The prisoner’s dilemma is a popular introductory example of a game analyzed in game theory that demonstrates why “rational” individuals are unlikely to cooperate, even when it could be in both of their best interests to do so, a win-win scenario. The prisoners dilemma game above simulates both what we’ll call the classical example, two.
Pigeons might do better than humans at game shows, at least on 'Let's Make A Deal.' These new findings — involving the pigeons superior ability to solve a perplexing statistical problem — might in.

The game play will consist of hawk attacks, bad weather, negative air currents and powerlines that you must watch out for and slow you down but also consist of positive air currents and powerups that will make your bird fly faster. Game Theory is a video game YouTube series on the channel The Game Theorists created by Matthew Patrick, aka MatPat. The channel posts videos analyzing video games and theories based on them. Patrick is also the creator of the channel The Film Theorists, which posts similar content related to film and television.

'All will be well if you use your mind for your decisions, and mind only your decisions.' Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.

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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.

Watch the clip or read my summary below.

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:

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.

If you like this post, you’ll love my introduction to game theory! It’s plainly titled The Joy of Game Theory. But I’ve worked to make it a lively read and it explains game theory in an intuitive way and requiring very little math (this post for example is the basis for one of the chapters). The book currently has nearly a 5 star rating on about 15 reviews on Amazon.

You can also check out my comprehensive list of the best game theory books which includes my reviews of general reads and textbooks.

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Game Pigeon Game online.

Game Theory Pigeons

In winter, birds have a hard time, so they are happy even with vegetables or fruit, slightly spoiled. In the game Pigeon Game you will help a very hungry pigeon to eat. To begin with, he will crack down on the corn cob. Give him a team to peck the grains that are not damaged by rot. They differ from the healthy in a darker color. The vegetable rotates, and from the grains greasy green worms periodically appear. Do not miss them, they will become a bargaining chip for the purchase of bonus items, as well as ripe fresh grains. To pass the level, it is necessary to peck good grains.

Game Therory Pigeons