Is population growth conducive to the sustainability of cooperation?

This paper asks whether population growth is conducive to the sustainability of cooperation. A simple model is developed in which farmers who live around a circular lake engage in trade with their adjacent neighbors. The payoffs from this activity are governed by a prisoner's dilemma rule of engagement. Every farmer has one son when the population is not growing, or two sons when it is growing. In the former case, the son takes over the farm when his father dies. In the latter case, one son stays on his father's farm, whereas the other son settles around another lake, along with the other sons of the other farmers. During his childhood, each son observes the strategies and the payoffs of his father and of the trading partners of his father, and imitates the most successful strategy when starting farming on his own. Then mutant defectors are introduced into an all-cooperator community. The defector strategy may spread. A comparison is drawn between the impact in terms of the sustainability of cooperation of the appearance of the mutants in a population that is not growing, and in one that is growing. It is shown that the ex-ante probability of sustaining the cooperation strategy is higher for a community that is growing than for a stagnant community.