negotiation of Brexit

To Develop a Game Theory Model
Analyzing the Negotiations between
Britain and European Union
11/26/2016Brexit Negotiation 1

 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.
 Use the analogy of two cars speeding toward each other.
 The effect would be more adverse on the economy of
Britain than on the other states who are current members
of the European Union.
 Brexit might only be a delusion and can be another one of
the repeated games played by Britain with European
Union.

 For a very long time there have been talks of Brexit.
 Since the very beginning U.K. has had fractious
relationship with the rest of E.U. claiming that it is quite
meddlesome.
 Developed game theory model to explain the payoffs and
the strategies involved in this scenario and 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.

 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.

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 (UK rebate or UK
correction).
 It also opted out of many justice and home-affairs
policies.
 …

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 utilizing 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 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.

Game Theory?????
What is game?
Lets us first understand what is a Game??
Game, in the mathematical sense, is defined as strategic
situation in which There are multiple participants.
 Is Sudoku a "game" ?
No.
 Is Chess a "game" ?
Yes.

Some notable Game Theorists
 John Von Neumann– Founder of field-1928
 John Nash– Nash equilibrium-1950
 John Harsanyi– Incomplete Information(Bayesian
Games)(Bayesian Games)-1966
 Roger Myerson– Mechanism Design-1976
 Many others: Morgenstern, Selten, Maynard Smith,
Aumann…

What is Game Theory?
 layman’s language: Game Theory is one way of studying
how an individual or a group makes a strategic choice.
 Formal Definition: Game Theory is a set of tools and
techniques for decisions under uncertainty involving
two or more intelligent opponents in which each
opponent aspires to optimize his own decision at the
expense of the other opponents.
 The mathematics of human interactions.
 Uses mathematical tools, called games, to study
situations that involve both conflict and cooperation.

Key Elements of a game
Players: Who is interacting?
Strategies: What are their options?
Payoffs: What are their incentives?
Information: What do they know?
Rationality: How do they think-
maximize gains and minimize losses-?

Some of the popular Games of Game Theory
 Prisoner's dilemma
 Battle of the sexes(BoS)
 Deadlock
 Rock, Paper, Scissors
 Trust game
 Cake cutting
 Chicken(aka hawk-dove)
 Traveler's dilemma
 …

Chicken Dilemma Game
 In the prototypical chicken dilemma, also known as the
hawk-dove game or snowdrift game two rebellious teens
race towards each other in the car.
 Whoever swerves is considered a ‘chicken’ and loses.
 If neither turns away a bad crash happens and both
loose.

Nash Equilibrium
 In game theory, the Nash Equilibrium is a solution
concept of a non-cooperative game involving two or
more players in which each player is assumed to know
the equilibrium strategies of the other players, and no
player has anything to gain by changing only his or her
own strategy.
 The Nash equilibrium is not usually the most effective
strategy; it is only the best one without co-operation.
 So when each player within a game follows their best
strategy, taking into account the decisions of the others,
a Nash equilibrium will occur.

Continue…
 Two strategies sw. and st. are in Nash equilibrium when:
 under assumption agent A plays sw., agent B can do no
better than play st.
 under assumption agent B plays st., agent A can do no
better than play sw.
 Neither agent has any incentive to deviate from a Nash
equilibrium.

Analysis of Chicken Game
 Both lose when both swerve.
 One player wins when one swerves and other goes
straight.
 If both go straight, both lose(lose more than what they
would have lost when both swerve. Because if both go
straight they CRASH).
 Chicken Game has 2 Nash Equilibrium: (St, Sw) and
(Sw, St).

 Two players drive cars toward each other.
 If one player goes straight that player wins.
 If both go straight, they both die.
Figure 1: Analogy of 2 cars
St.
Sw.
St.
Sw.
A B Swerve Straight
Swerve 0,0 -1.1
Straight 1,-1 -5,-5
Car A Car B

Research Questions
1) How game theory is related to the Brexit scenario?
2) Finding an approximate outcome to the Brexit scenario
by using a game theory model.

How game theory is related to the Brexit scenario?
 The current negotiations can be clearly analyzed by the
concept of “Game of Chicken” which is a crucial element
of Game Theory.
 Two cars moving in opposite directions and closing in at a
very rapid pace towards each other (figure 1).

 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, 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.

Limitations of the model
 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.
 We have considered E.U. to be as a unified organization in
this case(instead of 1 to 27 independent nations), because of
infinite number of strategies and payoffs possible for the
multiple parties.
 We have considered only two strategies per party. There
can be various other strategies that are possible for the
multiple parties involved (including the 27 nations that are
a part of the E.U.).
 Another factor that can influence the negotiations between
Britain and European Union is how much time one takes to
defect from the path.

Game Theory Model
The model is a 2x2 matrix that helps determine which
strategy will dominate and which strategy will be
dominated.
Figure 2: Game Theory Model
E.U.
Britain
Swerve Straight
Swerve +1,+1 -3,+3
Straight +3,-3 -10,-5
Strategies
Players
Payoffs

when both the parties continue to move
in the same direction, 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.

Suggested outcomes of Brexit
If Brexit takes place;
 If there is a Free Trade Agreement that is signed with
European Union, GDP for Britain will decrease by 2.2%,
If not, then this could lead to a 6.3% to 9.5% decrease in
GDP for Britain. 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.
 However, if Brexit takes place, the GDP of Britain could
have increased by 1.6% by 2030

Continue…
 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.

Continue…
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.
 Britain contributes a significant amount to the budget of
E.U, so that the member states would have to contribute
more to the E.U. budget, for example Germany would
have to pay approximately 2.5 Billion Euros a year
extra.

Continue…
 There will be losses for the member countries as most of
these countries, which relied on U.K.’s trade.
 This would lead to a loss of “power” for the E.U within
the international politics and would be affected in terms
of global trade partnerships.

 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.
 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.

President Donald Tusk Former Prime Minister
David Cameron

Reference
 Maneesha, Nishant Vijay, Apoorva Singh, May 2016, To
Develop a Game Theory Model Analyzing the
Negotiations between Britain and European Union.
 Revised from:
http://www.slideshare.net/1991soumya/game-theory-
12530191
 Revised from
http://www.slideshare.net/PrithvirajRajDasgupt/1-
intro-gametheory

‫با‬‫از‬ ‫تشکر‬‫توجه‬‫شما‬
‫استاد‬:‫سلطانی‬ ‫خلیفه‬ ‫دکتر‬
‫گردآورنده‬:‫آرچونیانی‬ ‫آرمنوش‬

negotiation of Brexit

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