In all versions of the game, roughly 60% of players started out co-operating. However, in the first two, this decreased over time as the pernicious influence of the freeloaders spread. The larger the fraction of a subject’s partners who defected in a given round, the less likely that person was to co-operate in the next—classical tit-for-tat. However, this tit-for-tat retaliation was not enough to save co-operation, and after a dozen rounds only 10-20% of the players were still willing to co-operate.
In the variant where participants had some choice over whom they interacted with, though, the amount of co-operation stayed stable as the rounds progressed. When Dr Christakis and his team looked at how the relationships between players were evolving in this third version, they found that connections between two co-operators were much more likely to be maintained than links that involved a defector. Over time, the co-operators accumulated more social connections than the defectors did.
Furthermore, as they were shunned, the defectors began to change their behaviour. A defector’s likelihood of switching to co-operation increased with the number of players who had broken links with him in the previous round. Unlike straightforward tit-for-tat, social retaliation was having a marked effect.