What Is The Best Strategy?

Tit For Tat? Or Screw Your Buddy?

The other day I was riding my bike downtown, not going anywhere in particular. The weather was particularly nice, so I was just riding around. I had brought a couple of books in case I found a decent place to hang out. There wasn’t anything good playing at the movies, so I wasn’t in any hurry to be anywhere at any specific time.

I found this really strange bookstore. I hadn’t noticed it before. There were all these stacks of books that looked like they weren’t in any discernable order. Just slightly more organized than random. Like they just unloaded them from the used book truck and put them in stacks wherever there was space.

I went inside and started looking around. A sort of pattern emerged. The non-fiction books were over there, and the novels were up here in the front. And in the non fiction section, the how to books were kind of off to the side, the general non fiction books, like books about sociology, and the history and evolution of the sewing machine, and books about baseball were over there. And then the used textbooks were kind of off to the side next to up there.

As I started poking around, I was astounded by how cheap these books were. This one for twenty-five cents. That one for a dollar. The most expensive book I found was one titled “Step-by-Step Guide to Alchemy: How To Turn Any Object Into Pure Gold,” was three dollars. I turns out that it was a textbook that was used over at the university in an undergraduate course in metaphysics. I would have bought it, being able to turn anything into gold would seem to be quite a handy skill to have, but it was a really huge book, and even if it did fit into my backpack, there was no way I was going to haul this thing around the rest of the day.

So I continued to look, and I find this book about computer simulated game theory. It was written back in the seventies, and was about different programs that were developed to play a game called “The Prisoners Dilemma.” This is a classic puzzle from game theory. Here’s how it goes:

You have to people. Each has two cards. One card says “altruism,” the other card says “selfish.” Each player chooses which card to play. There are two players per game. If both players play the “altruism” card, they each get 500 points. If one player plays the “selfish card” and the other player plays the “altruism card” the selfish card player gets 900 points, while the altruism player gets nothing. If they both play the “selfish” card, each is penalized 100 points.

The game is called “prisoners dilemma” because if you have to supposed criminals, in separate rooms, they basically have the same choice. If they both claim innocence, the cops got nothing. If one guy rats out his buddy, while his buddy claims innocence, the first guy goes free (or gets a special deal) while his buddy is sent up the river. If they both rat out each other, then they both get penalized. This of course assumes that they both got caught unexpectedly, and didn’t have time beforehand to strategize.

So what they did, back in the seventies, was they had this round robin tournament. They invited whoever wanted to play to come up with a strategy that they thought would work best. Each player would play every other player (all computer simulated) and they would see who had the most points at the end. They would play a certain number of rounds per player, and then switch.

What they were most interested is what kind of strategy would work best, in the long run, with many different opponents. A selfish strategy, or an altruistic one.
I believe there is a game show in the UK that follows these same rules, but I don’t think it is as statistically relevant as this computer simulated tournament.

So which strategy do you think won? Selfish or altruistic? Which is better, look out for number one, or screw the other guy as often as possible?

The strategy that won, hands down, every single time, was a strategy called “tit for tat.” This strategy simply copied the last play made by your opponent. So if you met up with an opponent that played the altruism card last time, you’d play the altruism card in the current round. The reason this worked was that all the strategies that were based more on altruism, whenever they met a similar based strategy, they would quickly rack up points, as they would both play the altruism card most of the time. The tit for tat would just copy what it’s opponent did the last play, so it would play the altruism card most of the time with an altruistic opponent.

When the tit for tat strategy came up with a purely selfish opponent, neither of them would get any points, because the tit for tat would always copy the previous move of it’s opponent, which was always selfish.

The points accrued by two altruistic strategies when they met each other far out weighted the points lost when an altruistic strategy met a selfish strategy. Needless to say, whenever a selfish strategy met another selfish strategy, they didn’t get any points.

This computer simulated tournament was originally designed by evolutionists who wanted to see how altruistic strategies spring up in nature by organisms that are primarily selfish in nature. Like honey bees pollinating flowers in exchange for nectar, and monkeys that groom each other for no apparent reason. Somewhere, somehow, there is a payoff. And based on the computer simulation, you seem to get the most pay off with a “help the other guy out” mentality. While you might run into a few selfish people, you’ll more than make it up when you run into another like-minded “help the other guy out” strategist.

So anyway, I picked up that little book, which only cost fifty cents, and fit snugly into my backpack, and went pedaling off down the street, wondering what I would stumble upon next.