Posted by Gennao Sabbat.
Two days ago we played a game in class to demonstrate the prisoner's dilemma. I waited until the results were released today to verify my hypothesis before posting this. If you're unfamiliar with the prisoner's dilemma, you might pick up the idea from this post, and if not, look it up.
The game in this case is that there are two players, each with two cards: one red card and one black card. One round of this game consists of each player choosing red or black secretly, and then both show each other their choice, ending the round. If both players choose black, each player gets three points. If one player choose red and the other black, the player that chose red gets five points, and the other gets nothing. If both players choose red, each player gets one point.
The point of the game is to show that the way to get the most points is to play red such that your opponent gets nothing, but if both players play like that, both will do worse than if they had cooperated and both played black. In other words, the play that's best for all players is that both play black every time. Indeed, that's the point of the lecture that day, that cooperating is worth it in the long run.
In this particular game, the class was split up into twelve groups, and two groups were pinned against each other, making six pairs of groups. Each group was a player, and the winner was the highest score of the class. The winner got extra credit on the homework, and if multiple groups got the high score, all would receive extra credit. The game consisted of forty rounds. There are a couple ways to interpret strategies in this game, and I'll be discussing the one that I think is the most accurate and comprehensive.
As you can figure out, the highest cooperative score is 140 points for both players, playing black every time. Against this convention, playing red will get you a higher score in the short run, but it eliminates your trust with the other player that, as the results showed, was almost impossible to regain. Therefore, playing red is equivalent to starting a conflict, because if your opponent thinks you're going to leave them with zero points, there best play is to get at least one point by playing red themselves, and the final score will be much lower than 140.
The temptation is to cooperate until the last hand, and then play a red card, giving you a final score of 142. However, the other player knows this too, so they would do the same thing, giving you both a final score of 138, losing to the other cooperative groups in the class. This means that you'd have to play a red card in the second to last hand to gain back the advantage, but your opponent would know that too, leading you both to regression that would have you both playing red for most or all hands, putting you at a severe loss to the rest of the class.
Expressing this concept to the other team, I convinced them that if we played black every time, we would both get 140 points, and both likely get extra credit. They agreed and we began playing. Here's my grievance: the other team played red on the first round.
You may have figured out that the earlier you play a red card, the worse off you are (because it severs your trust with your opponent) and that playing red on the first hand is the absolute worst possible strategy in the game.
Predictably, the rest of the game we spent battling it out each hand, most of them red to red, but every time we tried to get them to cooperate again, they couldn't go more than three hands before reverting to their malevolent ways. The last fifteen rounds were almost completely red against red, and when our opponent figured out what a loss that was causing him, he offered a couple black cards, but it was too late, we couldn't trust him and thus had no choice but keep playing red.
I would later learn in the class discussion that their strategy was to play red the first hand or two, to gain an early advantage, and then we would cooperate for the rest of the game. Hearing that, one word came to mind to describe that strategy: stupid. Really, really stupid. That strategy is basically starting the conversation by saying, "We're going to win and your going to lose; if you could just go along with it, we'd appreciate it." Obviously, them playing red on the first hand puts us at a disadvantage, probably irrevocably, leaving us only with the power to make sure that they lose right along with us, and also leaving us with enough spite to do just that.
For anyone curious, three teams got 140 points, meaning that six groups -- half the class -- got extra credit, by sticking to the best cooperative strategy. Our team got 72, and our opponent team got 76. So congratulations, asshole, you beat us: hope it was worth it.
