A Beautiful Mind - An Ugly Problem

The prisoner's dilemma is a situation in which rational individuals, fully aware of the consequences of their actions, choose not to cooperate even though it would be in their best interest to do so. Given self-interest, the actors end up in a situation that is paradoxically not in anyone's best interest. If this sounds contradictory, it is, and it has baffled many great minds.

One notable figure associated with the prisoner's dilemma is economist and mathematician John Nash. In the movie A Beautiful Mind, based on Nash’s life, a famous scene depicts a moment in time when Nash has a sudden glimpse of brilliance into the dynamics that underlay such problems.

Nash, played by Russel Crowe, sits in a dingy college bar with his friends/classmates. They see a group of women enter and discuss how to pick them up. Nash, clearly deep in thought, says:

Adam Smith said the best result comes from everyone in the group doing what's best for himself, right? Adam Smith was wrong! The message: Sometimes it is better to cooperate!

Nash gets up and runs out with excitement; in that instant, he suddenly understands exactly why his friends are doomed to strike out and, more importantly, why Adam Smith was wrong; or, more accurately, why Smith’s theory was incomplete.

Why is Smith Incomplete?

Before returning to the dingy bar, an important clarification is required - what exactly was Adam Smith wrong about?

For those unfamiliar, Smith was a Scottish economist, philosopher, and author who is considered the father of modern economics. Smith is best known for his work "The Wealth of Nations."

Smith observed that when markets work well, everyone acting in their self-interest allocates resources to those who value them the highest, or at least to those willing to pay the highest price.

It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest ~ Adam Smith

Smith suggests that the combination of self-interest and prices produces the greatest good*. I will italicize and use a * for a reason, as Smith’s use of the phrase - the greatest good* - is perhaps the mother of all suitcase terms. Meaning you need to unpack it very carefully. With that said, let's leave the term mostly unpacked and take out the bit we need.

While there exist all sorts of reasons why markets could fail in producing what many would consider the greatest good*, they do result in a greater good. If everyone makes a voluntary exchange, they must be better off, or they wouldn't have agreed to the exchange.

Smith saw a world where markets led to everyone being better off despite a self-interested motive, and this is generally true. Nash saw that everyone acting in their self-interest could make no one better off. To be precise, what Smith was wrong about was that self-interest always leads to at least one person being better off.

Smith saw self-interest guiding everyone to an improved situation; Nash saw self-interest guiding people off a cliff.

Now, it needs to be said. Smith is synonymous with capitalism. Nash did not mean Smith was wrong about capitalism. As far as I know, Nash was never anti-capitalist. What Nash saw was a much more deep-rooted problem endemic to all humanity that pervades the choice of capitalism or socialism or (insert ____ism).

Indeed, the dynamics in the bar, and the ones I will describe, are human to the core. While there are solutions, they are not found by switching from socialism to capitalism or vice versa; in a way, the issue is deeper and makes the problem so fascinating and devastating, but before we get ahead of ourselves, back to the dingy bar.

Deciphering the Dilemma

So, first of all, I will warn this story is horribly politically incorrect, but for the sake of completeness - what did Nash see in the dingy bar that resulted in such a profound insight?

It follows from the following two assumptions. To set the stage, suppose there are four guys and five gals. One gal is very attractive, I will call A, and the rest are equally less attractive, let's call them B, C, D, and E. All the guys are similarly attractive, and except for the introverted Nash, they are full of confidence. Let's suppose the following:

1. Gal A will go home with one guy if only courted by said person but will turn them all down if hit on by multiple men (too many to choose from, I guess).

2. B, C, D, and E will go home with a guy only if the guy hits on them first; they will not go home if the guy hits on A and turns to them after being shot down.

What's the optimal strategy?

Every guy should pick one of B, C, D, or E and only hit on them; avoid A altogether. Everyone goes home with a girl.

Why won’t this work? Well, every guy has the incentive to say they are committed to the plan, but at the last moment, go over to A and be the lucky guy who goes home with her. All think the same, all hit on A, and no one goes home with anyone. Smith was wrong; self-interest is not the optimal strategy.

From a Dingy Bar to the Westen Front

The dynamic that Nash saw eventually developed into a formal model called the prisoner's dilemma (for the most common depiction of a prisoner’s dilemma, watch this video). What is important is that while this bar scene is rather trivial and, as noted, not particularly tasteful, the insight and underlying dynamic can be applied to much less trivial real-world scenarios.

In fact, many have argued that war is a prisoner’s dilemma - a particularly tragic and ugly one. Solve the problem, and you solve war. That is quite an incentive. In part 2, I will argue that the onset of WW I was a prisoner’s dilemma as it involved the same dynamics that Nash saw at the bar, but indeed, the stakes were orders of magnitude higher.