Using Game Theoretic Modeling to Analyze the United Kingdom's Exit from the European Union

Abstract

This paper uses modeling techniques from Game theory to analyze Brexit, Britain’s choice to exit the European Union. First, a brief history of the Brexit negotiations over the past 4 years is present. It is followed by a macroeconomic cost-benefit analysis of Brexit to both players (Britain and the European Union) in which food security, trade, and migration rules are considered. Information from this cost-benefit analysis is then used to assign payoffs, create a simple ‘static game’ modeling Brexit as of 2018, and find the mixed Nash Equilibrium that gives us the best strategies that both sides can play. A more complex ‘Bayesian extensive-form’ game (Tree Z) is then built to reflect the real-world Brexit negotiations more accurately. This game shows the European Union to be of two types: i) Humanitarian-goal oriented and ii) Economic-goal oriented. Backward induction techniques are used to derive the optimal strategy that the United Kingdom should play given its beliefs about the European Union’s type.