Author: Charles Cazals, Economics and Financial Editor, The London Globalist

Should women be wearing make up? Do you need to find an internship for this summer? Should your country limit its CO2 emissions to fight global warming? If you can’t see the link between these questions, don’t worry, you soon will.

Game theory is everywhere, and you do not have to be an economist to understand its most insightful aspects. In this article, I will explain the notion of a Nash Equilibrium (named after the economist John Nash, 1928-2015) and illustrate its applications on real-world examples.

The definition of a Nash equilibrium is straightforward: it is a situation in which all people are using a Nash Strategy. What is a Nash Strategy? Simply the aim of doing what is best for yourself, taking as given what others around you are doing. In economic terms, you are “best-responding” to other people’s actions in a purely individual and self-interested way.

For example, if there were two convenient stores right next to your house, your Nash Strategy when buying milk in the morning would be to go to the cheapest store, given each store’s price. And similarly, the Nash Strategy for the storekeeper would be to price their milk just below their competitor in order to attract you, given their competitor’s price and your strategy of going for the cheapest store.

So far so simple, but you may wonder how this leads to anything insightful… This is where the Prisoner’s Dilemma comes in. In A Beautiful Mind, a movie inspired on John Nash’s exceptional life story (which I unreservedly recommend), Russell Crowe pronounces this memorable quote: “Adam Smith was wrong! “. What is meant by this? Well, in classical Economic theory, Adam Smith stated that individuals, by pursuing their own interest, were maximising the collective welfare of society as whole, a notion that developed throughout the allegory of an “invisible hand”. The beauty of Nash equilibrium is precisely that it shows how acting rationally from an individual’s point of view can lead to collectively undesirable (or even disastrous) outcomes.

To illustrate this, we use the extremely famous example of the prisoner’s dilemma.

Imagine two burglars who are being accused of robbery by the police. The police have no evidence but decide to take both burglars to separate rooms and give them the chance to confess for their crime. They cannot communicate with each other in order to decide wether to confess or not.

Each of the burglars know the following:

• If both of them confess, they each get 5 years of prison
• If none of them confesses, they each get 1 year of prison
• If one of them confesses and the other does not, the confessor gets 0 years of prison (collaboration is rewarded by the police) and the non-confessor gets 10 years of prison (he pays for the entire crime).

Clearly in this situation, the collectively optimal outcome for burglars is for nobody to confess, so that they each get only 1 year of prison. However will this outcome be attained as predicted by classical theory?

Put yourself in the burglar’s position when he decides wether to confess or not:

-If the other burglar confessed, your self-interest is to confess, to get 5 instead of 10 years of prison.

-If the other burglar did not confess, your self-interest is to confess, to get 0 instead of 1 year of prison.

We conclude that no matter what the other burglar does, your best response is to confess. Since both burglars reason in the same way, they will both end up confessing, which leads to the Nash equilibrium: both burglars confess no matter what the other burglar does, and they both end up getting 5 years of prison, even though this is not the collectively optimal outcome for them. Both of them would in fact be better off if they agreed not to confess, but their personal temptations make this agreement infeasible.

The reason why this example is so famous is that it relates to many real-life phenomena in which individualistic behaviours lead to negative outcomes for society.

In sports, all professional athletes would be better off if no one used performance-enhancing drugs. The problem is that when no one uses these drugs, an individual athlete is tempted to use them in order to perform better than everyone else (the equivalent of confessing when the other burglar does not in the prisoner’s dilemma). This then leads everyone to consume performance-enhancing drugs, and any athlete who decides not to consume theses drugs would suffer from a major comparative disadvantage.

This also applies to environmental policies regarding CO2 emissions. The world as a whole needs to stop climate change, but each country individually has an economic interest in emitting CO2 for their industrial production, which leads to global inaction. You can think by yourself about the others examples I introduced with: women having to put on make up because everyone else does, LSE undergraduates desperately looking for internships because everyone else will have one to show on their CV… Examples are everywhere, and sometimes they entail inefficiencies that are extremely frustrating to economists.

The concept of Nash equilibrium allows us to understand why some society issues require particular forms of intervention if we want to reach desirable outcomes. Legally binding agreements and communication are generally the way to overcome the problem caused by personal incentives in situations such as global warming. Of course, this is much easier said than done in a global context of economic competition where no country wants to go first in depriving themselves of polluting for production.