How can Game Theory help understand post-Brexit UK-US trade negotiations?

By Paul-Henri Minet*
Guest Contributor 

Since the launch of official trade negotiations between the United Kingdom (UK) and the United States (US) in May 2020[1], the trade position of these two countries has significantly evolved. The reality of Brexit and the election of President Joe Biden are turning points which undoubtedly have an impact on the dynamic in place. As such, the aim of this paper is to put the spotlight on the relevancy of Game Theory to provide an insightful analysis of the US-UK trade negotiations.

The Brexit context

Sovereignty in trade policy was one of the key components of the Brexit campaign. The argument supported by the pro-Brexiters relied on the benefits of regaining a complete trade independent policy. This concretely translates in the ability to negotiate and secure trade deals in UK’s own terms rather than being constrained in any way by the European Union (EU).

On the other hand, Brexit also meant leaving the EU single market and its advantageous conditions as a member state. In the absence of a trade agreement with the EU, a direct consequence of a hard Brexit would have led to great difficulties for UK businesses. As such, the rules of the World Trade Organization (WTO) would have applied to their trade relation, including tariffs and other trade barriers[2]. Since the EU is UK’s largest trade partner[3], a hard Brexit would have significantly hit the British economy. Indeed, export data of 2019 stresses the importance of the EU, taken as a whole, in the UK’s trade balance, accounting for 43% of the UK’s exportations and around half of its importations[4]. Fortunately, after four years of negotiations, a deal has been secured although the reality of the post-Brexit situation is not advantageous for either the UK or EU. Higher trade barriers are now in place which will significantly impact trade and the future of these two economies.

As soon as the results of the Brexit referendum had been declared, Westminster started to prepare the post-Brexit situation by seeking to reproduce the effects of the trade agreements with countries holding trade agreements with the EU. Indeed, leaving the EU also translates to being side-lined of numerous trade deals that it had established with other trade partners[5]. The recent UK-Japan trade deal is actually the first to differ from the EU-Japan economic partnership. This might be seen as a victory for the UK, proving that reaching agreements without the EU is feasible. However, it should be stressed that Japan only represents 2% of British trade[6].

UK-US trade dynamic

The UK has stated that reaching a trade agreement with the US, known as its biggest export market as an individual country, as a key priority. In 2019, the US accounted for 21% of UK exports which is a significant part of its trade in goods and services [7]. It is economically but also politically important for the UK to reach a trade agreement with the world’s biggest economy since it would be an ideal opportunity to foster the idea of “Global Britain”, demonstrating that Brexit was the right choice. It would also be considered as a symbolic victory following the failure of the controversial Transatlantic Trade and Investment Partnership (TTIP) between the EU and the US which has now been declared as “obsolete and no longer relevant”.[8]

Under Donald Trump’s presidency, Prime Minister Boris Johnson had found a pro-Brexit ally with whom he officially started negotiations. However, the situation has now drastically changed following Joe Biden’s election as the American president and considering he has openly stated a far different view.[9] Moreover, US officials have made it clear that reaching an agreement with the UK is not a priority for President Biden and that there will be no “treatment of favour” compared to the EU. Interestingly, while Trump was pro-Brexit and keen to reach a deal with the UK, Joe Biden openly declared that he would have voted to stay in the EU if he were a British citizen[10]. Furthermore, a trade agreement with the UK is perceived as relatively unimportant[11] as the UK only represents the 5th biggest trade partner of the US, far behind countries such as China or Canada[12].

A game theory approach

The unique situation in which the UK has found itself following the Brexit referendum coupled with the influence of Biden’s election bring about many uncertainties. The UK is now finding itself at a crossroad with a change in its dynamic with the US and holding less bargaining power in trade talks. Future choices the UK will take are of great consequence, which leads the path to the relevancy of Game Theory to deliver an insightful analysis of the situation.

Game Theory is, broadly speaking, the study of strategic interactions in decision-making[13]. Although only mathematically developed in 1944 by von Neumann and Morgenstern, game theoretic-insights can be found in various sources as far back as Ancient Times[14]. Applied frequently in our world today in fields as diverse as biology, politics and of course economics, game theory is particularly insightful as it relies on formal models to analyse strategic interactions. Furthermore, a key concept in Game Theory is the interpretation of “strategic interactions”. This refers to taking into account other actors who have the power to influence an outcome. An actor or agent should take other agents’ strategies into account in their own decision-making[15].

UK-US framework

Before deep diving into game theory framework, let us wrap up the trade dynamic between the UK-US. It is apparent that the UK has more economical and political interests to reach a deal than when compared with the US. Biden does not consider it as a priority and holds more bargaining power to achieve a potential trade deal which serves US interests subsequently leading the UK to a weaker position in the negotiation process. Nevertheless, we still assume that both parties would be better off by reaching a trade deal as each country’s economy, in their own proportion, would benefit from lower trade barriers overall.

This dynamic can now be formalised through a game theory framework. As such, and without diving into too many details, let us assume that the dynamic can be seen as a finite “game” between these two “players”. Their strategies/actions are taken in a simultaneous way which will result in defined outcomes for each player.

Following the previous assumptions, we assume that the US can follow two strategies:

  • “Generous deal”: the US decides not to take full advantage of its bargaining power and offer a generous deal to the UK.
  • “Tough deal”: the US decides to extensively use its bargaining power to its own agenda, which would be considered as a tougher deal for the UK.

And as for the case of the UK:

  • “Accept Deal”: considering the economic and political interests are highly important, the UK accepts a trade deal no matter how the US decides to undertake the negotiations.
  • “Refuse the Deal”: the UK eventually decides to refuse a deal with the US.

The next step is to assign an outcome for each of these strategies. The numbers assigned are outcomes based on each players’ strategy given the other players’ own strategy. These numbers are based on our assumptions but are purely illustrative and should only be interpreted in a comparative perspective.



Let us illustrate to better understand the matrix: if the US chooses the strategy “Generous Deal” and the UK chooses “Accept deal”, this will result to an equilibrium on the top left of the matrix leading to a payoff of 10 for the UK and 4 for the US.

Analysis and insights

The matrix indicates to us that the UK has a dominant strategy to accept the deal. Indeed, no matter the strategy the US follows, the UK should accept a deal because the payoff will always be higher (10 > -1  and 5 > 0). On the other hand, the US has a dominant strategy to use its bargaining power and to decide on a tougher deal since its payoff will always be higher no matter the strategy the UK follows (6 > 4 and 1 > 0).



Consequently, the equilibrium of the game lies on the top-right of the matrix: the US decides to go for a tough a deal, which the UK will accept. At this equilibrium, no player has any incentive to deviate from its strategy given the other player’s strategy: this is formally described as a “Nash equilibrium[16].

The analysis and equilibrium of the game underline that, given our assumptions, the UK will eventually reach a trade agreement but under the US’s conditions and agenda. Based on this foreseeable outcome, the UK should consider if a deal with the US is still desirable, especially since concerns regarding the potential negative impacts of the deal on health and environment standards have been raised[17]. These concerns are actually part of a more global critique against the government with regard to the pace the UK reaches trade agreements. Following the recent announcement of the UK to apply to join the Comprehensive and Progressive Trans-Pacific Partnership (CPTPP), the shadow international trade secretary, Emily Thornberry, has questioned the trade strategy of the UK: “More generally, people will rightly ask why we have been through five years of debate in Britain over leaving a trade bloc with our closest neighbours only to rush into joining another one on the other side of the world without any meaningful public consultation at all.”[18]. As such, Westminster should address these concerns and ensure that the trade agreements, notably the potential UK-US trade deal, will not lead to dilution of standards and thus eventually harm British consumers.

Moreover, looking back at the matrix of the game, the UK would be better off if the game equilibrium was on the top-left of the matrix (10 > 5). Therefore, British negotiators and policymakers should aim for this equilibrium by developing opportunities to change the US’s perspective and influence them to decide on a “generous deal”. Starting with successful mini trade deals could be a possibility. By demonstrating the success of these deals, this might give incentives to undertake a mutually beneficial trade agreement on a much higher scale. Another opportunity would be to consider this trade deal as part of a more global UK-US cooperation. If the US sees the UK as a stronger ally in other important points of its agenda, it might be more inclined to undertake a more generous trade deal with the UK.

Limitations and conclusion

To build a model, one needs to rely on assumptions that can inherently be challenged. This paper is not an exception. Game theory relies on the rationality of actors but humans are not purely rational actors in their decision making and much bias has been covered by scientific literature. There is also room for debate in regard to the payoffs attributed to each strategy. Although the important aspect is the comparative value rather than the absolute, a more extensive analysis in the dynamic in play would be useful to define more accurate payoffs for each outcome. Furthermore, in the scope of this paper, we did not go deeper in the various types of models and opportunities game theory offers, which would undoubtedly enhance the analysis.

These limits should not however undermine the insights generated by this paper. Game theory is an effective toolbox to analyse strategic interactions within a decision-making context and this model has proved useful to understand the trade dynamics between the UK and the US. Standing itself at a crossroad, the UK needs to decide on which direction to take. The future will tell if an agreement will be found (if yes, under which conditions) and how British consumers will eventually be impacted.

*Paul-Henri is a guest contributor at Unfiltered Voices. He is a digital performance expert working in the field of Digital Analytics for the last two years for the public sector. He studied his BA in Economics at UCLouvain (Belgium) and holds an MSc in Economics & Management from the Louvain School of Management (Belgium) where he specialised in microeconomics and digital transformation. 


[1] UK parliament, “UK-US Trade negotiations”,, accessed 28/02/2021.

[2] Tom Edgington. “Brexit : what trade deals has the UK done so far?”, 08/02/2021,

[3] Ibid.

[4]UK Parliament (House of commons library), “Statistics on UK-EU trade”, 10/11/2020,,.

[5] Department for International Trade, “UK trade agreements with non-EU countries”,, 02/03/2021.

[6] Graham Lanktree. “5 things to know about the UK-Japan trade deal”, 11/09/2020,

[7] Matthew Ward. “Geographical patterns of UK trade” (25/10/2020), briefing paper number 7593, House of Commons Library.

[8] European Commission. “The Transatlantic Trade and Investment Partnership (TTIP)”, 15/04/2019,

[9] Associated Press News wire. “Britain’s Boris Johnson presses Biden for new trade deal”, 23/01/2021,

[10] Luke Hawker. “Joe Biden wants ‘UK to rejoin EU’ as Boris Johnson handed Brexit trade deal blow with US”, 23/01/2021,

[11] Graham Lanktree. “5 things to expect from Joe Biden on UK trade”, 20/01/2021,

[12] Trading Economics. “United States Exports By Country”, , accessed 25/02/2021.

[13] Steven J. Brams. “Game theory”, 24/01/2021,

[14] Stanford Encyclopedia of Philosophy. “Game Theory”, 08/03/2019,by%20none%20of%20the%20agents.

[15] Bernhard Von Stengel. “Game Theory and Politics“. Talk, London School of Economics, London, 20/02/2020.

[16] Policonomics. “Game Theory II: Nash Equilibria”,, accessed 24/02/2021.

[17] Trade Justice Movement. “UK-US Trade Deal”, accessed 01/03/2021.

[18] PA media. “UK to apply to join free trade pact with nations on the other side of the world”, 30/01/2021,

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