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Using Game Theory to Predict Brexit Outcomes

Paper Type: Free Essay Subject: Mathematics
Wordcount: 1771 words Published: 1st Apr 2019

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“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.

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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.


  • 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-brexit
  • Muthoo, 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-a4af20d5575e
  • Fairchild, 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-result
  • Exton, 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/


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