What you need to know about Game Theory

Here is a brief excerpt from an article by Keshav Parwal. Game theory has proven to be one of the most influential influences on contemporary thought. Parwal suggests what you need to know about it.

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Game theory is the fascinating study of how people interact. It is the foundation for economics, law, politics, psychology, and artificial intelligence. Under the simple assumption of rationality (which is more reasonable than you might think), it’s possible to build models for behavior.

The simplest models don’t quite look right, in the same way the simplest physics problems ignore friction. But as they grow more complex, patterns of behavior, or “strategies”, emerge, and they grow more and more reasonable as copmlexity increases.

Many game theory concepts are directly applicable to our lives. Concepts like repeated games, the endgame problem, matching games, and more have direct correlations to our world. Let’s examine one simple game.

You’re Bonnie, and Clyde is your partner in crime. You’ve been caught by the police after robbing a bank, and now you’ve been stuck into an interrogation room with no escape and no way to get a message out.

You’re caught. But you won’t rat out Clyde. The interrogator presents you with an option. If you snitch on Clyde, they’ll go easy on you. Clyde is in another room, presented with the same option. What would you do?

If you’ve studied game theory before, you’ll immediately recognize this as the famous prisoner’s dilemma, one of the most important games. Let’s examine how to play the prisoner’s dilemma.

If neither of you snitch, you both get three years in prison. If one of you snitches, and the other doesn’t, then the one who didn’t snitch gets nine years, and the one who snitched gets off scot free. If you both snitch, then you both get six years.

From now on, to match game theory parlance, we’ll call snitching “competing” and not snitching “cooperating”. And we’ll call the “joint payoff” the negative sum total time you both spend in prison. If both cooperate, then the joint payoff is -6. If both compete, then the joint payoff is -12. Which is worse. If only one snitches, then the joint payoff is -9. If you both compete, you get the worst outcome! You should clearly both cooperate, you’ll both get the least possible amount of jail time.

But you’ll compete (snitch) every single time.

Go back to the interrogation room. Now imagine you have those individual and joint payoffs in front of you (or, the game is of perfect information), and you know that Clyde is making his decision at the exact same time as you (or, the game is static). You’re in a static game of perfect information. Remember, there is no communication at any time after your arrest.

You’re sitting there, the decision in front of you, and with the knowledge that Clyde is making the same decision. You know you should both cooperate. He knows that too. Let’s suppose you think he’ll cooperate. You could get -3 by cooperating. But you could get that sweet, sweet 0 by competing! Okay, let’s suppose you think he’ll compete. If you cooperate, you’re going to get a -9, but if you compete you could turn that into a -6! No matter how bad -6 is, it is better than -9.

No matter how Clyde acts, it is always in your best interest to compete!

The kicker is, Clyde has figured this out too. You two are tragically fated to compete with one another and make yourselves both worse off.

What we discovered there was a Nash equilibrium. There is never any reason for one player in the game to deviate from the compete-compete outcome, so the game has reached equilibrium — you’ll always compete. That’s the evil of the prisoner’s dilemma. It was designed to get you both to rat each other out. Without some way to change the payoffs of the game, even communication before you are arrested cannot change this outcome. Even if the game is made dynamic, where Clyde (or Bonnie) chooses first, and Bonnie (Clyde) is told what decision their partner made before making their decision, you will still always compete-compete.

People simply cannot be trusted, it seems.

This game, made more complex, becomes the tragedy of the commons — public resources will always be overutilized (there is also a tragedy of the anti-commons, where rightholders will exclude one another from using a resource, to the point it provides value to nobody).

A short side note, most formal literature on game theory will talk about socially efficient outcomes, Pareto efficient, or Kaldor-Hicks efficient, but these all essentially mean the “best” outcome — the one with the highest joint payoff. This isn’t necessarily the best outcome for you, but it’s the best outcome for everyone. It’s the same way that greedy algorithms find local optima, but almost always fail to find the global optima.

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Here is a direct link to the complete article.


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