 / 16
Model Model setup two countries 1 and 2 endowed with initial stocks x 1 > 0 , x 2 > 0 stock of country i increases by flow ǫ i ≥ 0 final stock: y i = x i + ǫ i each flow takes value in finite set Ω ⊂ R + E [ y i ] characterizes the expected stock of player i ∈ { 1 , 2 } � � ⇒ E [ y i ] = x i + E [ ǫ i ] = x i + ǫ i p ( ǫ 1 , ǫ 2 ) ǫ 1 ∈ Ω ǫ 2 ∈ Ω Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 4 / 16
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 s i 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 Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 5 / 16
Model Model setup countries cooperate if the following condition is fulfilled s i ( x i + E [ ǫ i ] , x ¬ i + E [ ǫ ¬ i ]) > E [ s i ( x i + ǫ i , x ¬ i + ǫ ¬ i )] (1) probability mass function is assumed to be symmetric p ( ǫ 1 , ǫ 2 ) = p ( ǫ 2 , ǫ 1 ) for any ǫ 1 , ǫ 2 ≥ 0 Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 6 / 16
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 Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 7 / 16
Results Proposition 2 Proposition Players cooperate if x 1 = x 2 and the joint distribution is perfectly positively correlated. ǫ 2 h l h . 6 0 ǫ 1 l 0 . 4 Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 8 / 16
Results Proposition 3 Proposition Players do not cooperate if the joint distribution is perfectly negatively correlated. ǫ 2 h l h 0 . 5 ǫ 1 l . 5 0 Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 9 / 16
Results Proposition 4 Proposition Given any uniform and dyadic joint distribution, players cooperate if and only 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 s i ( x i , x ¬ i ) � k / 2 Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 10 / 16
Discussion Cooperation in the Arctic NATO vs. Russia cooperate to clarify the Arctic resource potential jointly? Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 11 / 16
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 Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 11 / 16
Discussion Exhaustivity after Cold War rise of China, India, Brazil the world became more multipolar → no exhaustivity Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 12 / 16
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. Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 13 / 16
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? Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 13 / 16
Conclusions Conclusions theoretical analysis finds the following minimum requirements for cooperation: 1 no exhaustivity 2 x 1 = x 2 and perfect positive correlation of the joint distribution 3 no hegemony in the context of the Arctic (1) is fulfilled, but (2) is disputable Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 14 / 16
Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 15 / 16
Thank you for your attention! Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 16 / 16
Back up Basic assumptions Anonymity: s 1 ( y 1 , y 2 ) = s 2 ( y 2 , y 1 ) for all y 1 , y 2 ≥ 0 Monotonicity: s i ( y ′ i , y ¬ i ) > s i ( y i , y ¬ i ) if y ′ i > y i and s i ( y i , y ′ ¬ i ) < s i ( y i , y ¬ i ) if y ′ ¬ i > y ¬ i Risk aversion: s i ( x i + E [ ǫ i ] , x ¬ i ) > E [ s i ( x i + ǫ i , x ¬ i )] for all x 1 , x 2 ≥ 0 Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 1 / 3
Back up Further restrictions Independence of normalized payoffs: s i ( y i , y ¬ i ) / r ( y 1 , y 2 ) = s i ( y ′ i , y ′ ¬ i ) / r ( y ′ 1 , y ′ 2 ) if and only if y i = y ′ i Independence of residual: r ( y 1 , y 2 ) = r ( y ′ 1 , y ′ 2 ) if and only if y 1 + y 2 = y ′ 1 + y ′ 2 Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 2 / 3
Back up Example uniform dyadic joint distribution ǫ 2 δ 0 δ . 25 . 25 ǫ 1 0 . 25 . 25 Schulten & Vesperoni Cooperation in the Arctic October 27, 2015 3 / 3
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