Game Theory and the Kingdom of God (A Quirky Series Installment), Part 10: "Nice Guys in a Darwinian World"

We are back to thinking about the Prisoner's Dilemma (PD).

Recall that in a single-move PD defection is the rational choice. Which is problematic in that mutual defection leads to a sub-optimal outcome. However, cooperation can emerge in what is called the "iterated Prisoner's Dilemma."

In an iterated PD you play the PD with your partner over and over. Cooperation can emerge in the iterated PD because if the players keep playing defection moves it gradually dawns on each of them that if they would cooperate then each would get a higher payoff. There is little risk in trying to cooperate in the iterated PD because if, after a period of mutual cooperation, your partner defects on you, hurting you for a turn, you can respond/retaliate by returning to mutual defection on the next move. Again, this brings both you and your partner back to the sub-optimal outcome of mutual defection. So, opportunistically defecting on a partner whom you will have to play with again on the next turn tends to not pay off in the long run. It is better to just stick with cooperation.

In real life we see the iterated PD at work all the time. We rarely defect on people if we are going to see them again tomorrow. The repeated contact and the concern over retaliation makes most of us cooperative. Thus, defection tends to only emerge when we are not planning to ever see this person again. In one-time anonymous interactions, defection is a real problem. But we don't fear defection from people we regularly associate with. We don't defect on these people because we don't want to "burn a bridge." The point being that we will have future interactions with these people and we want them in a cooperative mood when we see them again.

I'm discussing the iterated PD because I want to talk today about a famous PD tournament conducted by Robert Axelrod. You can read Axelrod's account in his book The Evolution of Cooperation.

Here's what Axelrod did. He invited all kinds of people to submit a computer program that would play other programs in an iterated PD. In the computer tournament all the programs would play each other with point totals added up from each round (the payoffs were: Temptation to Defect = +5, Payoff for Mutual Cooperation = +3, Payoff for Mutual Defection = +1, and the Sucker's Payoff = 0; see my Risk post to get clear on this if you are new to this series).

After pitting the programs against each other in a kind of Darwinian environment, where the programs were competing against each other to gain the highest point total, a very curious winner emerged.

The winner was a now famous program called Tit for Tat (henceforth TFT). Interestingly, TFT was the shortest (as in computer code) and simplest (as in strategy) program submitted. TFT's program simply did this:

1. Cooperate on the first move.
2. Copy what your partner/opponent did on the prior move.

That's it. That's the Tit for Tat strategy. To be clear, imagine TFT is playing a program called, creatively, "Program." Here is how TFT would play.

Move 1: TFT plays "Cooperate"; Program plays "Cooperate"
Cumulative Payoffs after Move 1: TFT = +3; Program = +3 (these are the payoffs for mutual cooperation)

Move 2: TFT plays "Cooperate" (because Program cooperated on Move 1); Program plays "Defect"
Cumulative Payoffs after Move 2: TFT = +3 (TFT got the sucker's payoff at move two so +3 from Move 1 plus 0 at Move 2 keeps TFT at +3); Program = +8 (Program got +3 on Move 1 and +5 on Move 2 for collecting the Temptation to Defect payoff)

Move 3: TFT plays "Defect" (because Program defected on the prior move); Program plays "Defect"
Cumulative Playoffs after Move 3: TFT = +4; Program = +9 (both get +1 to their totals for the Payoff for Mutual Defection)

And so on. You get the idea of of TFT's strategy.

Amazingly, this simple little program won the whole tournament. That is, its cumulative total from all rounds was higher than any other submitted program. But here is the interesting part. Axelrod when back and classified all the submitted programs, noting qualities of each program's strategy. Here is how TFT was classified:

TFT was a NICE program: Programs were "nice" if they showed a bias toward cooperation AND were never the first to defect. Notice, TFT is biased toward cooperation (its first move is to cooperate) and it will never move off that cooperative move unless YOU defect first. TFT will never stab you in the back. It wants to play nice.

TFT was an UNENVIOUS/UNCOMPETITIVE program: Notice, if you look at the logic of TFT, TFT could never "win" a head's up match. The best it can do is tie you. TFT won the overall title without winning a single individual round. Only its cumulative total was higher. Interestingly, TFT won it all without trying to beat anyone.

Finally, TFT was FORGIVING: If you defect on TFT, TFT will protect itself by defecting on you the next move. But, if you return to cooperation, TFT will follow. It will "forgive" you and return to cooperation. TFT will give you a second chance (and a third, and a fourth, etc.)

I want to reflect on this outcome more next week. But let me just leave you with this amazing conclusion. The reason why Axelrod's tournament and TFT are famous is this:

In a Darwinian competition the nice guy won.

Think about that: A nice, unenvious, forgiving strategy won the tournament. It was the Darwinian victor. In the "survival of the fittest," as defined by the rules of Axelrod's game, niceness was most "fit," niceness was "strongest."

A nice guy finished first.

Now that is something to think about...

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One thought on “Game Theory and the Kingdom of God (A Quirky Series Installment), Part 10: "Nice Guys in a Darwinian World"”

  1. Of course, "nice" is relative. One basis for the strategy of mutual assured destruction when it came to nuclear war was the correctness of tit-for-tat as a strategy. If your opponent's not nice, TFT isn't nice at all. It's ruthless.

    Someone might interpret Jesus as saying you never should punish your opponent because of your opponent's evil. I don't believe that. I know the math. TFT is the way if the game you're playing makes it the way. Of course if God says I should let them kill me, I know I'd ask Him if He means it, but it does change the game quite a bit.

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