Game Theory scene from A Beautiful Mind

Two Introductory Announcements

First, welcome to the Mind Your Decisions “week of skepticism.” All this week I will address misguided or crooked financial advice. The general theme is to be more careful about advice from people who sell you products or don’t consider strategic implications. Especially watch for well-intentioned but poorly reasoned advice, as I discuss today.

Second, I want to announce the newly launched website BrazenCareerist.com. I am one of the fifty bloggers of the blog network. If you’re young and looking for great career advice, see the full blog list to explore for yourself or subscribe to the feed for hand-picked highlights. My articles have already been featured a couple of times in the feed and have generated some interested comments. See the gender discussion I inadvertently started in my trust article and a nice compliment about my risk article.

Today’s Game

The motivation for today’s skepticism comes from a scene from the excellent movie A Beautiful Mind. The scene is about how to pick up women at a bar. You can watch the following two and a half minute clip from the movie (highly recommended), or read my summary of the problem below.

Video: Bar Scene from A Beautiful Mind

The Problem

You and three male friends are at a bar trying to pick up women. Suddenly one blonde and four brunettes enter in a group. What’s the individual strategy?

Here are the rules. Each of you wants to talk to the blonde. If more than one of you tries to talk to her, however, she will be put off and talk to no one. At that point it will also be too late to talk to a brunette, as no one likes being second choice. Assume anyone who starts out talking to a brunette will succeed.

The Movie

Nash suggests the group should cooperate. If everyone goes for the blonde, they block each other and no one wins. The brunettes will feel hurt as a second choice and categorically reject advances. Everyone loses.

But what if everyone goes for a brunette? Then each person will succeed, and everyone ends up with a good option.

It’s a good thought, except for one question: what about the blonde?

The Equilibrium

The movie is directed so well that it sounds persuasive. But it’s sadly incomplete. It misses the essence of non-cooperative game theory.

A Nash equilibrium is a state where no one person can improve, given what others are doing. This means you are picking the best possible action in response to others—the formal term is you are picking a best response. (For more, see my article on why Nash equilibrium exist).

As an example, let’s analyze whether everyone going for a brunette is a Nash equilibrium. You are given that your three of your friends go for brunettes. What is your best response?

You can either go for the brunette or the blonde. With your friends already going for brunettes, you have no competition to go for the blonde. The answer is clear that you would talk to the blonde. That’s your best response. Incidentally, this is a Nash equilibrium. You are happy, and your friends cannot do better. If your friends try to talk to the blonde, they end up with nothing and give up talking to a brunette. So you see, when Nash told his friends to go for the brunettes in the movie, it really does sound like he was leaving the blonde for himself.

The lesson: advice that sounds good for you might really be better for someone else. Be skeptical of the strategic implications.

Now, in practical matters it will be hard to achieve the equilibrium that only one person goes for a blonde. There is going to be competition and someone in the group will surely sabotage the mission. So there are two ways you might go about it using strategies outside the game. One is to ignore the current group and wait for another group of blondes (the classic “wait and see” strategy). The second is to let a random group member go for the blonde as the others distract the brunettes (also practiced as “wingman theory”).

Buying Used Products

Many personal financial articles tell you to buy used products. Here’s a small sampling:

The Stuff I Never Buy Used

Why First-Rate Folks Love Second-Hand Stuff

This advice sounds good for you, but could it be even better for the writer? Let’s do a thought experiment to find out.

Imagine you and all the readers listen to those people. Suppose enough people really stopped buying new products and created a large demand for used products.

This would in turn make used products priced higher as people recognize unrealized value. Used products would no longer be great bargains, and consequently, new products would relatively become less expensive as their resale value increases—that is, buying new would be the bargain choice.

The first people to recognize this would likely be personal finance experts, who have diverted your attention so they can buy new products without competition (i.e. go for the blonde). After the trend is clear, the advisers would turn around and write articles advising you to buy new products, starting the cycle once again.

The overall point is that friendly financial advice is part of a competitive game. It might be good for you, but better for the adviser. Talk is cheap. Unless I learn some real information or strategy, why should I listen to it?

This is why I am skeptical and consider much personal finance advice to be insulting. So much of it is the equivalent of a friend telling me to go for the brunette.