# Repeated Prisoner’s Dilemma Tournament

I have played this with my classes and although not in the CIE A2 syllabus, found it useful to go into greater detail as to the strategies available.

Robert Axelrod used an experimental method – the indefinitely repeated PD tournament – to investigate a series of questions: Can a cooperative strategy gain a foothold in a population of rational egoists? Can it survive better than its uncooperative rivals? Can it resist invasion and eventually dominate the system? Contestants submitted computer programs that select an action, Cooperate or Defect, in each round of the game, and each entry was matched against every other, itself, and a control, RANDOM.

Prisoner’s Dilemma in the classroom.

This game can be played over as many rounds as you wish and played between two players in the classroom environment. The pay offs shown – Win = 3 or 5, Lose = 0 or 1

Below shows the first 14 rounds of a 100 round PD game between John and Kate that includes the comments that were apparently written after each player had decided on strategy in that particular game, but before the other player’s choice was known.

Strategies – see below

• D (ALWAYS DEFECT): Defect on every move.
• C (ALWAYS COOPERATE): Cooperate on every move.
• T (GRIM – TRIGGER): Cooperate on the first move, then cooperate after the other cooperates. If the other defects, then defect forever.
• TFT (TIT FOR TAT) cooperates in the first round, and then does whatever the opponent did in the previous round.
• PAVLOV: 1st round, Cooperate. Thereafter if you win use the same action on next round. If you lose switch to the other action.

PAVLOV v M5. Time-average payoffs can be calculated because any pair will achieve cycles, since each player takes as input only the actions in the previous period. Here there is an average of 2 per player per cycle.