# Not Quite The Prisoners' Dilemma

I intend to run a simultion experiment with an adapted version of the prisoners' dilemma in order to try to establish which strategy for choosing between co-operation and defection is the most successful. While this will be by no means conclusive, it should offer some insight into what strategies are useful on the small scale; not extrapolating behaviour to a wide variety of 'games'.

Apologies to those who know nothing about game theory.

#### Prisoners' Dilemma

The payoff matrix is as follows:

 Co-operate Defect Co-operate (3,3) (0,5) Defect (5,0) (1,1)

#### Co-operation Game

The payoff matrix is as follows:

 Co-operate Defect Co-operate (8,8) (0,5) Defect (5,0) (1,1)

#### The Full Game

At each iteration the two players do not know which of the two games will be played, the prinosers' dilemma is chosen with probability r and the co-operation game chosen with probability (1-r). Success is measured in terms of total payoff over n games. There are three types of competition to test:

• Swiss Tournament: All plays all for n games.
• Knock-out: After each n games the worst performer is removed.
• 'Evolutionary': There are s duplications of each strategy. After each n games any players with a score less than k are removed.

The intention is to run each type of game with a range of values of r and see which strategies do well and which do not.

• The Naif: Will always co-operate.
• The B*stard: Will always defect.
• Optimistic Bayesian: Uses Bayesian learning about how likely the opponent is to defect, starting believing the opponent will co-operate. Backer: Queex
• Pessimistic Bayesian: Uses Bayesian learning about how likely the opponent is to defect, starting believing the opponent will defect. Backer: Queex
• Tit-for-tat optimist: Plays tit-for-tat starting with co-operation. Backer: dogster
• Tit-for-tat pessimist: Plays tit-for-tat starting with defection. Backer: dogster
• Unforgiving: Plays co-operation until the first defection, then plays defection forever.
• Flip-flop: Alternates co-operation and defection.
• 3 Co-op: Starts with three co-operation. If more than one defection was played, plays tit-for-tat until there are three consecutive co-operations, then starts again. Backer: formerly Lear
• Random: Randomly chooses to co-operate or defect with equal probability.

If you have any other candidates, please describe them below and I'll name you as backer.