It’s not a question I ask often, but it crossed my mind the other day in my ECN 122 class as we were talking about The Prisoners’ Dilemma. For anyone not familiar with it, The Prisoners’ Dilemma is a classic game theory scenario that goes something like this:
Two suspects are brought in by the police because they are believed to be involved in a major crime. The police have enough evidence to convict them of a minor crime, but not enough to convict them for the major crime. The two suspects are held in separate cells and cannot communicate with each other. When each prisoner is questioned, he is told that he will be spending a year in prison for the minor crime. However, if he confesses that he and other suspect committed the major crime, the police will set him free and imprison his friend for twenty years. And if both prisoners confess, then they will both spend sixteen years in prison.
If you were in this situation, what would you do? It’s a very interesting case, from a game theory perspective. (You might have a different opinion of it if you were taking the ACLU’s perspective.)
In game theory, The Prisoners’ Dilemma is an example of a finite strategic game, which means that there’s a finite number of players, a finite number of actions available to each player, and a preference profile on the outcomes for each player. In this case, there’s two players, and they each have two actions available — confess or not confess.
Assuming that the players do not enjoy prison, they will prefer no prison time to one year in prison to sixteen years in prison to twenty years in prison. That means that they want to confess and have the other suspect not confess. But failing that, they would would neither to confess. Or at least both confess. But the worst possible outcome is to not confess and have the other suspect confess.
So in game theory, you’re supposed to look for a dominant action, or an action which gives you the best possible outcome no matter what the other player(s) do. In this case, the dominant action is to confess. If the other player doesn’t confess, confessing gives you a better outcome — going free versus a year in prison. If the other player does confess, confessing still gives you a better outcome — sixteen years in prison versus twenty years. But if both players play the dominant action, they would both get sixteen years… much worse than if they had just both cooperated and gotten one year each.
So… knowing all that, what would you do? When we played in class, David Y and I were paired up, and we both chose to not confess. It takes a certain amount of trust to do that, though. David Y said that if he was just paired up with some stranger in class, he definitely would have confessed.
I think in pure game theory, the concept is that in its simplest form you have no idea what the other player will do, nor do you have any idea of what any players ever have done in the past.
Personally, how I feel about the game is that, given both players are theoretically equal, they would both eventually come to the same line of thought, and the same conclusion. Given that, I assume both choices will be equal, and I think about which equal answers will give the best combo, which is obviously no confess-no confess.
However, if you say, “Well Jimmy, not everything thinks exactly like you”, it introduces outside variables into the game, which means the game is no longer played at its simplest form. I can only assume that every player thinks exactly like me, if I am a player.
My other understanding of game theory is that, if you’re applying it into a real world situation like class, then the dominant strategy is always shifting depending on the meta, and that the meta over time tends to be close to the equilibrium. If you’re doing it over one class period, I don’t think that gives nearly enough time for the meta to develop.
Yes, in this game, you have no idea what the other player will do, and you only play once. By allowing communication of any sort, or by playing multiple times, you’re changing conditions and possibly player preferences.
For instance, if we were playing multiple times and I had the chance to talk with you, I could say, “If you confess, I will ALWAYS confess in the future,” and that would probably strongly influence you to not confess.
We made a simulation of this in Psc something-or-other. It was fun to see how much the results changed when you made one little adjustment, like adding an obstacle or something.
Anyway, back to your question. I think most people will refuse to confess at first, but consider confessing when they get paranoid about the other person’s response.
The game is nice and all but it would have no outcome, so the game really means nothing. I think the professor should of made it an assignment or assigned points to it so there would be an outcome.
For instance: 10 points for both if no one confesses, 5 points for confessing and your partner doesn’t, and none if both confess. That would have made for a more real scenario, turning friends against friends.