Using Game Theory to Predict Brexit Outcomes

“Consider the negotiations over Brexit between the UK and the
EU. Use Game Theory to describe the players’ strategies, their payoffs and how
the game is played. Solve your model to predict the outcome(s).”
The essay thesis is that due to Brexit, the EU will achieve more
of its aim and objectives during negotiations than the UK will. The prediction
which is encompassed within my essay is that the EU controls the deal and they
can chose to give the UK either a good or a bad one. As a result, the UK can
either accept the deal negotiated whether that be good or bad, even though they
may have to pay £50 billion to maintain access to the single market which is in
the news currently. (Boffey, Ramkin and
Asthana, 2017) Or the UK can reject the deal and exit from the EU without one.

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As reflected by McCulloch,
(2017) game theory was invented by John Nash who using a mathematical
strategy which could determine the likely outcome of 2 or more players with
valuations assigned for the range of potential outcomes. According to the
principles, a player will take action to try and secure the best deal to
improve their bargaining power and therefore there no deal payoff to remain
stronger than the other player. (Muthoo, and Benita, 2017).
The prediction of negotiation is supported through the use of a pay off matrix which seeks to identify the pros and cons of accepting the deal based on the negotiations. However, Britain has more to lose than the whole of the EU so can be assumed that they will receive a worse deal as a consequence. The matrix is set up 2×2 as shown below, which helps identify the combinations that are dominate, and the ones being dominated. This ensures Nash equilibrium can be detected which is defined by Core (2017) as ‘A set of strategies, one for each player in the game, such that each player’s strategy is a best response to the strategies chosen by everyone else.’ In the negotiation this is the point when both the EU and the UK defect from their original course to observe and see what the opposing players are offering, as part of their negotiation. This would be the most favorable if both parties were to defect from the path allowing a stable outcome.

The number present in the bracket illustrates the benefit to that
player if the strategy is undertaken. As shown in the box on the matrix above,
the first number is the result for the UK and the second is the EU. The
relative size and comparison between the two numbers is important.
The top tight cell indicates the strategy that the UK has accepted
a good deal offered by the EU. According to my game, the outcome is still negative,
as in my opinion it is unlikely that the deal the UK accepts will give them the
same full access to the single market which the UK currently has, this enables
them to trade freely amongst each other without tariffs. (Cadman and Tetlow,
2017) However, as it is a good deal the loss cannot be that bad.
The top left cell displays the UK accepting a bad deal offered by
the EU, hence the more negative number than the right cell as the UK will be
worse off. In my opinion the payoff would be more negative, but it is the most
negative for when the UK does not accept a deal yet leaves the EU regardless
whether the deal offered was good or bad. This will detrimentally damage the
UK, consequently the UK should accept whatever deal is offered as accepting no
deal would damage the future for the country in an economic and a political
sense.
From the perspective of the EU, it would like to give the UK a
good deal as it will benefit the EU economically in the future. However, it
would want to punish the UK for deciding to leave and try and ensure that it
puts off other countries from leaving too. This is further discussed by
Maidment (2017) who quoted ‘that two of the EU’s top Brexit chiefs want to “punish” Britain to stop other
countries trying to leave the bloc.’
In this situation, the dominant strategy for Britain which is
defined by Core (2017) as ‘Action that
yields the highest payoff for a player, no matter what the other players do.’
Is for them to be granted with a good deal for example maintaining access to
the single market without having to pay the £50 billion, this has the potential
to result in the highest pay off. In comparison, the EU has the dominant
strategy if Britain are not part of the EU with a higher pay off.
The outcome is determined due to a combination of political as
well as economic costs to the EU, the UK have limited control so in this case
are being dominated by the EU. For the UK, if the deal is not worse than
leaving with no deal it would be rational for the UK to accept it. (Muthoo, and
Benita, 2017).
However, being rational acts as a major limitation which is drawn
upon by Fairchild (2016,) who presents the case that as humans are not always
rational so are not always unemotional and self-interested individuals who have
no regard for others. As stated in Prisoners dilemma, the rational strategy is
for each player in the game to gain the worst outcome possible. However, once
empathy is added and individuals are not perceived as rational each player
cares more about the others. Consequently, it can transform the game into a win-win
situation for both players creating mutual cooperation. For this game the
relationship amongst nations would improve creating more awareness and hence
softer negotiating approaches with the potential of better deals for both
parties.
Other limitations of game theory are explored by Maneesha, Vijay
and Singh (2016) who quoted ‘we have only considered only two strategies per
party.’p.4. This helps ensure simplicity and makes the whole scenario much
easier to understand. Even though there are often many other strategies in
place where more than 2 groups are involved with contrasting ideas.
Additionally, the pay
offs which are the outcomes for each of the possible combinations of actions,
can also be affected for both the EU and UK determined by the course of action
taken and how long it takes for either player to change their mind and move
from their original plan. If the EU were to swerve first, consequently it would
be a more profitable outcome for the UK and vice versa.
When one applies an even value system to each successful outcome,
Brexit deal negotiations can represent the ‘chicken game’ which is defined by
Exton (2016, p.4.),’ If both parties in marital conflict choose escalation to
full conflict in order to get their way (mutual defection) in the game
situation a bad deal offered and hence the deal not accepted, this may be very
harmful to both parties , so trying to reach a compromise (mutual
cooperation) for example a good deal which is accepted  is usually preferable over mutual defection’.
Each party has the ability to make threats before starting
negotiating, so the more powerful party in this case the EU will intimidate the
UK as they are deemed the weaker party in the game. In this situation, they
would present them with a bad deal, for example implementing a cost to
cultivate their access to the single market, in recent speculation a cost of
£50 billion has the potential to be enforced.
In conclusion, it is predicted the UK will achieve less of their
objectives during the recent Brexit negotiations. Through the use of game theory,
it is attempted to prove that the UK will receive a worse deal than the EU. By
assigning values to each strategy it is possible to create a pay off matrix
showing all options available. Based on my findings I can conclude, that the UK
should accept any deal given to them from the EU, however, the EU are dominant
in this game, so it is likely that any deals will be unfavourable for the UK.
References
Boffey, D., Rankin, J. and Asthana, A., 2017. UK could pay £50bn Brexit divorce bill after bowing to EU pressure [Online]. Brussels: The Guardian. Available from: https://www.theguardian.com/politics/2017/nov/28/uk-and-eu-agree-brexit-divorce-bill-that-could-reach-57bn McCulloch, N., 2017. The Game Theory of Brexit [online]. Politics.co.uk: Neil McCulloch. Available from: http://www.politics.co.uk/comment-analysis/2017/03/15/the-game-theory-of-brexitMuthoo, A. and Benita, S., 2017. Game theory experts: credibility is key for a successful ‘no deal’ Brexit strategy. The Conversation,pp. 1-3.Muthoo, A., 2017. How a clever bargaining strategy can secure Britain a good Brexit deal. The Conversation, pp.1-3.Cadman, E and Tetlow, G., 2017. The EU single market: How it works and the benefits it offers [Online]. Available from: https://www.ft.com/content/1688d0e4-15ef-11e6-b197-a4af20d5575eFairchild, R., 2016. Game theory offers a better way forward in Britain’s EU drama. The Conversation, pp. 1-3.Core-econ, 2017. Social Interactions [Online]. Available from: https://www.core-econ.org/the-economy/book/text/04.html?query=pay+off#first-search-resultExton, G., 2016. Brexit and game theory: A single case analysis. Merici, 2, pp.1- 9.Maidment, J., 2017. EU’s Brexit chiefs want to ‘punish’ Britain to stop other countries leaving, senior German MEP claims [Online]. Available from: http://www.telegraph.co.uk/news/2017/07/19/eus-brexit-chiefs-want-punish-britain-stop-countries-leaving/