Article last updated 22 July 2025.
Rebecca Tunstall, Investment Manager, Rathbones
It is no surprise that investors prefer the clear blue seas of economics to the relatively muddy waters of political analysis when it comes to making decisions. Game theory suggests that there is a unifying model that can provide a clear analysis of both.
The recent rising tide of populism and anti-globalisation have arguably strengthened the influence of politics on economies. Brexit and other political issues could have a significant impact on economic growth.
Hunter S. Thompson once described politics as the art of controlling your environment. Put simply, game theory provides a model for understanding how competing parties negotiate to reach the best outcome for themselves. As it turns out, economics is actually a subset of game theory, which also provides a model for how political outcomes are reached.
In 1950 Albert Tucker came up with what is still probably the best known “game” in the field – what he called the Prisoner’s Dilemma. Here is Tucker's description:
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity to either betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent — as shown in our illustration.
The Prisoner's Dilemma
Do nice guys always finish last?
Though it seems to defy reason, it turns out that the rational choice for both prisoners is to betray each other. It results in the less than optimal outcome of both serving a five-year sentence, when they could have reduced that to one year each by cooperating and both remaining silent. But it is logical that both players, acting rationally, would choose not to cooperate.
This helps shed some light on why Brexit negotiations may not be as amicable as we might hope. And it seems to provide hard evidence for the old adage that “nice guys always finish last”.
Why is it rational to behave this way? In this simple, binary application of game theory betraying the other party, or non-cooperation, works out as the better option for each individual, and humans are essentially selfish. This is technically what has become known as the Nash equilibrium, mathematically proven by John Nash, hero of Sylvia Nasar’s biography and the eponymous film A Beautiful Mind.
If we apply the Prisoner’s Dilemma to Brexit negotiations, that does not bode well for future economic cooperation and growth in either the UK or the EU. But fortunately, game theory has moved on from the limitations of the Prisoner’s Dilemma. In real life, negotiations are much more complex, and the ‘games’ involved have multiple iterations. If you play the game multiple times with full memory of what occurred previously, a more cooperative outcome can evolve.
Political scientist Robert Axelrod tested this by inviting game theorists to join a tournament, the results of which he describes in his book The Evolution of Cooperation. The winning model submitted by mathematical psychologist Anatol Rapoport, called “Tit for Tat”, was one of the simplest: cooperate on the first move and then reciprocate with whatever the other player does in response. This and other cooperative strategies generally came out on top, Axelrod concluded, "by promoting the mutual interest rather than by exploiting the other's weakness."
So, approaching negotiations with a willingness to cooperate seems to improve the chances of achieving the optimal outcome. Intuitively, it makes sense not to burn your bridges with your neighbours and trading partners, and this goes for both sides in the Brexit negotiations.
But once having shown a willingness to cooperate, if this is not reciprocated, as per the Tit for Tat model, the response should be to switch back to playing hardball. So, while we hope for a growing spirit of cooperation as Brexit negotiations unfold, signs so far suggest a more combative approach.
Is Brexit too complex for game theory?
Of course, Brexit is not a simple negotiation between two parties — it involves a myriad of stakeholders and issues, adding layer upon layer of complexity. Can game theory cope?
The economist Woody Brock, in his insightful book American Gridlock, made many prescient warnings that seem to have largely gone unheeded amid what Brock called a “dialogue of the deaf” in US policymaking circles. One of the warnings was the need for a proper analytical model as compelling to politics as the law of supply and demand is to economics.
Fortunately, such a model does exist, according to Brock, but it is hidden in plain sight and largely ignored in the field of political science (and apparently even more so in the actual day-to-day business of governing). Its technical name is the Nash-Harsanyi-Selten (NHS) model of multilateral bargaining, named after its 1994 Nobel-Prize winning authors and game-theory experts.
It is not a name that trips easily off the tongue, and it does not seem as though it is being applied by either side in the fraught Brexit negotiations. But as Brock puts it, “Bargaining behaviour turns out to be the magnetic north of politics, and the Nash-Harsanyi model is the missing ‘core model’ that could play a unifying role in political science.”
