Proceedings of the Fourth Middle East Conference on Global Business, Economics, Finance and
Social Sciences (ME16Dubai May Conference) ISBN: 978-1-943579-30-3
Dubai-UAE. 13-15 May, 2016. Paper ID: D633
To Develop a Game Theory Model Analyzing the Negotiations
between Britain and European Union
Maneesha,
Faculty of General Sciences,
BITS,Pilani-Dubai Campus, Dubai.
E-mail: [email protected]
Nishant Vijay,
BITS,Pilani-Dubai Campus, Dubai.
E-mail: [email protected]
Apoorva Singh,
BITS,Pilani-Dubai Campus, Dubai.
E-mail: [email protected]
___________________________________________________________________________
Abstract
Through this paper, we analyze the ongoing deliberations between Britain and European
Union and develop a better understanding through the help of a game theory model. This
model will allow us to gain an insight on the strategies available for the parties involved and
the payoffs for the same. We can also use the analogy of two cars speeding toward each other
to examine the situation in an efficient manner. The metaphoric crash of the two cars will be
the Brexit. Also discussed are the implications of the supposed Brexit and how it would be
detrimental for the two parties involved. The effect would be more adverse on the economy of
Britain than on the other states who are current members of the European Union. We also
come to a conclusion that Brexit might only be a delusion and can be another one of the
repeated games played by Britain with European Union.
___________________________________________________________________________
Key Words: Brexit, GDP, game theory, strictly dominated, swerve, and continue
JEL Classification: C 19, G13, G 14
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Proceedings of the Fourth Middle East Conference on Global Business, Economics, Finance and
Social Sciences (ME16Dubai May Conference) ISBN: 978-1-943579-30-3
Dubai-UAE. 13-15 May, 2016. Paper ID: D633
1. Introduction
For a very long time there have been talks of Britain’s exit from the European Union
(E.U.) commonly known as BREXIT. Since the very beginning U.K. has had fractious
relationship with the rest of E.U. claiming that it is quite meddlesome. This has finally led
Britain to put forward a referendum which clearly states that Britain will no longer be a part
of the E.U. until and unless its demands are met. The outcome of this will have a major
impact on the world economy. This paper will discuss the implications of the Brexit and how
game theory can be used to analyze the ongoing negotiations between the E.U. and Britain.
In this paper we will discuss the various outcomes that are possible and the probable effect
on the GDP of the countries that will be affected. For a better understanding we have
developed game theory model to explain the payoffs and the strategies involved in this
scenario. We can use the analogy of two cars moving in opposite directions and closing in fast
towards each other. The metaphoric collision of the two cars can be considered as the Brexit.
Through this paper, we will also explain how the model is an ideal one and what other various
factors govern the payoffs.
2. Literature Review
The European Coal and Steel Community (E.E.C.) was an international entity formed in
1951 after the World War II to unify the European countries for a better tomorrow. After
various struggles Britain finally joined E.E.C. in 1973. This organization led the way for the
formation of European Union (E.U.) in 1993. Currently there are 28 members that form the
E.U. and Britain is one of them.
The history of Britain and European Union has always been very unstable. There are
various instances in the past that indicate that Britain and E.U. have not shared the same
ideals. Within the E.U. lies the Eurozone which consists of 19 members who share the same
currency of Euro. Britain is not a part of the Eurozone because of the 1975 referendum for the
membership of the nation. Britain is not in the euro or the Schengen passport-free travel zone.
Britain has a different budget rebate. It also opted out of many justice and home-affairs
policies. All these indicate to the fact that U.K.’s non-compliance has led people to believe
that it is a non-reliable partner that slows down the European Integration process by
attempting to achieve sovereignty in the fields it has interests on and that lives on a constant
‘bluffing-basis’ position to achieve desirable outcomes at a national level.
There are three reasons for Britain to want Brexit: (1) Britain paid approximately 17.4
billion dollars in 2013 and it believes that the money is spent on Bureaucrats in Brussels
rather than utilising that money to improve the infrastructure for the countries that are in need.
(2) During the past few years, there has been an increase in the migration of cheap labor from
Soviet bloc countries to the U.K. which leads to job losses for the Brits and an increase in the
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Proceedings of the Fourth Middle East Conference on Global Business, Economics, Finance and
Social Sciences (ME16Dubai May Conference) ISBN: 978-1-943579-30-3
Dubai-UAE. 13-15 May, 2016. Paper ID: D633
unemployment rate for the nation. (3) There has been an increase in the amount of people
coming to Britain only to claim free benefits like unemployment and healthcare and have
negligible contribution to the nation’s economy.
These factors along with some minor ones have led to Britain putting forward a
referendum on whether Britain should still be a part of the European Union. There are a few
demands put forward by U.K. Prime Minister David Cameron. Some of them are –
restrictions on state benefits for E.U. citizens and protection for Britain’s financial sector.
Whether a Brexit will take place or not cannot be determined but the implications of the same
can be analyzed.
3. Methodology
3.1 Research Questions
As indicated in introduction, we have two major research questions. One of them is to find
out how game theory is related to the Brexit scenario. The other one relates to finding an
approximate outcome to the Brexit scenario by using a game theory model.
3.2 How is Game Theory related?
The current negotiations can be clearly analyzed by the concept of “Game of Chicken”
which is a crucial element of Game Theory.
Consider two cars moving in opposite directions and closing in at a very rapid pace
towards each other (Figure 1). There are two strategies possible for the drivers. They can
either defect from their path (swerve) or cooperate on the same path with the same intensity
(speed). In this case U.K. can be considered as car A and E.U. can be considered as car B. If
they both defect from their path, there will be no collision and this can lead to both parties
coming to a consensus where the demands of both parties are met. One possible outcome is if
car A defects from its path (swerve) while car B is still speeding on the same course which
might lead to a better payoff for car B. Another possible outcome is if car A continues to
follow the same path, however car B defects from the path allowing car A to have a better
payoff than car B. Finally, the last possible outcome of this scenario will be if both cars
continue to speed on the same course and finally collide with each other. This will be a
scenario where the payoffs of both the parties involved will be very low and will be the
lowest for car A due to various factors involved.
Figure 1: Analogy of 2 cars
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Proceedings of the Fourth Middle East Conference on Global Business, Economics, Finance and
Social Sciences (ME16Dubai May Conference) ISBN: 978-1-943579-30-3
Dubai-UAE. 13-15 May, 2016. Paper ID: D633
This metaphoric collision of the two cars is the Brexit which will lead to a drastic effect in
the world economy. It will majorly affect the economy of the 28 nations which are currently a
part of the E.U. From the historical evidences available to us, we come to know that U.K. has
been playing this game repeatedly and has always managed that E.U. defects from its path
first (swerve) to avoid a collision.
The next section will analyze this situation by the help of a game theory model and will
explain the strategies that the 2 parties have and the payoffs possible. This will just be an
ideal model because there are various other factors that affect the payoffs of the game and
which cannot be accounted for.
3.3 Limitations of the model
This game theory model (Figure 2) is only an ideal model to analyze the scenario as there
are numerous other factors that affect the game theory model. We have however developed
this model to provide an overview on the situation for Brexit. Neglecting the other smaller
factors, we can arrive at this game theory model. Some of these factors that might affect the
model are provided in the subsequent paragraphs.
The game theory model that we have put forward for the analysis of the ongoing
negotiations between Britain and the European Union is a 2x2 matrix. However, this might
not be a pragmatic scenario. We have considered E.U. to be as a unified organization in this
case, but this might not be the case in real life. European Union has to be considered an
organization that consists of 28 independent nations including Britain. This would mean that
we would have to develop a game to be played in a 1 to 27 constellation which would be very
difficult to handle due to the infinite number of strategies and payoffs possible for the
multiple parties.
There will always be an element of uncertainty due to mixed motives present in the
overarching institutional arrangement. Eventually, politics will come into picture. Each of the
nations will have to vote on the referendum based on how it would affect the economy of
their respective states. Each of them would have to do what is profitable for them rather than
to do what is necessary.
One of the other challenges faced by our game theory model is that we have considered
only two strategies per party. To simplify the scenario and to have a better understanding for
the ongoing negotiations, we have considered only two strategies per party. However, there
can be various other strategies that are possible for the multiple parties involved (including
the 27 nations that are a part of the European Union).
Another factor that can influence the negotiations between Britain and European Union is
how much time one takes to defect from the path. If any party swerves, the duration taken for
the party to swerve might also be a factor that can influence the payoffs that are possible for
the parties involved. There can be various political implications that affect the same. In a
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Proceedings of the Fourth Middle East Conference on Global Business, Economics, Finance and
Social Sciences (ME16Dubai May Conference) ISBN: 978-1-943579-30-3
Dubai-UAE. 13-15 May, 2016. Paper ID: D633
different scenario, we can expect Scotland to rebel a Brexit which would lead to various
national level problems for Britain.
The model used for the analysis is as follows:
3.4 Game Theory Model
After going through his analogy we can analyze the current situation between Britain and
European Union with the help of a game theory model. This model depicts the various types
of strategies and payoffs possible for both the parties. The model is a 2x2 matrix that helps
determine which strategy will dominate and which strategy will be dominated.
With the help of this matrix we can observe that Nash Equilibrium occurs when both the
parties defect from their current course of action and agree to hear out what the other party
has to say.
Figure 2: Game Theory Model
Through the help of this model we observe that if both parties swerve, that will be the
most profitable outcome for both parties. However, we can also see that there are other
possible payoffs as well. If Britain defects from its current path, while European Union
continues on the same, this will be more profitable for E.U. as it would have a payoff of +3
while Britain would have a payoff of -3. This is the case because U.K. has a tendency to play
game of chicken again and again, all these times forcing E.U. to swerve. If this time U.K.
swerves, then that would be seen as a sign of weakness for Britain and will eventually lead to
a weaker status in Europe as well as around the world.
If European Union swerves first, as it has done for the past couple of years against Britain,
then that would be a profitable outcome for Britain than compared to E.U. The payoff of E.U.
will be -3 while that of Britain will be +3. This is the case because if E.U. swerves first, then
this would lead to a bad impression for the organization (as well as the other 27 countries
involved) which would lead to a weaker global positioning. This would prove the point that if
you aren’t comfortable with any rule that has been established by the European Union, you
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Proceedings of the Fourth Middle East Conference on Global Business, Economics, Finance and
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Dubai-UAE. 13-15 May, 2016. Paper ID: D633
can easily negotiate with the organization. This will be a profitable scenario for Britain as
they would get what they want and all of their demands will be met.
The most unlikely scenario is when both the parties continue to move in the same
direction. This crash of the two cars is our supposed Brexit. In this scenario, Britain would no
longer be a part of the European Union which would have adverse effects on all countries
which are currently a part of the European Union. In this situation, Britain will have a payoff
of -10 however; European Union will have a payoff of -5. This is the case because this
scenario will not be ideal for both the parties in the short run and will be more adverse for
Britain as compared to European Union.
3.5 Suggested outcomes of Brexit
If Brexit takes place, GDP for Britain will decrease by 2.2% if there is a Free Trade
Agreement that is signed with European Union. If the Free Trade Agreement is not signed
between the two parties, then this could lead to a 6.3% to 9.5% decrease in GDP for Britain.
However, if Brexit takes place, the GDP of Britain could have increased by 1.6% by 2030.
This means that Britain loses access to a market that comprises of 500,000,000 people and
will have to face tariffs and regulatory barriers to trade. Also, its access to worldwide trade
will be compromised.
Migration of people is another factor that would be affected due to Brexit. Free movement
of people might be rejected like in the case of Norway. Such restrictions on travelling might
lead to losses in public finances for U.K. Apart from this; we can also assume that there will
be a denial of E.U. rules and regulations. The standards and institutions set by E.U. will not
be met. Apart from these consequences, one of the major cultural consequences for Britain
would be the loss of interest in the English language and culture.
In this scenario, U.K. would have a weaker position while trying to negotiate bilateral
deals with the European Union. This would lead to depreciation in the influence and status of
the nation.
For the European Union, a Brexit could mean that there will be economic losses for all the
member nations. The GDP for Germany will have 0.1% to 0.3% decrease. Other countries
that suffer the most are Belgium, Ireland and Luxembourg. As we know Britain contributes a
significant amount to the budget of European Union. A Brexit could signify that the member
states would have to contribute more to the E.U. budget. Brexit would mean that Germany
would have to pay approximately 2.5 Billion Euros a year extra. There will be losses for the
member countries as most of these countries relied on U.K.’s trade which might no longer be
accessible after the Brexit. This would lead to a loss of “power” for the European Union
within the international politics and would be affected in terms of global trade partnerships.
However, a Brexit could mean that European Union would have one less member that is
highly euro skeptical and declines most of the proposals put forward by the European Union.
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Proceedings of the Fourth Middle East Conference on Global Business, Economics, Finance and
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Dubai-UAE. 13-15 May, 2016. Paper ID: D633
This could lead to more common approaches and unified proposals which could lead to
deepening of the European Union.
4. Results and Discussion
Through this paper, we have developed a basic 2x2 game theory model to provide a clear
understanding for the ongoing negotiations between Britain and European Union. We have
established the payoffs and the strategies for the parties involved using the analogy of two
cars speeding towards each other. We established that the only favorable outcome for the two
parties will be if both parties defect from the path. This will be the Nash Equilibrium and will
be the most stable outcome. We also analyzed the various scenarios possible and explained
the payoff that can be possible.
If in case Brexit takes place, Britain would be the nation that will be most affected and will
face severe losses in the short run. However, they would experience a 1.6% increase in GDP
by 2030. Some of the other nations who will be most affected from the Brexit are Germany,
Belgium, Ireland and Luxembourg. Political, cultural and economic implications of a Brexit
on the European Union as a whole were taken into consideration.
The other factors that can be influential in the game theory model that we developed and
why this model is only an ideal or a more approximate model to understand the current
situation between the two giants. A more practical model would consist of 1 to 27
constellation which takes into account the strategies of the 27 other nations that area part of
the European Union and who will vote on the Brexit referendum.
It is clearly analyzed and observed that Brexit is fantasy as it will not be beneficial for
either of the parties in the short run. The Tusk Proposal is an example of the same. It is a
proposal set forward by President Donald Tusk to address the important areas of the British
discontent. This addresses various demands set forward by the British.
Another such example is of Prime Minister David Cameron to change the strategies halfway through the negotiations and to re-engage with the practice of bilateral diplomacy in
contact with the other state heads.
5. Conclusions and Recommendations
It can be inferred from the simple game that there will be numerous implications of a
Brexit for both the parties and hence, this will not be a viable option. One of the parties will
have to swerve to avoid the collision. But will it be European Union like always or will this
time be any different. This would depend on the strategies that the two parties play and the
payoffs that they expect from those strategies. Will the strategy be dominated or dominating
will devise the outcome of such a game.
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Proceedings of the Fourth Middle East Conference on Global Business, Economics, Finance and
Social Sciences (ME16Dubai May Conference) ISBN: 978-1-943579-30-3
Dubai-UAE. 13-15 May, 2016. Paper ID: D633
References
Aggarwal, V. and Dupont, C. 2011. Cooperation and Conflict in the Global Political Economy. In:
Oxford (ed.3) Global Political Economy. John Ravenhill ed.
Borysiewicz, S. L. 2015. Why the UK Should Stay In: The Social Case. Business for New Europe.
Available: http://www.businessforneweurope.org/the_social_case
Clements, B. 2014. IEA: Brexit Prize: Britain outside the European Union.
WALSH, J. 2015. David Cameron: Playing games in Europe? The Parliament Magazine: Politics,
Policy and People. Available:
https://www.theparliamentmagazine.eu/articles/opinion/david-cameron-playing-games-europe
Watt, N. 2013. Britain and Europe: the essential guide. The guardian. Available:
http://www.theguardian.com/world/2013/jan/18/britain-europe-eu-essential-guide
Lord Leach of Fairford, P. 2015, What if...? The consequences, challenges and opportunities facing
Britain outside the EU. Open Europe. Available:
http://openeurope.org.uk/intelligence/britain-and-the-eu/what-if-there-were-a-brexit/
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