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Game Theory

19 Jun

(Russel Crowe as John Nash in A Beautiful Mind describing some Game Theory)

Again, a post not directly related to religion. This is a post about bare bones rationality. But first, a quote from Robin Hanson:

“Students are often quite capable of applying economic analysis to emotionally neutral products such as apples or video games, but then fail to apply the same reasoning to emotionally charged goods to which similar analyses would seem to apply. I make a special effort to introduce concepts with the neutral examples, but then to challenge students to ask wonder why emotionally charged goods should be treated differently.”

If you don’t know about Game Theory (GT) you should, since it is a situation that you’ve probably been in in some form or another in life. My first exposure to GT was the Prisoner’s Dilemma (PD).

Let’s say two people who have robbed a bank are under arrest and sitting in jail. The cops don’t actually have enough evidence to get a high probability of conviction, so they try to get them to admit to the robbery. They separate the two criminals and offer each a plea deal if they admit that the other one was involved.

If neither of them accuses the other, then they go to trial with a 50% chance of getting convicted. If they both accuse each other, they both have a 99% chance of getting convicted. If only one accuses the other, the accused has a 75% chance of getting convicted while the accuser gets granted immunity.

Which would you choose, if you were one of the criminals? From Wikipedia:

Because betrayal always rewards more than cooperation, all purely rational self-interested prisoners would betray the other, and so the only possible outcome for two purely rational prisoners is for them both to betray each other. The interesting part of this result is that pursuing individual reward logically leads the prisoners to both betray, but they would get a better reward if they both cooperated. In reality, humans display a systematic bias towards cooperative behavior in this and similar games, much more so than predicted by simple models of “rational” self-interested action

There is also an extended “iterative” version of the game, where the classic game is played over and over between the same prisoners, and consequently, both prisoners continuously have an opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by backward induction) two purely rational prisoners will betray each other repeatedly, for the same reasons as the classic version.

[…]

Doping in sport has been cited as an example of a prisoner’s dilemma. If two competing athletes have the option to use an illegal and dangerous drug to boost their performance, then they must also consider the likely behaviour of their competitor. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor (reduced only by the legal or medical dangers of having taken the drug). If both athletes take the drug, however, the benefits cancel out and only the drawbacks remain, putting them both in a worse position than if neither had used doping.

Which would you choose?

As is evidenced by the reference material in Wikipedia, the rational decision is to betray your accomplice/gangmate, since that has the highest personal payoff. Of course, most people are not rational and have a bias towards cooperation. Which is even worse, because people who actually are rational and study rationality would win almost every time; at least in single play PD games.

Here is another good example of the PD when it comes to other types of collaboration:

Say X is a writer and Y is an illustrator, and they have very different preferences for how a certain scene should come across, so they’ve worked out a compromise. Now, both of them could cooperate and get a scene that both are OK with, or X could secretly change the dialogue in hopes of getting his idea to come across, or Y could draw the scene differently in order to get her idea of the scene across. But if they both “defect” from the compromise, then the scene gets confusing to readers. If both X and Y prefer their own idea to the compromise, prefer the compromise to the muddle, and prefer the muddle to their partner’s idea, then this is a genuine Prisoner’s Dilemma.

Here is yet another example of the PD that is actually an iterative version written by a Less Wrong (that blog devoted to refining the art of human rationality) member:

Ganaj: Hey man! I will tell you your fortune for fifty rupees!

Philosophical Me: Ganaj, are you authorized to speak for all Indian street fortune-tellers?

Ganaj: By a surprising coincidence, I am!

Philosophical Me: Good. By another coincidence, I am authorized to speak for all rich tourists. I propose an accord. From now on, no fortune-tellers will bother any rich tourists. That way, we can travel through India in peace, and you’ll never have to hear us tell you to “check your [poor] privilege” again.

Ganaj: Unfortunately, I can’t agree to that. See, we fortune-tellers’ entire business depends on tourists. There are cultural norms that only crappy fraudulent fortune-tellers advertise in the newspapers or with signs, so we can’t do that. And there are also cultural norms that tourists almost never approach fortune-tellers. So if we were to never accost tourists asking for business, no fortunes would ever get told and we would go out of business and starve to death.

Philosophical Me: At the risk of sounding kind of callous, your desire for business doesn’t create an obligation on my part or justify you harassing me.

Ganaj: Well, think about it this way. Many tourists really do want their fortunes told. And a certain number of fortune-tellers are going to defect from any agreement we make. If all the cooperative fortune-tellers agree not to accost tourists the defecting fortune-tellers will have the tourists all to themselves. So if we do things your way, either you’ll never be able to get your fortune told at all, or you’ll only be able to get your fortune told by a defecting fortune-teller who is more likely to be a fraud or a con man. You end up fortuneless or conned, we end up starving to death, and the only people who are rich and happy are the jerks who broke our hypothetical agreement.

This is a situation that you’ve most definitely been involved in. Not because it’s about being confronted by Indian beggars, but because it’s an allegory for dating. So again, which one would you choose: cooperate or defect? Or which one have you chosen?

To see how this allegory is one about dating, I’ll have to make it more explicit. Say in some alternate universe, women who wanted to be approached by men on the street/at a coffee shop/dance event/etc. wore some sort of special wristband. The agreement was that men should only approach women with the wristband, and women would expect to be approached if they were wearing the wristband and would be friendly and welcoming when approached.

Because society is what it is with humans running around with their bunny brains, some men decide to approach even women without the wristband, and sometimes they get positive responses/dates and what have you; they’ve defected from the agreement and got more dating opportunities than by just approaching women wearing the wristband. Again, society being what it is, some women wore the wristband because they liked getting attention from men; even if they weren’t open to dating because they were married or in a relationship. Over time, men notice these other men getting more dates and eventually all men defect. Over time, women notice that other women are getting more attention just by wearing the wristband and eventually the wristband loses its initial function (some women even wear the wristband just because they like the color, and then get upset when they get approached); all the women have defected.

Dating. One massive game theory defection scheme.

As the Game Theorists have noted, if everyone defects in the iterated PD, then eventually this becomes a losing strategy. The issue with dating is that the iteration takes place over numerous generations. Meaning that the initial defectors are dead by the time the damage has been done and everyone has started losing out because everyone is now defecting. But why would a rational person not defect after multiple generations? Agreeing to the now generations-old cooperation scheme only results in the other prisoner reaping the rewards.

What I think is the worst part of GT and other decision theories is that we’re not consciously aware of our values. Playing a game of “let’s pretend” doesn’t solve that intractable problem. Furthermore, as I’ve been writing about a lot recently, our values are socially constructed. Our “conscious mind” is more like a press secretary for the government, meant to put a feel-good spin on whatever it is that our unconscious mind (the actual government) values and the actions we make due to those unconscious values. This is the main reason why people are religious, why some are suicide bombers, why some are feminists, and the main reason for many other political groupings.

The link to religion will be made in a subsequent post 🙂

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2 Comments

Posted by on June 19, 2013 in decision theory

 

2 responses to “Game Theory

    • J. Quinton

      June 26, 2013 at 5:28 pm

      That’s great!

       
 
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