Harsh environments and the evolution of multi-player cooperation.

The game-theoretic model in this paper provides micro-foundations for the effect a harsher environment on the probability of cooperation among multiple players. The harshness of the environment is alternatively measured by the degree of complementarity between the players' cooperative efforts in producing a public good, and by the number of attacks on an existing public good that the players can collectively defend, where it is shown that these two measures of the degree of adversity facing the players operate in a similar fashion. We show that the effect of the degree of adversity on the probability of cooperation is monotonous, and has an opposite sign for smaller and for larger cooperation costs. For intermediate cooperation costs, we show that the effect of a harsher environment on the probability of cooperation is hill-shaped.