The Iterated Prisoner’s Dilemma: Press-Dyson Interactive
The Game
In each round, each of us can choose to cooperate or to defect. We play repeated rounds. In each round:
- If we both cooperate, we both get 3 points.
- If you cooperate and I defect, I get 5 points and you get none.
- If you defect and I cooperate, you get 5 points and I get none.
- If we both defect, we both get 1 point.
In this game, I’ve decided I want your average score to be 2. You’ll see that, however you play, after a few hundred moves your average score will be approximately 2.
How does it work?
I am playing a very simple strategy in the game above. My play is based purely on how both of us played in the previous move:
- If you cooperated last time, then I cooperate with probability 2/3.
- If I cooperated and you defected, then this time I defect.
- If we both defected last time, I cooperate with probability 1/3.
These probabilities were obtained by deciding I wanted your average score to be 2, and solving equations [8] and [9] in Press and Dyson’s paper for a target score of 2.
Note
Although this strategy does belong to the new and interesting class of Press-Dyson strategies, it turns out that this particular type of Press-Dyson strategy (ones that force your opponent to have a particular fixed score, on average, however they play) was described earlier by Maarten C Boerlijst, Martin A Nowak and Karl Sigmund in their 1997 paper Equal Pay for All Prisoners.