Prisoners’ Dilemma

0

Today, in my first Social Gaming lecture, I found myself thinking about Game Theory, specifically the Prisoners’ Dilemma, and how to translate this into an actual game. For those of you, who aren’t familiar with this gedankenexperiment, I will outline it in a few sentences, the others can safely skip the following paragraph.

The basic idea is that you have two prisoners, A and B. The two of them committed a crime together, but you cannot exactly prove it. Both of them get the same deal: rat out on the other and go free, the other gets to serve three years in prison. If both talk, both get a two year sentence, if both keep their mouths shut, both will get one year. They are held separate from each other and have no means to communicate. Now, while it would be more beneficial for them collectively to keep silent, each individually would always benefit from betraying the other, resulting in a higher penalty for both of them, than they would have to serve, if they cooperated.

But the Prisoners’ Dilemma is basically a ‘solved’ problem. There is a really simple optimal strategy, betray the other, and thus this would not make for an interesting game. So I modified a bit and set some constraints that the rules would have to ┬ásatisfy. Firstly, betrayal must not always be the better strategy. Its consequence has to be either good or bad depending on which strategy the other player adopts. So if one player choses to cooperate, it should be beneficial for the other not to, and vice versa. Secondly, cooperation should have the bigger collective gain, while betrayal should have a higher personal gain, but at a higher risk. Cooperation must also have a certain risk, albeit a smaller one compared to betrayal. These rules should make the game quite interesting, further modification would require some testing.

The game I came up with is really simple. You have a single button that you can press, if you elect to do so. You are connected to a random person to play with (or against). You don’t know anything about your ‘opponent’, not the name, age or sex, not even his current score. Each round takes 15 seconds and in that time you can press the button, or pass on doing so. After the time has run out, you get points (or lose them) and are connected to the next randomly chosen player.

The rules are also very simple:

  • if Player A presses the button and player B doesn’t, B gets 2 points, A loses 2
  • if neither preses the button, both lose 1 point
  • if both press the button, both get 3 points

This way there is no pure strategy Nash Equilibrium. Player A’s optimal strategy is depending on Player B’s choice, and vice versa. Cooperating is still better than Defecting, if both do it, but if one betrays the other, the best thing would be to also betray.

Now all that is left (besides actually implementing the thing) is giving it a name. I think I’ll simply call it Dilemma.

Comments

Your email address will not be published. Required fields are marked *