In 1950, Merril Flood and Melvin Dreshner devised a fairly simple and unassuming game. Little did they know, this game underpins almost all social behaviour, from the heat of the Cold War to the guppies of South America, and from advertising between rival companies to doping in sports.

The prisoner's dilemma works simply. There are two prisoners locked in separate interrogation rooms, for the same crime. If you both stay silent - you both co-operate with each other, there is not enough evidence to prosecute you for the serious crime, so you both get 3 years in prison. If one of you talks (defects), but the other does not (co-operate), the person who talked gets 1 year whereas the person who stayed silent gets 10 years. If you both talk (defect), you both get 7 years in prison.

Let’s say your opponent defects. You have a choice between defection and cooperation. Cooperation leads to 10 years, but defection leads to 7. Therefore, if your opponent defects, you should too. Now let’s say your opponent cooperates. You have another choice. Cooperation leads to three years this time, and defection leads to one. Therefore, acting rationally, you should always defect. However, if your opponent also acts rationally, they will also defect. This leads to a game where both you and your opponent end up in a sub-optimal position.

Now, we change one thing. Instead of playing once, you now play this game an unknown number of times (if the number of times is known, it leads to only defection). In 1980, political scientist Robert Axelrod held a competition at the University of Michigan, though he modified it to be about points, rather than prison sentences. He had 14 different computer programs (submitted by his students) play this game against each other (and against themselves) and ran it five times, to ensure that the success was not an accident. The strategies of the programs were massively varied, and some were up to 77 lines of code, while some of them were as short as 4 lines.

The results from these games were tallied up, and each of the different strategies were ranked. At the very top was the simplest, called ‘TiT for tat’. It worked by starting with a cooperation, then mirroring what the opponent did in the last move.

After more careful analysis, Axelrod found four key traits in the top strategies. Firstly, all the winning strategies were forgiving and didn’t hold grudges. In other words, they didn’t let defections from previous turns affect their judgement. Secondly, all the winning strategies were kind. This simply meant that they were never the first to defect. This meant that they were not a pushover, any defection was immediately met with a follow-up defection. Finally, the best strategies were obvious, not seeming like random actions, and then they were easy to trust. Interestingly, any strategy with these four principles is unable to win; they can only draw and lose (similarly, strategies that don’t obey these principles can only win and draw). However, it is not a zero-sum game (the opponent doesn’t lose what you win, unlike in poker); success is defined by the total points, not the relative points or number of wins. These strategies led to the most consistent wins, while strategies that didn’t abide by these almost always lost.

In 1945, the first atomic bomb was dropped on Hiroshima. President Harry S Truman, a hard-line anti-communist, chose not to inform the Soviets, who were planning to invade Japan to help the West. Stalin, enraged, called for the building of the USSR’s first nuclear bomb. From this point, both sides had a choice of defection (building up their arsenal) or cooperation (reducing their arsenal). Due to fear of unilateral cooperation (only one side cooperates) and asymmetric risk (the other country having an advantage over you), both the US and the USSR repeatedly defected, leading to both countries being in a sub-optimal situation (maintaining the arms race was massively expensive for both sides, especially for the USSR, who, due to the nature of Stalinism, was already struggling with economic growth). They had reached Nash equilibrium (named after one of the fathers of game theory): the point where there was no longer an incentive to change tactics as neither player would gain any advantage. However, in 1985 (marked by Mikael Gorbachev coming into power), there was a shift in attitudes, as both sides started to cooperate. They passed nuclear-reduction treaties and both slowly decommissioned weapons in their nuclear arsenal. This cooperation saw a period of peace and prosperity and low international tensions, from which everyone benefited. 

Picture two rival companies, competing for the same audience. Both of them are trying to maximise their profit. They each have two options, they can either choose to advertise (defect), or to not advertise (cooperate). If they were to both advertise, then they would both end up poorer: their market shares stay exactly the same, but both now have to pay the advertising bills. If only one advertises, then they will get an increase in customers, and therefore profit, while the other will lose customers. However, if neither were to advertise, they keep their original customers and save their money. While advertising is the best move for each individual company, it ends up putting both companies in a worse position.

Now picture the Olympics, where there are two athletes competing to get gold. Each of them have the individual option to dope, which, while risky, would give them the competitive advantage over their competitors. If both choose to dope, neither gains an edge, meaning they took a massive risk for zero reward. If only one chooses to dope, then that means that they have an unfair advantage over the other, increasing their chances of winning, though they have the risk of being caught. If neither dope, it is a fair game, and they have no risk of being caught doping. Even though doping is the logical move for an individual athlete looking to win, it would put them both in a collective state of disadvantage.

Game theory, above all else, advises us how to act. In order to get the most benefit, you need to be nice, forgiving yet firm, and clear. Whether it be in complex geopolitics, the wild savannahs of Africa or a work lunch with colleagues, the organisms that cooperate thrive, while the ones who don’t fail. Recent events have led to a tribalist ‘us versus them’ mentality. This contributes to rising levels of political violence and oppression. Those outside the group are seen as malicious, leading to constant defection. However, this puts the whole of humanity in a worse situation. Maybe to fix the world, we need to extend an olive branch to those outside our tribe.