Alexander Adamou, Ole Peters

Paper #: 15-07-028

The present study asks how cooperation and consequently structure can emerge in many different evolutionary contexts. Cooperation, here, is a persistent behavioural pattern of individual entities pooling and sharing resources. Examples are: individual cells forming multicellular systems whose various parts pool and share nutrients; pack animals pooling and sharing prey; families firms, or modern nation states pooling and sharing financial resources. In these examples, each atomistic decision, at a point in time, of the better-off entity to cooperate poses a puzzle: the better-off entity will book an immediate net loss – why should it cooperate? For each example, specific explanations have been put forward. Here we point out a very general mechanism – a sufficient null model – whereby cooperation can evolve. The mechanism is based the following insight: natural growth processes tend to be multiplicative. In multiplicative growth, ergodicity is broken in such a way that fluctuations have a net-negative effect on the time-average growth rate, although they have no effect on the growth rate of the ensemble average. Pooling and sharing resources reduces fluctuations, which leaves ensemble averages unchanged but – contrary to common perception – increases the time-average growth rate for each cooperator.