This is a really elegant little paper.
Evolutionary model of iterated PD game.
Major assumptions:
1. A player's strategy is n, defined as the number of rounds he will cooperate before defecting.
2. An iterated game ends after either player defects.
3. Games last a maximum of N rounds.
If players reproduce purely, than the only ESS is always defect. To show this, imagine if everyone plays n. Then the best strategy is to play n – 1.
However, what now imagine that the average strategy is n, but there is variation around this. Since mutual cooperation is better than mutual defection, if there is Normal variance around this mean, then the optimal strategy can be larger than n (Fig. 1).
They ran simulation models with agents, and a mutation rate e. The probability of a parent with strategy n reproducing an offspring with strategy n was 1 - 2e, with mutation equally likely to produce n + 1 or n – 1. This mutation could maintain variation in the population, and a threshold value of e drove the population to cooperation (Fig 2a).
Other results:
- Variation could also be maintained by error in addition to mutation, and error lowered the threshold mutation rate (Fig 2b).
- Weaker selection on cooperation (the smaller effect payoffs had on reproduction rate) helped maintain variation, and so lowered the threshold mutation rate (Fig. 3a).
- The transition to cooperation is largely independent of the maximum number of games, N, provided N > 2 (Fig. 3b).
