# 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**.

- Fixed score
- Extortion
- Generous

This is possibly the strategy that slightly bettered generous Tit for Tat in Stewart and Plotkin’s simulation. It is fair in the sense that if you always cooperate then I will too. It is a self-sacrificing strategy: if you do *not* always cooperate I will do worse than you. In fact on average I lose precisely twice as much as you: if your average score is less than 3, mine will be less by as much again.

## How does it work?

My play is based purely on how both of us played in the previous move:

- If we both cooperated last time, then I cooperate.
- If I cheated you last time (you cooperated and I defected), then I cooperate with probability 8/10.
- If you cheated me last time (I cooperated and you defected), then I cooperate with probability 3/10.
- If we both defected last time, I cooperate with probability 2/10.

These probabilities were chosen to establish the relation *S _{X}* − 2

*S*+ 3 = 0 using Press and Dyson’s results, where

_{Y}*S*is my score and

_{X}*S*is yours.

_{Y}This may or may not be the same as the strategy called ZDGTFT-2 by Stewart and Plotkin. Unfortunately they don’t describe their strategy explicitly, only saying that it satisfies the relation above; but there are infinitely many such strategies.