The Nash Equilibrium: Simple concept yet big implications.

John Forbes Nash was an american mathematician who was awarded the Nobel Prize for Economics (1994) for his landmark work on the mathematics branch known as Game Theory.

Hold on David, did you just say Game Theory? What on Earth is that? Are those theories useful to win a Monopoly game against my friends? Do you mean theories used to win card games?

Let me explain this to you, my beloved readers.

Game Theory is the branch of mathematics concerned with the analysis of strategies to deal with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants. Game theory has been applied to contexts in war, business, economics…

Wait! I guess some of you are still not grasping how this works. Let’s jump to a simple example.

The prisoners dilemma:

Our game is the following: Two men have murdered a woman during a robbery. They have been arrested and are now being interrogated. The officer proceeds to make the same offer to both of them: If they both confess the murder, they each face eight years in jail. If one stays quiet while the other one confesses, then the snitch will get to go free, while the other will face ten years in jail. And if both hold their tongue, then they each face a minor charge, one year locked-up in their cells.

One would think that both prisoners will cooperate and stay quiet, as this is the best for both of them given that offer. However the Nash Equilibrium differs.

The Nash Equilibrium is a proposed solution of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players and acts in their own best interest. Additionally no player has anything to gain by changing only their own strategy while the other players keep theirs unchanged.

Then, returning to the prisoners dilemma, if each player chooses their best option, both of them will choose to confess, as it can save them from a 10 year sentence. As both of them choose to confess, our Nash Equilibrium (solution) would be both of them stay 8 years in prison.

John Nash emphasized the idea that as every individual acts in their own interest, the final result will not always be the best for the community. This is, if individuals act in their own interest the collective suffers.

Adam Smith, the father of modern economics, explains: "The best economic benefit for all can usually be accomplished when individuals act in their own self-interest."

I never thought I would say this, and from my humble point of view as Finance Undergraduate, Adam Smith was wrong (partially). The Nash Equilibrium can seem confusing at first instance, however there are plenty of examples that confirm Nash’ theory.

One example that quickly comes to my mind is: Carbon Dioxide Emissions. Each country has to choose whether they keep pushing the rates of CO2 emissions, which directly correlate with their growth and development, or cut them and grow less than their fellow nations. Using the governmental point of view, there is no chance to cut our emissions if the rest of countries do not follow the same policy, as a government we cannot tolerate to grow less and face economic recessions. As a citizen, you would probably think we would be better off if all nations agreed to strenghten their emissions regulations. However, in the end, all nations would choose to continue with this never-ending trend of increasing emissions. Why? The overall economic payoff is the highest, however the environmental situation worsens. As Nash said, individuals acting in their own interest will not always imply a collective improvement.

This tragedy of the commons can also explain situations like: overfishing, fracking, the 17th century slavery, athletes using enhancing drugs, … where the payoff of giving up those activities was not justified if not all parties agreed to do so.

Nash Equilibrium is not always as straight forward as the examples I provided, however we can see this behavioral pattern in many real-life examples.

David Sánchez