Part I: Rational Cooperation in the Finitely Repeated Prisoner’s Dilemma

Rational Cooperation in the Finitely Repeated Prisoner’s Dilemma: Experimental Evidence

James Andreoni and John Miller

Economics Journal, Vol 103, 1993, pp 570-585

This article contains a lot, so like Weingast’s article, it will need to be split into multiple posts. Which reminds me to finish Part II of Weingast, but I got too excited with Constitutional Showdowns and such. At any rate, let’s look at altruism.

Preliminary thoughts:

Now, we are talking about a finitely repeated prisoner’s dilemma. That means we set a number, let’s say 100, of times that we will have the two players interact. Importantly, this means that people know when the last time they play will be. So, Round 100 (the 100th time they play) is going to be important to look at. Let’s start at the beginning though.

I think Round 1 is really the most important round. I think it would set the “tone” for how the whole interaction will go down. Intuitively, I think cooperation is only going to “work out” if both players cooperate on the first round. I think the following scenario is unlikely to ever happen:

Scenario 1

P1 D D D D D D D C C CCC
P2 D D D D D D D C C CCC
Round 1 2 3 4 5 6 7 8 9 10…

This is probably even less likely to ever happen:

Scenario 2

P1 D D D D D D D C C CCC
P2 D D C C C C C C C CCC
Round 1 2 3 4 5 6 7 8 9 10…

Again, not going to happen:

Scenario 3

P1 D D D D D D D C C CCC
P2 C C C C C C C C C CCC
Round 1 2 3 4 5 6 7 8 9 10…

There is a lot going on in all 3 examples, but all of them start off with not having a CC play on the first round.

In Scenario 1, once you are in a “Defect-Defect echo” it seems very unlikely you will ever (a) get out of it, (b) do so spontaneously on the same round. Remember the players still can’t directly talk to each other.

In Scenario 2, same DD echo for 2 rounds. Then P2 throws out a C in Round 3, maybe just to see how P1 will respond. That’s fine- P2 could just be reasonably testing the water, knowing that CC does better than DD (and hoping P1 knows the same). But, when P1 doesn’t return the C on the next turn, P2 is probably not going to keep giving P1 chances to cooperate. Even less likely is that P1 will suddenly have a change of heart on round 8 and reward P2 for their earlier cooperations.

Scenario 3 has all of those problems, and even more so, it is hard to imagine a long string of DC, DC, DC, DC, DC, with P2 getting taken advantage of for so long. I can’t imagine even the most forgiving, idealistic, selfless person would let someone take advantage of them 7 times. And, again, the person who would defect 7 times against 7 cooperates is unlikely to have a change of heart at Round 8.

But enough of my intuitive thoughts about iterated PDs. What’s this have to do with altruism or this article? I posited earlier that I think that any level of significant sustained cooperation is most likely (only possible?) to occur when you have CC on the first round. Otherwise chances seem low. So, the first round is huge!

When faced with a first round repeated PD what are you going to do? You need to think about what the other person is going to do. If you “know” (using the term lightly- it could be gossip you’ve heard about them) anything about the opponent you will try to “guess” what they will play and play accordingly.

{Super Rambling side note warning: But of course you are going to have to really be thinking about how you will play the whole 100 rounds. Maybe you think you will be playing against a sort of smart sucker. You will throw out D on the first turn and get the temptation payoff. It would be cool to keep getting the 12 every turn, but this person was maybe just naïve or idealistic and too trusting. But they aren’t going to be taken advantage of  the whole game. The first 0 they get will be a very sharp learning experience. So, now you should play a C to sort of apologize and get yourselves off on the right foot again. In Round 2, the other player is mad and throws out the D while you played your C. What!? Now you are mad. So mad that maybe you want to just go all Grim trigger and play straight D the rest of the game. Other considerations exist though- what is the “point” of this PD tournament? Is it for you to get more points that the other player? Is it for you to crush the other player at every turn? Is it to get as many points as you can, but not go out of your way to hurt the other player? Is it to get as many total points as possible for you and your “partner” combined? Is it to build a reputation as a cooperator? Is it to build a reputation as a cooperator so you can exploit that later by being the defector?}
 
 

What if I told you that you were playing against a college volleyball player? Or what about if I told you that you were going to playing against a singles tennis player? A doubles tennis player? A high school policy debater? A Lincoln Douglas debater? Mother Theresa? Scrooge McDuck?

What do those have to do with anything? Each of those activities or persons generally have some sort of socially constructed idea about altruistic or cooperative tendencies. Team sports players might be more likely to cooperate than individual sports players. Policy debaters have to work extremely closely with a partner for many months or years, whereas a Lincoln Douglas debater may have made the choice to work alone. Mother Theresa’s reputation is as an altruist, McDuck’s is as a…scrooge (but also a shrewd capitalist who could probably be convinced of the utility of CC versus DD).

Let’s bring it back to the paper. The authors are going to have real people play PDs. They are also going to manipulate the players’ beliefs about their opponent’s “type”. That type being “cooperative” (altruistic) or “competitive”.

We’ll end with listing off the three models of altruism, or the reasons why people might be inclined to cooperate, and in a later post look at the results of the study: (p. 572)

(i)                 Pure Altruism: Care directly about the payoff of the other player

(ii)               Duty altruism: Feel obligated to cooperate

(iii)             Reciprocal Altruism: Some special pleasure in successful cooperation

{Edit- I forgot! A special post coming Friday at around 11:00 a.m!}

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Posted on August 19, 2011, in Uncategorized and tagged , , , , , , , , , . Bookmark the permalink. 1 Comment.

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