The Arctic Saga - Game Theory Analyses

The Arctic Saga
A Game theory Analyses
By Sriram Pakeerathan
A Masters Research Paper presented to the University of Waterloo in
fulfilment of the Masters Research Paper requirement for the degree of
Master of Arts in Political Science
Waterloo, Ontario, Canada, 2014
© Sriram Pakeerathan 2014

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I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis,
including any required final revisions, as accepted by my examiners.
I understand that my research paper may be made electronically available to the public

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Abstract
Previous attempts at explaining Arctic governance using game theory has often been in
favour of the “Arctic race”; a prisoner’s dilemma application to resource extraction. However, this
paper utilizes cooperative coalition game theory to explain various facets of Arctic governance.
This paper concludes that these theories in game theory validate the current trajectory of Arctic
governance despite the perceived media bias towards conflict. Specifically, the application of Risk
Limits and Shapley Value help explain why specific agreements have occurred between member
states of the Arctic Council despite the lack of hard-law in this area. Using three events, this paper
deconstructs the agreements according to the outlined game theory postulates. The first event is the
Barents Sea agreement between Norway and Russia. The second is the stalemate between Denmark
and Canada over Hans Island. The final event is the completion and ratification of the Arctic
Council led Search-and-Rescue (SAR) agreement. As a result of this analyses, it is clear that the
Arctic governance trajectory is firmly in a cooperative coalition structure rather than non-
cooperative and zero-sum as predicted by some.

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Acknowledgements
I would like to thank Dr. Whitney Lackenbauer for his continued support and supervision
throughout this paper. His work on Arctic governance has been a tremendous asset for me to utilize and
this paper would not have been possible without his help. In addition I would like to thank the faculty of
University of Waterloo’s Political Science department for allowing me to write on this topic, in addition to
providing the necessary documents necessary for this completion.

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Table of Contents
Abstract............................................................................................................................................................. ii
Acknowledgements ......................................................................................................................................... iii
Introduction...................................................................................................................................................... 5
Canada .......................................................................................................................................................... 8
Russia.......................................................................................................................................................... 10
USA.............................................................................................................................................................. 12
Denmark ..................................................................................................................................................... 14
Norway........................................................................................................................................................ 16
Game theory................................................................................................................................................... 19
The Role of Equilibrium Points: Nash, Zeuthen, and Game Theory Postulates.......................................... 22
Risk Limits: Payoff Dominance, and Bayesian approach ............................................................................ 26
Coalitions: Shapley value and Communication Bias................................................................................... 29
Game Theory Application ............................................................................................................................... 32
Norway-Russia Agreement: The Barents Sea & the Arctic Ocean.............................................................. 33
Hans Island: Canada versus Denmark......................................................................................................... 38
Search-and-Rescue: Coalition application of Shapley Value ...................................................................... 42
Conclusion....................................................................................................................................................... 46
Bibliography.................................................................................................................................................... 49

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Introduction
Global warming has seen the rise in various conflicts such as drought related impacts in
Africa, to flooding in Bangladesh. However, the role of the Arctic in the post-Cold War era has
shifted from geopolitical and militarized strategy point, to a source of economic growth and
boundary disputes. The Arctic is unique in terms of the actors involved; five developed states
attempting to resolve a boundary dispute with significant consequences both economically, as well
as environmentally. Also referred to as littoral states, they are Russia, Norway, Denmark, Canada,
and the USA. These states alongside Sweden and Finland compose the Arctic Council. In addition
to states, this institution also includes indigenous groups, and members of the science and
environmental community. To various degrees, the Arctic is seen as both an area of cooperation
and conflict; states disagree, but willfully embrace each other’s political ambitions. Despite
growing distrust between NATO members and Russia as a result of Syria and Ukraine, the Arctic
has been left off the negotiation table as a means of sanctioning Moscow. Why has the Arctic
evolved this way despite historical contempt and distrust between NATO and Russia? Why do
states continue to cooperate in a fairly anarchical system? What encourages cooperation in the
Arctic Council despite lacking any meaningful sanction mechanism?
Arctic governance discourse can be divided into two camps; “Arctic race” supporters, and
“Arctic saga” supporters. The former refers to the traditional Realpolitik zero-sum approach of
competition for resources with unilateral action (Lackenbauer, Mirror images? Canada, Russia, and
the circumpolar world, 2010, p. 882). This is in stark contrast to the Arctic saga, which seeks
“stronger collaboration and compromise rooted in sustainable development and stable governance”

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(Lackenbauer, Mirror images? Canada, Russia, and the circumpolar world, 2010, p. 882). The key
premise for this paper is that the Arctic saga is a rational approach by all littoral states. This
challenges traditional assumption of the zero-sum Arctic race rhetoric.
Previous attempts at explaining Arctic governance using game theory has often been in
favour of the “Arctic race”; a prisoner’s dilemma application to resource extraction. However, this
paper utilizes cooperative coalition game theory to explain various facets of Arctic governance.
This paper concludes that these theories in game theory validate the current trajectory of Arctic
governance despite the perceived media bias towards conflict. Specifically, the application of Risk
Limits and Shapley Value help explain why specific agreements have occurred between member
states of the Arctic Council despite the lack of hard-law in this area. This paper will first review the
policies of the five littoral states and their policy trajectory. Following this review, this paper will
outline the specific game theory postulates that will be utilized to explain specific scenarios. For
this paper, three events in Arctic governance are analyzed.
The first is the Barents Sea agreement between Norway and Russia. This agreement looks a
cooperative two-person (bilateral) agreement that successfully emphasize the role of Zeuthen-Nash
equilibrium. The second event is the continued stalemate between Denmark and Canada regarding
Hans Island. While no equilibrium (in the standard game theory sense) is reached, this stalemate
reflects some of the more realistic aspects of Arctic governance. Here the paper looks are the Risk
Limits application, as well as the other game theory concepts that vie in favour of Coalition
cooperation games. The final event is the Search-And-Rescue (SAR) agreement. This sees a
coalition led cooperative agreement between states. Looking at the role of coalition, this paper uses
game theory to justify the rationality postulates utilized in creating such an agreement despite
perceived ineffectiveness of sanctions. These three were picked for very specific reasons. The first

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reflects a complete agreement that can model other bilateral agreements. While this precedence is
not necessarily reflective of all negotiations in the Arctic, it does provide a context of rational
postulates that may determine future negotiations. The second event could be swapped with most
other unsolved “conflicts” such as the Beaufort Sea maritime boundary, or the Northwest Passage.
Assumptions made with Hans Island should theoretically be extrapolate to those events as well.
The final event was chosen due to the collective action by the coalition. The Arctic Council is a
soft-power institution, so such an agreement like SAR seems a bit idealistic in terms of
enforcement. This paper concludes with reflecting on future challenges and how these three events
have set the precedence for a peaceful Arctic governance approach.

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Canada
Canada’s policy in the far north continues to revolve around the idea of national security.
The first active set of policies in terms of the Arctic came as a result of the post-WWII
developments that saw USSR surge into a global power. This period of revived interest in the
Arctic, referred to in the literature as the “polar passion”, saw increased “cooperation and
involvement by both USA and Canada” to counter-act or deter an USSR led invasion across the
Arctic (Charron, Plouffe, & Roussel, 2012, p. 41).Subsequent cooperation also led to the
development of NORAD as several Arctic-based military exercises. However, with the fall of the
USSR, interest in the Arctic weaned.
Despite falling off the radar of public interest, Canada’s involvement in the issues of
Arctic sovereignty has not been completely diminished. Canada is a founding member of the
Arctic Council which is an integral cog in the development among the circumpolar nations
(Charron, 2012, p. 765). Canada was also integral in the signing of the Ilulissat Declaration in
2008 which saw the founding members of the Arctic Council (referred to in the text as “Arctic
5”) promise to adhere to the UN Convention of the Law of the Sea (UNCLOS).Prime Minister
Harper, in his new ‘Canada First’ Defense policy, reiterated his government’s aim “to increase
the Canadian forces’ capacity to protect Canada’s Arctic sovereignty and security” (Crawford,
Hanson, & Runnalls, 2008, p. 4).
While Canada’s role in the governance of the Arctic remains a key role for Canada, there
remains a severe lack of capacity to enforce Arctic interest in the region. Despite promising to
increase Canadian military capacity in the Arctic, little has been done to improve Canada’s navy.
Canada’s only two supply ships capable of operating in the Arctic were built in the late 60s and
are now “so obsolete that replacement parts are often difficult to find” (Crawford, Hanson, &

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Runnalls, 2008, p. 4). In addition, the 2013 Federal Budget saw the military lose $2.4 billion of
their $20 billion budget (Brewster, 2013). Arctic operations were one of the most likely
operations to be cut down as it cost five to seven times more to conduct Arctic operations than
other missions (Brewster, 2013). In addition, Canadian scholars are skeptical about the approach
to Arctic security. Griffiths noted that “sovereignty is an overrated issue, and we [Canadians]
should move beyond it [Arctic security] to an emphasis on Arctic stewardship” (Chater, 2012, p.
836).

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Russia
Russia’s role in the Arctic, more than any other littoral state, clearly reflects real interest
and vested investment in the region. Due to this, Russia is perceived as the true Arctic hegemon;
longest and most populated coastline, largest ice-breaker fleet in the world, biggest year-round
port in the entire Arctic Zone (Murmansk), conducted the most Arctic sorties, and the
establishment of the Arctic as the top domestic and foreign policy goal clearly reflects Russia’s
hegemonic status (Charron, Plouffe, & Roussel, 2012, p. 38). This is unlike most circumpolar
states whose policies have little to no real investment in the region. Russia’s stake in the Arctic
has two elements; resource extraction and commercial maritime activities. These two elements
alone contribute 20% of Russia’s GDP and a total of 22% of Russia’s exports (Charron, Plouffe,
&Roussel, 2012, p. 43). This is on top of the estimated value of Russia’s Arctic minerals which
exceed US$ 22.4 trillion (Charron, Plouffe, & Roussel, 2012, p. 43). In terms of maritime
commercial routes, the Northern Sea Route could see major reduction in transportation costs,
increased port activity in Russia, and better relations between Europe and Asia. The Northern
Sea Route is “expected to shorten shipping routes between northern Europe and north-east Asia
by 40% compared to the existing routes through the Suez and Panama Canal (Ebinger &
Zambetakis, 2009, p. 1221). In addition, Russia’s ice-breaker fleet at 20 is more than Canada
and USA’s combined fleet (Ebinger & Zambetakis, 2009, p. 1220). As a result, Russia maintains
a clear advantage in terms of Arctic security enforcement.
President Gorbachev in 1987 called from the circumpolar states to establish a “zone of
peace” in the region that would encourage cooperation and sustainable development (Charron,
Plouffe, & Roussel, 2012, p. 43). In addition, Russia was the first nation to embrace the
UNCLOS and the first nation to submit scientific data that would legitimize Russian land claims

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with the Lomonsov Ridge (Charron, Plouffe, & Roussel, 2012, p. 44). So far, Russia has been
cooperating well with other Arctic Council nations in terms of establishing boundaries.
Norwegian and Russian ties have been stretched in terms of the rules regulating Svalbard. This
situation pits Norwegian environmental interests against Russian fisheries, but this too has been
passively resolved through diplomatic means (Kriz & Chrastansky, 2012, p. 131). From these
actions, and Russia’s reinforcement of cooperation as key to the Arctic, it can be concluded that
Russia proves less of a threat than perceived.
Russia’s continued enforcement of the UNCLOS in addition to the signing of the Ilulissat
Declaration reflects Russia’s intention to follow international law. This means that only
scientific proof on continental shelves can allow Russia to encroach on to Canadian land. In
other words, even if Russia militarizes their land, they are unable to extend their existing
boundaries due to UNCLOS, Ilulissat Declaration, as well as the deterrence provided by other
Arctic states. As a result, Russian threat is null; despite having the military capacity, they lack
the incentives to attack and the presence of deterrence remains too high.

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USA
The USA’s Arctic policy, post-USSR, has been limited. However, under George W.
Bush, a revival in the idea of ‘fundamental homeland security’ resulted in a resurgence of
emphasis on Arctic security (Rosamond, 2011, p. 43). Despite the rhetoric of increased security
and militarization, the USA has done very little in terms of increasing their military capacity in
the region. USA currently only owns one ice-breaker that is acceptable to participate in Arctic
excursions (Ebinger & Zambetakis, 2009, p. 1220). These ice-breakers take almost a decade to
construct with a price tag of nearly $1 billion (Ebinger & Zambetakis, 2009, p. 1220). In
addition, Holmes noted that there seem to be very little interest in expanding military capacity
under the current economic climate (Holmes, 2013). The USA’s lack of interest in the Arctic is
finally highlighted by the fact that the USA remain the sole Arctic nation not to ratify the
UNCLOS, putting further doubt in terms of US involvement in the region (Parlee & Furgal,
2012, p. 8).
The inability of the US to ratify the UNCLOS remains a major obstacle. For the USA, the
inability to ratify the UNCLOS robs them of the ability to claim further sovereignty around
Alaska. This is problematic due to the abundance of offshore resources in the immediate region
surrounding Alaska. A 2009 report by the United States Geological Survey concluded that over 90
billion barrels of oil, 1,669 trillion cubic feet of natural gas and 44 billion barrels of natural gas
liquids are located in the Arctic for which 84% are offshore (Ebinger & Zambetakis, 2009, p.
1216). While majority of Alaska’s capacity remains within already established Exclusive
Economic Zones (EEZ), estimates suggest that by ratifying UNCLOS, the USA may be able to
access even more offshore resources (Crawford, Hanson, & Runnalls, 2008, pp. 5-6). Despite the
economic opportunity, the National Security does not reflect this possible impact. The report by

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the National Security Strategy on energy only saw the Arctic mentioned at the very end, but in
terms of environment and scientific research (Rosamond, 2011, p. 45).
The end result is that the USA remains very passive in terms of establishing Arctic
sovereignty. In terms of policy, both Canada and USA depend on healthy relations amongst each
other as a result of NAFTA, and despite this dispute, it is unlikely that either nation will attempt
anything drastic. The issue with the Northwest Passage is similar. Here Canada wishes to
establish Canadian laws which seek to regulate fishing and shipping. However, the USA see this
area as international waters and therefore under the judiciary of the UNCLOS. In this situation,
the USA has very little to lose; at most Canadian law would regulate pollution and transportation
which would not affect US vessels to a great degree. As a result, it can be concluded that despite
the security rhetoric, it is highly unlikely that Canada and USA will resort to militarization of
their Arctic claims and should therefore aim to cooperate and open further dialogue.

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Denmark
The role of Denmark is fairly complex. While Canada, Norway, USA, and Russia maintain
circumpolar sovereignty due to direct coastline, Denmark maintains circumpolar influence through
Greenland. Denmark colonized Greenland in 1775, and has since remained in control of
Greenland’s foreign policy (Rosamond, 2011, p.56). However, Greenland has been seeking more
autonomy from Denmark despite being heavily reliant on Danish aid (Rosamond, 2011, p. 55). In
2008, a new arrangement between Denmark and Greenland emerged; as Greenland is able to
exploit resources, they will reduce the amount of Danish financial contribution, thus making it
profitable for both Greenland and Denmark (Rosamond, 2011, p. 56). However, Denmark will
remain in formal control over Greenland’s foreign and security policy while providing Greenland
with domestic control (Rosamond, 2011, p. 56). In addition, recent surveys by US Geological
Survey (USGS) has reduced the amount of expected oil outside Greenland by almost half and have
also added that it would be at least 20 years before this oil will be financially viable at all
(Rosamond, 2011, p. 57).
Despite the seemingly little role Denmark has in terms of Arctic sovereignty, Denmark
continues to prove a proactive member in both the Arctic Council and as a sovereign state. The
conflict Canada has with Denmark, comes in terms of Hans Island. This small island is fairly
insignificant; an unpopulated “bare rock” of 2km2
, has yet to yield any conclusion despite
seemingly active role of both Danish military and Canadian military in planting flags on this island
(Kriz & Chrastansky, 2012, p. 119). Argument could be made that control over the island would
extend EEZ, but further analysis by Kriz and Chrastansky suggest otherwise. The sovereignty
claim would “not change the approved borders” established under UNCLOS, thus invalidating any
claim that this island is of any economic or strategic significance (Kriz & Chrastansky, 2012, p.

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119). This is reinforced by a report by Rosamond outlining policy recommendations for the Danish
government which portrays the Hans Island as lacking any real benefit for Denmark and to avoid
“the framework of Realpolitik” and instead see the “Arctic as a fruitful site for community-building
clustered around good inter-state relations” (Rosamond, 2011, p. 66). As a result, the fear of
Danish invasion of the Hans Island is unfounded; neither Canada or Denmark (or Greenland) will
gain anything by establishing control over Hans Island and dispute will be more detrimental to
overall Arctic relations than what possible gains Hans Island may provide if any.

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Norway
Unlike the other states, Norway’s role in the Arctic is primarily due to environmental
protection and fishing. While mineral extraction is part of Norway’s Arctic Strategy, the
Norwegian expected boundaries are primarily to secure fishing rights. In addition, Norway’s
approach to Arctic governance is more in line with the cooperative nature of the Arctic Council.
Norway’s focus on environmental protection is similar to that of Denmark; the intent is to be “the
best stewards of the environment” to an extent that helps safeguard the livelihoods, traditions, and
cultures of indigenous peoples in the High North (Norwegian Ministery of Foreign Affairs , 2009,
p. 6). To materialize this policy goal, Norway continues to invest a large amount of money in
climate and environmental research in Tromso (Norwegian Ministery of Foreign Affairs , 2009, p.
8). This research center is one of the world’s foremost facilities in climate and environmental
research in terms of the Arctic.
In terms of the value placed on the environment, the rational for Norway and Denmark is
essentially the same. They both recognize the fragility of the Arctic environment as a major
obstacle to development in the far north (Heininen C. , 2012, p. 15). In addition, they both
acknowledge that indigenous populations are heavily dependent on the environment, thus adding a
human dimension to environmental protection (Norwegian Ministery of Foreign Affairs , 2009, p.
43). With Norway’s heavy investment in the far north in existing facilities, as well as new
infrastructure, the focus on environmental protection is key. Unlike other states, (i.e. Canada)
whose environmental protection agenda has faltered with new regimes, Norway continues to focus
on the environmental aspect of the Arctic.
Norway’s commitment to environmental protection differs greatly from other states. First,
Norway’s commitment to environmental commitment has a long history, with Kyoto and several

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domestic regulations to protect the environment. As such, Norway’s commitment to environmental
regulation is not affected by the multilateral or unilateral expectations of other states. As such, the
value given to Norway’s unilateral strategy is relatively high. Note, however, that the multilateral is
significantly higher.
Norway’s strategy for fishing is perhaps one of the better examples of multilateral cooperation in
the high north. Specifically, Norway’s bilateral agreement with Russia over the Barents Sea which
reinforced Norway’s domestic laws regarding fishing regulation and has led to the creation of the
“Joint Norwegian-Russian Fisheries Commission” (Honneland, Norway and Russia in the Barents
Sea: Cooperation and Conflict in Fisheries Management, 2007, pp. 10-11). This is a significant step
to the multilateral direction for two reasons. First, relations between NATO members and
USSR/Russia have been historically strained, and thus collaboration between Norway and Russia is
a significant milestone. The second impact was setting precedence in international law between
member states. While Russia was perceived as relatively ‘rogue’, Russia’s continued cooperation
with Norway has helped other states through negotiations as a means of precedence. Despite this
agreement, Russian overfishing continues to be an obstacle. Norway, in a manner of “tit-for-tat”
negotiation style, granted Russian relatively high quotas for fishing after accusations of artificially
keeping cod prices higher (Honneland, Norway and Russia in the Barents Sea: Cooperation and
Conflict in Fisheries Management, 2007, p. 10). Despite these conflicts, Norway-Russian relations
remain positively and relatively open.
With Norway’s existing bilateral agreement as precedence, multilateral agreement is not a
farfetched scenario. Norway’s existing agreement would function as precedence in terms of the
protection of fishing and quote assessment for fishing. With newer fishing grounds in the North,
Norway would rely on a collaborative “search-and-rescue” of the Arctic Council. While Norwegian

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navy and air support is training for such scenarios, joint efforts are more efficient. Especially with
Denmark whose bases in Greenland allows for safe haven in the far north. Despite this, there are
extensive benefits of Norwegian unilateral enforcement of fishing grounds. Note that this is
contingent on Russia maintain current agreement. In the event Norway defects and encroach onto
Russian sovereignty, the benefit would be significantly less. However, Norway could act on their
own sovereign waters to enforce heavily their own fishing industry.
So far, multilateral approaches have shown to reinforce the protection of production, for
which mineral extraction is crucial. Norway is relatively smaller than majority of the actors
involved in the Arctic. As such, multilateral approach is in Norway’s best interest. Statoil continues
to conduct multilateral talks with several partners including Russian energy industry, Shell, as well
as Greenland (Norheim, 2010, p. 2). Despite this, Norway’s existing production allows from a
fairly autonomous production of petroleum due to existing access to technology and market. This
justifies better than 0 score for Norway’s unilateral mineral extraction.

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Game theory
Arctic Game Theory is analyzed using three key elements of Game Theory application;
the first is the role of equilibrium points, the second is the role of Risk Limits, while the final one
is coalition creation. These three pose key levels of analyses that support the current trajectory of
Arctic Governance. Equilibrium points looks at the differences between Nash and Zeuthen, as
well as the role of the game theory postulates and theory of optimal threats. These help aid the
deconstruction of Arctic cooperation and will setup the next elements. Risk Limits build on the
concept of Nash-Zeuthen equilibrium points; risk-dominance and risk-aversion severely impact
the expected utility and thus affect subsequent equilibrium points. In the Arctic context, Risk
Limits play a major role, which can be illustrated by combining the theoretical framework and
drawing the parallels in current Arctic negotiations. The final element is coalition creation. The
previous two elements build on the concepts of coalition; however this section will further
explore coalition creation in game theory. Concepts such as minimum resource theory, the
Shapley Value, and the Coalition Problem, are all present throughout Arctic governance. From
this discussion, the following section drawing direct parallels with Arctic development will be
evident. Prior to this, this paper will establish basic aspects of Game Theory which will establish
terminology and procedure.
The play of games in Game Theory has a very concrete structure. The first is the
establishment of ‘strategy’. The assumption is that each player (every participating actor) has a
“complete plan of behavior which specifics the player’s behavior” which includes all possible
circumstances which is referred to as strategy space (Burger, 1963, p. 1). The key premise of a
strategy is to maximize their respective payoff function which is best understood as the benefits

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from winning a game in line with respective objectives (Gibbs, 1974, p. 7). Strategy, as such, is
only interpreted as all known and possible strategies. The extension of this statement is that all
“impossible” or highly unlikely scenarios are omitted from the possible strategies. Players
committing to any such strategy, which has been omitted from the rational strategy space, is
therefore considered a “bluff”.
A game situation, as such, is when the player commits to a strategy. Game Theory
differentiates between three levels of game; one-person game, two-person game, and games
involving more than 2 players. This is represented as n-game, with n representing the number of
players involved. One person game can only be played against nature; all strategies are one-sided
with the other actor committing to strategies interdependent of any other actor. A two-person
game, the most common form of Game Theory application, revolves around two actors
interacting in either a sequential manner (branch) or one-shot (2x2 form) (Harsanyi, A General
Theory of Rational Behavior in Game Situations, 1966, p. 87). Games involving more than two
players pose a special problem unique to 2+ games; coalition formation and creation greatly
affects the strategy space available (Harsanyi, Papers in Game Theory, 1982, p. 87). Current use
of game theory in political science has been primarily applied using 2-player non-cooperative
game. Examples are primarily journalistic; majority of peer-reviewed material accepts that the
Arctic is more cooperative than mainstream media suggests. However, usage of coalition
strategy in political science is limited. One notable paper by Reichenvater and Vondolia explores
the Arctic Treasure hunt using Game Theory. This paper, uses some coalition models, however
mostly for resource distribution rather than strategy choice.
The rules of the game has three elements; action(s), information, and consequence(s)
(Harsanyi, Papers in Game Theory, 1982, p. 88). An action refers to a player’s commitment to a

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strategy. Information is integral for this matter; amount of information can indicate the type of
game as well as the expected outcome of the utilized strategy. Complete information refers to
100% information to all players whereby (i) they know their own strategy and other players’
strategy options, (ii) amount of information available to each player, and (iii) other player’s
utility function (Harsanyi, Papers in Game Theory, 1982, p. 91). Anything less, in terms of
information distribution, is referred to “imperfect information” games. In majority of social
situations, players act on imperfect information. However, as will be discussed later, coalitions
have a way of circumventing this condition. Note that the information available to each players
and information regarding utility function are different. Information regarding a player primarily
revolves around a player’s resources and capacity to maximize their utility function, whether
perceived or real. Information regarding another player’s utility function is primarily is knowing
the payoff that player will derive from any particular physical outcome (Harsanyi, Papers in
Game Theory, 1982, p. 90). Consequences play into the calculation of actions in all games. Each
player can assume their utility function to have x-value pay-off, but have to calculate any
difference between such pay-off (x) with the consequence. This can range from resources
expanded, to material losses, and punishments. Punishments are mostly considered in sequential
games whereby players interact beyond the game played (Handa, 1983, p. 298). The point of
interaction, with all these three factors taken into account, is what is known as an ‘Equilibrium
Point’.

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The Role of Equilibrium Points: Nash, Zeuthen, and Game Theory Postulates.
The interaction between two players, or coalitions, will yield specific outcomes. The
best-off outcome, is commonly referred to as the Nash-equilibrium (Colman, 1995, p. 58).
Developed by John Nash in 1950, his theory of equilibrium points state every finite non-
cooperative game will have at least one equilibrium point for which that equilibrium point is
“simply the set of all pairs of opposing good strategies” (Nash, 1951, p. 286). The key part of his
findings is that no player has an incentive to change their strategy from which the Nash
equilibrium is derived (Colman, 1995, p. 59). In the following table, (X1,Y1) represents the Nash-
equilibrium.
X
Y
X1 X2
Y1 (2,2) (-1, -1)
Y2 (0,0) (1,0)
Nash’s initial calculation behind this equilibrium point was conducted in a two-person
non-cooperative game. However, the Arctic context is not necessarily a two-person non-
cooperative game. Game theory defines a non-cooperative game whereby commits have no
bindings force (Harsanyi, A General Theory of Rational Behavior in Game Situations, 1966, p.
145). Cooperative game, as a result, is a game where commitments (i.e. agreements, promises,
threats) are fully binding and enforceable (Harsanyi, A General Theory of Rational Behavior in
Game Situations, 1966, p. 145). This definition of ‘cooperative’ game, thus is not one whereby

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players are willingly interacting, but rather on the assumption that threats and agreements are
enforceable. As such, the Arctic context is best analyzed using a cooperative framework.
The rationality postulates are the framework from within each player acts within a game.
This framework is very specific and allows players to anticipate specific outcomes. These are the
basis of all theoretical gameplay and outcomes of such games are contingent on these postulates
being fulfilled. They can be divided into two sections; postulates of rational behaviour, and
postulates of rational expectations. The first postulate of rational behaviour is that of expected
utility maximization. By this, each player is expected to choose the strategy with the higher
payoff (after all things have been considered) (Harsanyi, Rationality Postulates for Bargaining
Solutions in Cooperative and in Non-Cooperative Games, 1961, p. 144). The second is that of
individual efficiency; no player will utilize a strategy that is too costly in respect to expected
utility (Harsanyi, Rationality Postulates for Bargaining Solutions in Cooperative and in Non-
Cooperative Games, 1961, p. 147). The efficiency argument is conjunction with the utility
maximization, but will be considered on a player’s cost function. This is related to threat (which
will be discussed later). Efficiency in truncated game, the 3rd
postulate in rational behavior,
refers to shortened games without long-term bargaining. In other words, most games are played
on the basis that “tit-for-tat” negotiations and long-term bargaining are not the best approach.
Instead, games work on two or three sequences of bargaining (Harsanyi, Rationality Postulates
for Bargaining Solutions in Cooperative and in Non-Cooperative Games, 1961, p. 147). This is
not necessarily an important factor when considering the overarching structure of Arctic
Governance, but helps aid the deconstruction of cited games. The final postulate of rational
behavior is referred to as mutual optimality and joint efficiency. Here the emphasis is on “best
response” strategy; if player X uses strategy X2
and the best response (highest payoff, lowest

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cost) for player Y is strategy Y2
, then player Y will always use strategy Y2
(Harsanyi, Rationality
Postulates for Bargaining Solutions in Cooperative and in Non-Cooperative Games, 1961, p.
148). These postulates define the rational behavior of each player within any game.
The second part is postulates of rational expectations. Games run on the premise that
each player not only adhere to the rational behaviour, but also on specific expectations that help
model games. The first is that of mutually expected rationality. This refers to the collective
utility of rational behaviour; players will aim to maximize their utility function, use most
efficient strategy, as well as best responses. The second is symmetry; every player will assume
that the other player will not make a move that he himself would not make. In addition, the
player cannot anticipate that the other players will make concessions that he himself would not
be willing to make (Harsanyi, Rationality Postulates for Bargaining Solutions in Cooperative and
in Non-Cooperative Games, 1961, p. 150). The final part of rational expectation is the restriction
of variables. This revolves around the premise that no one player expect variables that are not
directly affecting the utility function to be included at any part of the game (Harsanyi,
Rationality Postulates for Bargaining Solutions in Cooperative and in Non-Cooperative Games,
1961, pp. 150-151). The importance of this is primarily for uniformity. While application of
games to social and political situations do include non-essential variables, games are not
intended for that purpose. As such, these postulates help the creation of games, as well as the
application of games onto political and social situations.
The framework of threat in Nash’s equation is important. Nash’s theory of optimal threats
designs a framework whereby threats can be optimized in a manner that best functions with the
utility function of each player. Recognize that a cooperative game is contingent on threat being
enforceable. By extension, threats that cannot be enforceable are recognized as “bluffs” and thus

25
omitted by strategy options (Burger, 1963, pp. 19-20,45). Thus an optimal threat strategy is
heavily influenced by the utility function and subsequent payoff by enforced strategies. Nash
formulated that any optimal threat has to be beneficial to the player themselves. This threat
should not, therefore, reduce the utility function of said strategy. By extension, a player will
maximize the relative strength of his bargaining position (Harsanyi, Rational behavior and
bargaining equilibrium in games and social situations, 1977, p. 170). Therefore, the optimal
threat strategy attempts to “maximize the costs of a conflict to the opponent and trying to
minimize the cost of a conflict to oneself” (Harsanyi, Rational behavior and bargaining
equilibrium in games and social situations, 1977, p. 171). In regards to equilibrium points, the
theory of optimal threats suggests that a player’s optimal threat strategy is not only contingent on
their own utility function, but also that of opposing players. In cooperative games the opposing
players are more likely to bargain before assessing threat strategies. This is even truer in
coalition games. Optimal threat strategy within coalitions are based on the same premise,
however any non-coalition player has to account for the collective coalition threat. The coalition,
in turn, can account on the collective threat. This will be expanded upon in the final coalition
strategy section.

26
Risk Limits: Payoff Dominance, and Bayesian approach
So far, this paper has covered the perception of equilibrium payout and the utility of
threat. A key component of equilibrium deduction follows the rational of risk limit. The
rationality postulate has so far indicated that actors focus primarily on utility maximization,
which is most of the time shown in normal game as a positive payout. However, game theory has
added ‘risk limit’ calculation to more easily see the applicability of game deduction in real social
contexts. This is heavily utilized in the Arctic context. Developed by Harsanyi, the theory of risk
dominance and aversion looks at cumulative strategy payouts. At a basic level, any equilibrium
point is constructed on the basis that one player has a higher payoff than the other. Thus that
player is more likely to pursue the high payoff strategy. However, any strategy vector can also
have subsequent loss depending on what the other player decides to use (Harsanyi, Papers in
Game Theory, 1982, p. 230). The following diagram depicts such game between players X and
Y.
X
Y
X1 X2
Y1 (2,1) (-1, -100)
Y2 (0,0) (1,2)
This graph shows two possible equilibrium points; (X1,Y1) and (X2,Y2). However, if player X
commits to his strategy of highest payoff (X2), there is an imminent risk that conflict point
(X2,Y1) might the outcome. Utilizing the postulates established earlier in the paper, Player X has
to accept that player Y is more likely to resort to strategy (Y1) due to the assumptions of

27
symmetry. While both players lose at conflict point (X2, Y1 ), player X risks the highest loss that
is relatively disproportioned to his utility function. Another way of expressing this is using the
following calculation;
𝑞 =
𝑢 𝑥
𝑠1
− 𝑢 𝑥
𝑠2
𝑢 𝑥
𝑠1
− 𝑢 𝑥̅̅̅
This is the basic calculation for risk limits whereby the lower the sum of q refers to small risk
(Harsanyi, A General Theory of Rational Behavior in Game Situations, 1966, p. 630). The
variable u stands for payouts while x designation is for player identification. This calculation for
q is applied to both (or all) players for which this diagram is applicable. The player with the
lowest q value is what is referred to as ‘dominant’; this player has leverage in equilibrium
negotiations, and has the least to lose (as per the payoff diagram). The application of risk limits
is very important for Arctic Governance; the calculations allow us to deduce several key
negotiations happening in the Arctic as well as those that still have yet to be finalized. As such
this, concept will be applied heavily throughout this paper.
While application of risk limits are fairly intuitive, majority of games in social contexts
lack the same information condition. In other words, majority of games are played using
incomplete information. There are three conditions for which this is true. The first is the lack of
information on the payoff function of other players (Handa, 1983, p. 301). While this is truer in
business environment where companies can have sometimes either parallel or transcending
strategies, most state-actors know each other’s payoff function as they are in line with their own
expected outcome. This is truer at conflict points where ‘power’ and ‘territory’ are deducible
payoffs. The second is the lack of information on possible strategies available to others (Handa,

28
1983, pp. 301-302). Referred to as ‘strategy space’ (or policy space within political science), any
player can utilize which ever strategy best suits their utility function. In terms of game theory
modelling, only two strategies are utilized. Specifying these two specific strategies prove
challenging in certain games as strategy space is hard to deduce depending on available
information. The final aspect of incomplete information is lack of information on the rules
available to other players (Handa, 1983, p. 303). To mitigate any unknown variables, a player
can utilize the Bayesian approach.
For games with incomplete information, players will have to account for unknown
variables. Assume the previous game did not reach equilibrium, and players were pressed to pick
a strategy. Player X is aware of his own utility function, but cannot account for the utility
function of player Y. As such, player X could push for strategy 2 as long as this holds true.
Bayesian application allow players to account for unknown variables, using evidence from past
games, interactions, or even infer from other players actions (Harsanyi, Papers in Game Theory,
1982, p. 123). Application of this theory in statistics and computer programming are, however,
not the same. Bayesian inference in game theory is primarily for subjective probability and thus
yield particular results (Harsanyi, Papers in Game Theory, 1982, p. 139). More specifically,
running games applying Bayesian inference, Harsanyi developed an unexpected result; games
utilizing Bayesian inference devolved into “delayed commitment”, whereas a normal games
(complete information) saw the usage of “immediate commitment” (Harsanyi, Papers in Game
Theory, 1982, p. 145). This is primarily as a result of players requiring to take time to react and
infer, rather than commit and act. As such, acts between players that are delayed can be viewed
as a Bayesian inference by-product; negotiations, and actions that would be expected to have
occurred earlier in a game can be perceived as a lack of information problem. This will become

29
an important concept in Arctic Governance and will be applied, especially, in the contexts of
Canada.
Coalitions: Shapley value and Communication Bias
The application of Risk Limits and Bayesian inference has significant impact on two-
person games, for which the extension of these two concepts into coalition settings has an even
more profound setting. This section will discuss the role of coalition creation. In addition to
integrating Risk Limits and Bayesian inference through coalition participation, this section will
also discuss the role of Shapley value and minimum resource theory. Both of these help explain
why coalitions and collective agreements occur between largely competing players. Extension of
this coalition discussion is aimed at explaining why the Arctic Council is ideal, as well as
looking at the sustainability of the Arctic Council.
Coalition games are very different from 2-player games. Essentially, any game with more
than two players can lead to coalition creation as any additional n-player can cooperate together.
The key part of a coalition game is that there are “three or more players who are free to negotiate
binding and enforceable agreements about the formation of coalitions and the division of the
payoffs that result from their coordinated actions (Burger, 1963, p. 161)”. The key part for
coalitions is communication; it enables coordinated efforts, and thus provides incentives for
joint-equilibrium outcomes. The basic assumption of a coalition is that those participating are
allies; however, “each player’s only aim is to strengthen his bargaining position against the other
players” (Harsanyi, A General Theory of Rational Behavior in Game Situations, 1966, p. 629).
Each player within a coalition (i) of a coalition will have an interest in cooperating with the other

30
members for the sale sake of increasing the dividends from this coalition (Harsanyi, A General
Theory of Rational Behavior in Game Situations, 1966, p. 630).
The distribution of payoffs from a coalition is best understood using the Shapley value.
The logic within a coalition in terms of a payoff is that by pooling their collective demand, and
thus reducing join costs and competition, a coalition will be able to increase payoffs by reducing
costs and in specific cases reduce operating costs (Reinhardt & Dada, 2005, p. 997). The
calculation of Shapley value represents “each player’s incremental value to the pool (coalition)”
and thus derives a formula that distributes average input as a fair compensation (Reinhardt &
Dada, 2005, pp. 998-1000).
𝑆𝑉𝑖
= ∑ 〈[
𝑠! ( 𝑁 − 𝑠 − 1)!
𝑁!
]〉
𝑆∁𝑁
× (𝐶(𝛾𝑆𝑈𝑖) − 𝐶(𝛾𝑠))
Here, C represents the characteristic function of the cost allocation game; “the addition to profits
caused by a center acting jointly under all possible conditions with the other centers is evaluated
and an average is taken (Reinhardt & Dada, 2005, p. 999).” While the specific formula will not
be utilized in this paper as a numeric calculation, lessons from Shapley value application on
coalition structure are utilized. A study done on power sharing between competing power plants
in India found Shapley value to dictate the coalition structure, as well as the distribution of
pooled resources (Gately, 1974, p. 195).
A key indicator of coalition formation is the utilization of communication and
information exchange. Known as the communication bias, every n-tuplet of players can form any
given coalition, as long as the non-coalition player is unable to intervene (Harsanyi, A General
Theory of Rational Behavior in Game Situations, 1966, p. 630). Assume three players α,β, and γ.

31
Each player creates equal number of specific coalitions with each one other player (i.e. coalition
1 = α,β ; coalition 2= α, γ …etc). If player α and β attempt to create a grand coalition that
excludes player γ, it is in the interest of player γ to use established coalition structures to prevent
players α andβ from monopolizing the new grand coalition. Player γ would, using the logic of
rational postulate, utilize communication networks (established coalitions) that would allow him
to intervene (Harsanyi, A General Theory of Rational Behavior in Game Situations, 1966, p.
630). If communication networks are cooperative, in the sense that they are symmetric between
all players (symmetric in terms of perfect information established earlier in the paper), then the
resulting coalition will have no privileged position (Harsanyi, A General Theory of Rational
Behavior in Game Situations, 1966, p. 630). As such, communication bias encourages players to
communicate in enforceable agreements.
While Shapley value encourages collective distribution, and communication bias
proposes joint-collaboration of information, the application of Minimum Resource Theory
ultimately dictates the longevity and utility of coalitions between n-game players. Minimum
resource theory states that the cheapest winning coalition will form; to maximize rewards and
ultimately their utility function, players engage in coalition that not only minimize cost, but also
allow for (perceived or real) benefits (Crosbie & Kullberg, 1973, p. 476). Application of this
theory in laboratory settings (artificial games with 3-players) has been rather successful. Ofshe
and Ofshe (1970) found that coalition formation between 3-player games was heightened with
lowered coalition costs, encouraging such behavior and incentivized players to cooperate and
share resources. Games simulating this theory are primarily focused on limited resources; zero-
sum games with defined parameters (Crosbie & Kullberg, 1973, p. 477). This distinction favors

32
the application in the Arctic context as these games simulate the current conflict points in the
Arctic context.
Game Theory Application
So far this paper has covered several Game Theory aspects that is applicable in different
measure in the Arctic context. These key terms and concepts are critical in understanding the role
they play in deconstructing Arctic governance development, as well as current negotiations.
These concepts will be measured against several developments in the Arctic, and applied in some
cases to explain why equilibrium was reached, or why other equilibrium points were avoided.
There are three events of importance for this paper. The first is that of Norway-Russian
negotiations; a peaceful bilateral agreement denoting boundaries. This treaty catapulted Arctic
negotiations as it saw Russia and Norway engaging peacefully in what has been perceived a
critical juncture in boundary establishment. The second is that of Hans Island. Still unresolved
between Denmark and Canada, this section will look at the parallels between Norway-Russian
negotiations and the expected outcomes of Hans Island negotiations. This section combines
game theory with national policies of respective players. What will be discussed are the
overlapping priorities of both states. The final event is the establishment of “Search-and-Rescue”
protocol in the high north. This key agreement can be explained using the game theory postulates
established. Criticism against the Arctic Council on the lack of hard-law and sanctions has critics
deeming the Arctic Council as a toothless organization (Kao, Pearre, & Firestone, Adaption of
the arctic search and rescue agreement: A shift of the arctic regime toward a hard law basis?,
2012, p. 835). All of these events can be projected using the established game theory concepts

33
presented. The conclusion drawn is that the Arctic best represents a cooperative coalition game,
and is expected to continue along this trajectory for the future.
Norway-Russia Agreement: The Barents Sea & the Arctic Ocean
The Barents Sea represents a significant conflict point; both Norway and Russia are
exporters of energy, and their respective economies depend largely on this industry. The Barents
Sea is located at the northern tip of Norway and Russia, and thus has no physical boundary for
either state to claim. The potential of Arctic resources in the region is high; the Norwegian
Petroleum Directorate “estimates that about 930 billion Sm3
gas and 220 million Sm3
oil remain
undiscovered in the parts claimed by Norway alone (Dore, 1995, p. 217). Exploration in the
Russian sector is expected to be even higher with expectations almost exceeding 8 billion Sm3
total (Kullerud, 2012). With such a large potential for exploration, in addition to each state’s
dependency on energy exports, the perceived approach would for each party to maximize their
expected utility. In other words, a protracted negotiation or even military postulating similar
what is currently happening in China’s East Asia Sea.
The Barents Sea agreement was signed in 2010, and came into effect in 2011 (Arp, 2011,
p. 1110). The agreement highlights several key areas of concern ranging from the physical
delimitation of boundaries, to exclusive economic zones, and “search-and-rescue” (Arp, 2011, p.
1111). Specifically, the treaty states that neither part is allow “claiming or exercising any
sovereign right or coastal State jurisdiction in maritime areas beyond this line [delimitation line]
(Arp, 2011, pp. 1111-1112).” This is by design; Norwegian policy in the Arctic specifically
outlines cooperation with their Russian counterparts. Despite historic tension between Oslo and
Moscow, “Norway’s policy towards Russia is based on pragmatism, interests, and cooperation
(Norwegian Ministry of Foreign Affairs, 2006, p. 18).” The most Russian policy was published

34
in 2009 and extended to 2020. Here too the emphasis on a cooperative approach towards Arctic
negotiations (specifically Barents Sea negotiations with Norway) instead of unilateral approach
often associated with Russian foreign policy (Zysk, 2009). In the agreement itself, Article 9
clearly outlines “Cooperation among the Parties”. Considering the criticism of Russia’s strategies
(vis-à-vis Ukraine and Syria), this agreement reflect a different approach. Why did Russia
approach the Barents Sea agreement this way? What encouraged parties to collaborate? Why
would Russia agree to a relatively ‘even’ agreement against a player whose relative capacity
(both militarily, and diplomatically) to challenge any Russian demands?
The game theory interpretation of this agreement utilizes several of the concepts
mentioned in the earlier section. For this interpretation, the Norwegian-Russian negotiations are
represented in the following table:
Russia
Norway
R1 R2
N1
Θ1
(N1,R1)
Θ2
(N2,R2)
N2
Θ3
(N3,R3)
Θ4
(N4,R4)
Each conflict point is assigned θx depending on which quadrant is discussed. In addition, each
state’s payoff is represented in the vector quadrants. As such, Norway’s payoff is represented as
Nx and Russia’s payoff is represented as Rx. X value corresponds to the quadrant they are found.
These coordinates will be utilized to explain and apply game theory concepts, and thus justify the
outcome. For argument’s sake, the equilibrium reached will be θ1.

35
Equilibrium construction is analyzed using three concepts; rationality postulate, rational
expectations, and optimal threat. In terms of θ1 we can assume certain things in regards to these
three concepts. First, this equilibrium (θ1) satisfies the mutual optimality and join-efficiency
condition. For any given (Nx,Rx) payoff, θ1 represents the one that is mutually optimal. This
condition does not state that either payoff is higher than any single Xx payoff in the other
quadrants. What this condition does state, is that payoffs (N1,R1)provide both actors with a
mutually optimal strategy.
The extension of this argument into policy is reflected within the agreement. It is in the
best interest for Norway not only to resolve boundary issue with Russia, but to maintain state
integrity. For Russia, boundary resolution allows Russia to invest safely into new infrastructure
in the high North. The completion of this agreement saw rapid investment into Arctic research on
Russian waters. ExxonMobil and Rosneft agreed to a partnership exceeding $500 billion for
offshore resource extraction in Russian waters (Belton, 2012). Norway, on the other hand,
focused more so on fishing rights and the enforcement of Norwegian fishing laws to surrounding
areas (Honneland, Derfor skal Putin la Barentshavet i fred, 2014). In this sense, this agreement
was mutually optimal as both parties managed to cater to their larger utility.
Risk limit application of this equilibrium utilizes payoff dominance to Russia. Despite
Norway’s dependency on energy exports, northern communities depend heavily on fishing and
wildlife (Engo, 2014). The inability to establish clear boundaries and coast guard responsibilities
between these two states highly impeded Norwegian efforts in maintaining and policing
fisheries. Estimates by Norwegian fishery department estimates that over 100 000 tons of
Norwegian cod is illegally fished by Russian boats yearly (Naerings og Fiskeridepartmentet,
2006). Norwegian Arctic Strategy papers also reflect this sentiment, stating clearly that while

36
energy extraction is a core concern, protecting existing economic zones (e.g. fisheries) remains a
mandate (Norwegian Ministry of Foreign Affairs, 2006, p. 18). The perception, from Norwegian
documents, suggests that Russia had a lot less to lose. The agreement reflects similar concession
for the Norwegians. While Norway received concessions in terms of fishing and law
enforcement, a large portion of the Barents Sea negotiations favor the Russians. Norwegian
conceded large parts of the Barents Sea to Russia, drawing a large amount of criticism citing too
much area was granted to the Russians (Per-Vidar, 2010). A recreation of the assumed game
looks at the Θ4 quadrant as the ‘high risk’ vector with X2 assuming non-cooperative approaches.
For (N4,R4) we can assume that the values are skewed in favor of Russia. In other words, the
value of R4 is more in line with being a fraction of a negative N4 value.
R4 =
𝑥
−𝑁4
The interpretation of this is essentially that any value that is assigned to N4 is a negative value that is
significantly larger than R4. Therefore, the risk limit favors Russian negotiations. With the other two
quadrants (Θ3 and Θ2), only Θ2 could possibly offer a mitigating payoff as the payoff vector in this
negotiation lines up with that of Θ1 (equilibrium). For Norwegian negotiations to allow Russia to switch
from strategy R2 to R1, the necessary concession by Norway would align with Θ2 perceived higher payoff.
The Bayesian application of this for Norway thus worked in their favour; despite conceding land, Norway
managed to maximize two priority areas namely (i) fishing and (ii) environmental protection. Russia’s
continued commitment to those two factors in relation to Norwegian relations further emphasizes the
benefits. However, it is important to recognize that Russia too wished for swift and cooperative
agreements to be reached in this area. The primary rational for this is to improve Russia’s global
perception, especially with NATO members (Moe, Fjaertoft, & Overland, 2011, p. 155). This included
“reducing the risk of conflict” with neighbouring states in a collective effort to focus efforts on stabilizing

37
the economy post-2008 (Moe, Fjaertoft, & Overland, 2011, pp. 145, 157). While the argument is credible,
negotiation factors and the outcomes heavily favor Russian utility maximizations rational. As such, while
it was beneficial for Russia to commit for the rational provided by Moe, Fjaertoft, and Overland (2011), it
was in Norway’s best interest as their two primary concerns of (i) fishing and (ii) environmental has a
marginally higher risk factor involved.
The application of game theory on the Barents Sea negotiations reflects two parts of the three
major game theory concepts introduced. Coalition game was not utilized as this bilateral agreement works
independently of the Arctic Council, and does not, for the sake of coalition creation, hinder or create
additional coalition structures. The conclusion drawn from this analysis sees the rationality postulates and
expectations reinforced with both outcome and policy expectation adhering to their respective rationality
postulates.

38
Hans Island: Canada versus Denmark
Whereas as the Barents Sea agreement has been heralded as a breakthrough in Arctic
governance, the lack of development in other negotiations over other territories continues to be
cited as a site of conflict. The Hans Island conflict has yet to reach any equilibrium; neither
Canada nor Denmark have reached a standard game conflict point. Hans Island, on the other
hand, is not necessarily a large potential resource hub. It is a ½ square mile island that remains
unresolved since the 1970s (Carlson, Hubach, Long, Minteer, & Young, 2013, p. 32). Denmark’s
claim extends back to geological similarities with Greenland, thus claiming it as an extension of
Greenland’s ridge (Carlson, Hubach, Long, Minteer, & Young, 2013). A Danish flag, erected in
1984, was replaced by a Canadian flag in 2005 by Canadian military, thus escalating the
perceived “Arctic Race” rhetoric in journalistic circles (Carlson, Hubach, Long, Minteer, &
Young, 2013, p. 32). Despite the perceived hostilities between Canada and Denmark over Hans
Island, the island itself has very little impact on UNCLOS extension of sea shelves. Due to the
situation of the island on their respective shelf boundaries, any further extension of respective
state sea shelf is not applicable.
Escalation of the Hans Island is primarily the result of shifting domestic policy of
Canada. Prime Minister Harper increased funding to new military measures in the Arctic,
ranging from funding to navy and coastal guard, to more conventional Arctic bases and the
Canadian Rangers (Lackenbauer, Arctic front, Arctic homeland: re-evaluating Canada's past
record and future prospects in the circumpolar North, 2008, p. 2). Consequently, observers note
that “there is no conventional military threat in the Arctic” despite the perceived rhetoric
(Lackenbauer, Arctic front, Arctic homeland: re-evaluating Canada's past record and future
prospects in the circumpolar North, 2008, p. 3).The emphasis by Canada’s newer Arctic policy is

39
that of sovereignty and protecting Canadian interests; perceived inability by Canadian military to
protect the Canadian identity as “true North” and rising environmental concerns in the area has
pushed the Canadian policy agenda. Referred to as a “sovereignty-security framework”, this
shifting policy towards securing Canada’s territory is not necessarily necessary (Lackenbauer,
Mirror images? Canada, Russia, and the circumpolar world, 2010, p. 881). Further analysis of
Canada’s Arctic policy highlights the interest in maintain Canadian leadership, and facilitating
“good international governance in the region” (Lackenbauer, Mirror images? Canada, Russia,
and the circumpolar world, 2010, p. 888).
Denmark, on the other hand, emphasize heavily on “cooperation”. For illustration
purposes, the word “cooperation” was used 160 times in Denmark’s official Arctic strategy
whereas “war” or “conflict” was never mentioned in more than an illustrative manner. The
emphasis of Danish Arctic policy is simple; ensure that Arctic indigenous people can maintain
their livelihood, maintain Denmark as a global player in the Arctic, and ensure that high
standards are held in the Arctic vis-à-vis shipping and environmental protection (Kingdom of
Denmark, 2011, pp. 10, 13, 16).
In terms of policies, Canada and Denmark both maintain a heavy focus on (i) protection
of indigenous people and (ii) environmental protection. Canada’s key concern is shipping; the
North West Passage is deemed by Canadian officials as Canadian territory and thus subject to
Canadian environmental protection laws. Other states, specifically USA and Russia, feel that it
belongs to international regulation and thus not affected by Canadian regulations which is much
stricter. Denmark’s stance, holding their Arctic policy as a testament, would be in line with
Canadian interests. Despite this, there does not seem to be a clear resolution to Hans Island
dispute.

40
The game theory analysis of Hans Island relies on the existence of coalition game
outcomes. Both players participate in a grand coalition (the Arctic Council, and by extension,
UNCLOS) and invest resources into this grand coalition. Reintroducing the application of
Shapley value, and minimum resource theory (MRT), it becomes clear that neither Canada or
Denmark are interested in resolving the Hans Island dispute unless such dispute would allow for
marginal gains. In other words; the equilibrium outcome of a settlement is irrelevant as both
parties perceive such agreement to be neutralized by the coalition factor. Another way of
interpreting this would be to say that since both parties have the same goal, and since neither
parties gain significant resources, the unresolved conflict can be maintained as neither player is
interested in aggravating or escalating the conflict.
Canada
Denmark
R1 R2
N1
Θ1
(N1,R1)
Θ2
(N2,R2)
N2
Θ3
(N3,R3)
Θ4
(N4,R4)
For both parties, since their policies align, both the equilibrium point’s θ1 and θ4
represents a suitable equilibrium. This is because of their aligned policies; neither player will
aggravate the other player’s utility function as this could detract from their own policy. For
example, assume θ1 represents Canadian ownership of the island (0, 1). Any policy the Canadian
government would focus on would benefit (i) environment and (ii) indigenous welfare. For this
equilibrium point to have a negative outcome for Denmark, the policies of Canada would also
have to be negative to Canada as their maximization of utility utilize the same variables. In other

41
words, both Canada and Denmark follow their Risk Limit by adhering to a coalition structure
rather than assert their own policies. This is enabled by the game theory application of Minimum
Resource Theory, Shapley Value, as well as the cooperation coalition game. This differs from
the Barents Sea conflict point as Norway and Russia had different motivations to establish an
agreement. While no agreement has been established yet, it is not necessarily critical for Canada
or Denmark to resolve the matter either. While maritime shipping is touted as a focal point in
Arctic governance development, chances are slim that this specific shipping route will be
utilized, or even that Arctic shipping can be profitable. This is due to the dangers associated with
floating icebergs (vis-à-vis the Titanic), as well as monitoring. As such, neither player is
pressured into settling a strategy. The marginal gain is negated by the perceived risk of altering
the current coalition structure as neither player benefit greatly from any change in the Hans
Island dispute.

42
Search-and-Rescue: Coalition application of Shapley Value
Apart from the creation of the Arctic Council and respective states’ ratification of
UNCLOS, the “Search-and-Rescue” Agreement (SAR) of the Arctic Council is a key milestone
for Arctic Governance. This agreement outlines the areas in which Arctic states agree to uphold
rescue missions as part of a collective security measure. This agreement saw additional protocols
such as refueling, and request for docking privileges amongst Arctic members. These elements
remain a key indicator of Arctic cooperation; whilst states differ on the extent of boundaries and
resources, the protection of lives remain paramount. Herein lies the role of Game Theory
analyses; why is the SAR agreement successful?
It is important to recognize that while the Arctic Council acts in a manner similar to any
institution with access to hard power, and thus able to levy sanctions, it is in fact more akin to a
soft-power institution (Koivurova T. , The Actions of the Arctic State Respecting the Continental
Shelf: A Reflective Essay, 2011, pp. 211, 223-226). The result is an institution that theoretically
cannot fully punish members. Considering the extent to which Russia, USA, Canada, Denmark,
and Norway has agreed to cooperate, which elements provide security in this agreement? From
an individual perception, states would primarily focus on maximizing their boundary and
resource potential. The SAR agreement infringes slightly on this goal; as a collective, they have
now agreed to extend “shared” resources to members (as well as non-member states in distress)
without a sure guarantee that the same treatment will be extended to themselves. By “shared
resources”, states extend their coastal guard, navy, or air force for strategic use in aiding any
rescue and search attempts. Not only do states expend resources for the SAR, but they also risk
these valuable resources (e.g. icebreakers, Arctic capable ships and helicopters) during rescues

43
that may or may not lead to casualties. As such, the agreement seem slightly counter-intuitive in
terms of pure utility maximization.
A key portion of a cooperative coalition game, and an important element of why players
enter coalitions, is the ability to pool resources in a manner intuitively beneficial for all players.
Key questions, therefore, revolve around the factors that determine efficient outcome, and what
coalition structure will emerge if all participants act rationally? (Harsanyi, A General Theory of
Rational Behavior in Game Situations, 1966). While Risk Limits have been applied to two-
person cooperative games, the analyses of SAR will look at the role of Shapley value as well as
the Coalition Problem.
The main objective of measuring the Shapley value is to assess the reduction in joint-
costs and the subsequent payout (Reinhardt & Dada, 2005, p. 997). The rationality behind this
approach is that all players have intersecting interests. For the Arctic scenario, SAR agreement
represents one such intersecting interest. While all states seek to maximize their utility, they will
need to account for any difference a coalition structure utilizes. For any coalition, it is accepted
that players only enter coalitions that are beneficial to them. As such, any coalition that does not
provide their minimum utility, will not be successful as each player is better off alone. The
Arctic Council’s SAR agreement is a testament to this type of logic.
Player
Coalition
R1 R2
N1
Θ1
(N1,R1)
Θ2
(N2,R2)
N2
Θ3
(N3,R3)
Θ4
(N4,R4)

44
In this standard game, strategy 1 would be cooperation whereas strategy 2 would be to defect.
A coalition response for strategy 2, as it cannot theoretically defect, would be to capitulate against any
rogue members or non-members. An example would be Θ4 where both players would defect; any
defection from a coalition is seen as a threat to the coalition. Coalition thus can evoke collective
action and threaten non-coalition player’s existing utility. Risk limit application would also be
justifiable as a player will assess that risk for Θ4 is too high.
In terms of the SAR agreement, each individual player assess their capacity to maximize
their utility function. A key part of the SAR agreement sates that the boundaries set under this
agreement cannot be used to claim sovereignty as that is only a function of the UNCLOS
agreement. The due process of UNCLOS supersedes any other attempt at claiming land. The
result of this is that players are immune to any loss in sovereignty claims which is their primary
utility function. Another way of looking at this is stating that the SAR agreement does not affect
players’ respective utility function. However, the SAR agreements allow for a Shapley approach
to resource sharing.
𝑆𝑉𝑖
= ∑ 〈[
𝑠! ( 𝑁 − 𝑠 − 1)!
𝑁!
]〉
𝑆∁𝑁
× (𝐶(𝛾𝑆𝑈𝑖) − 𝐶(𝛾𝑠))
Revisiting the Shapley value equation, any derived positive value is associated with the coalition’s
willingness as well as the number of players participating. In other words, the incremental increase in
profits is determined by how many players participate, as well as the coalition distribution. In both
cases, it is in the best interest that all available players (for the sake of the Arctic context, this is limited
to littoral states and observer states) participate. If any one player defects, the marginal cost for the
coalition as per Shapley will decrease. The question therefore is whether the marginal cost of defecting

45
is higher or lower than the individual cost of maintaining existing boundaries. Judging by the SAR
agreement’s protocols, including that regarding refuelling, human life, and boundaries, one can
extrapolate that all players saw the marginal cost of defecting being less than the cost of maintaining a
domestic SAR agreement.
The lesson from the SAR agreement in the Arctic governance context is the role of shared assets
and coinciding domestic policies. While several states emphasize the role of indigenous peoples and
environment, the protection of hard assets (military capacity, coast guard, etc.) have paramount impacts
on not only the states’ respective capabilities in a non-cooperative game (vis-à-vis an Arctic race), but
also stats’ capacity to participate in a cooperative game. The primary lesson here is that while Arctic
states convey certain policies that appear counterintuitive to cooperation, such as investment into
military structures, collective agreement such as SAR continue to be an option. The role of a coalition, as
explain through game theory, help justify this. While concerns regarding the lack of hard-law to enforce
it, game theory continues to be an avenue for understanding such agreements. As all parties recognize
that defecting has an associated cost higher than the cost of participating, as well as the lack of cost for
participating in terms of utility function, it is the most rational approach to participate in the SAR
agreement.

46
Conclusion
Arctic policy coincides more often than not; environmental protection and sustainable
economic activity is the primary objective of several Arctic states. While the media promotes the
idea of a “race for resources” or a “new cold war”, Arctic governance continue to be an area of
cooperation rather than conflict (Huebert R. , The Newly Emerging Arctic Security
Environment, 2010, p. 1). Canada’s approach is double-edged; while promoting cooperation
internationally; domestic posturizing in terms of creating a “true North” has created a
misinformed public. Canada’s approach is far from the security complex associated with
Harper’s speeches. Rather, Canada’s approach is very much in line with the status-quo of Arctic
Council members. Continued support for research is a key part of Canada’s continued efforts in
the Arctic. While military cuts are a real concern, the inability of Canada to establish a scientific
argument for their UNCLOS boundaries is more detrimental. Russia, often seen as an aggressor,
continue to invest heavily in Arctic research. Despite recent events in Syria and Ukraine, no
sanctions directly affecting Russia’s Arctic policies have been implemented. This bodes well for
Russian exploration as their aging fleet require upgrades. The scientific contribution by Russian
research also benefit on a global scale; collective exploration and Arctic Council mandate
continue to push Russian cooperation to the forefront of their Arctic strategy. It is clear, with the
Barents Sea agreement with Norway and ratification of SAR, that Russia’s main objective is to
cater to the Arctic Saga rather than the Arctic Race. It is important, not only for Russia but other
members as well, that this remains true despite auxiliary conflicts elsewhere. USA’s inability to
ratify UNCLOS, while disturbing, does not appear to impact USA’s role in the Arctic Council.
While domestic actors call for more involvement by their government, USA’s passive role is in
stark contrast to their usual “world police” approach elsewhere. USA’s passivity may be due to

47
more pressing concerns, or a more rational effort in fracking than Arctic exploration. Regardless
of this, USA continues to actively participate in Arctic Council negotiations. Their ratification of
SAR is a key stepping stone. Denmark and Norway, the two smallest states by a huge margin,
have made major contributions to the Arctic Council. Both states have invested heavily into
Arctic research, with cooperation with other states such as Russia and China continuing to be a
major influence. Denmark’s role continues to grow as larger parts of Greenland becomes more
hospitable with climate change. Despite Denmark’s best efforts, conflicts with Canada and
Russia remain an obstacle for both Denmark in terms of environment, but also for longevity of
Greenland’s anticipated independence from the Kingdom of Denmark. This is unlike Norway,
whose role in Svalbard will not diminish regardless of the Arctic outcome. Norway’s agreement
with Russia in the Barents Sea is a major step forward, and continues to be an example to
Norway’s approach in the Arctic.
The game theory application is not without flaws. While applications are made
retroactively, predicting the future is more difficult. With the resources provided, primarily state
policies, the variables fit into the collective coalition game as outlined by Haranyi. Other
attempts at applying game theory are primarily for resource extraction, whereas this paper looked
at governance structure. Future predictions do require the added variables of future conflicts. As
seen with Syria and Ukraine, Russia’s role amongst NATO members is threatened. While the
Arctic has not been an area of sanctions yet, any attempts to dissuade Russian involvement
elsewhere might make the Arctic the next step. This would go against the rationality postulates
only in terms of collective bargaining. The moral argument for sanctions can be made, but as
stated by rational postulates, games “do not include moral value judgment of any kind”
(Harsanyi, Rationality Postulates for Bargaining Solutions in Cooperative and in Non-

48
Cooperative Games, 1961, p. 142). With the limitations of using state policies, this analysis
provides the basis of analyses using two primary concepts. Risk Limits is a key concept that is
often overlooked; too often is the Prisoner’s Dilemma constructed on basic measures rather than
assessing levels of payoffs. Shapley value is not so much an overlooked concept as it is a concept
that is not often associated with game theory. As noted, non-cooperative games are what pushed
Game Theory into the social sciences. Shapley value, however, relies solely on the cooperative
element of game theory.
While areas of conflict could pose future challenges, the continued efforts by all littoral
states to enforce UNCLOS and continue cooperative approaches is an exciting change to more
traditional Realpolitik. Despite seemingly failing agreements in areas such as the Middle East,
the Arctic continues to trot towards a collective coalition. With boundaries being resolved in the
Barents Sea, other states will take heed of Norway and Russia’s lead. The application of Game
Theory allows for another avenue of assessing potential conflict management opportunities.
Concepts such as Risk Limits and Shapley value may soon penetrate traditional political science
discourse, giving analysts the tools not only to assess but also demonstrate objectively using
formal models. As the Arctic continues evolve, the plethora of agreements that are to come in the
future continue to be an area of wonder. However, the Arctic Saga will continue as states and
non-state actors alike, continue to work for in a cooperative manner.

49
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