A Universal Lifetime Distribution for Multi-Species Systems

Lifetime distributions of social entities, such as enterprises, products, and media contents, are one of the fundamental statistics characterizing the social dynamics. To investigate the lifetime distribution of mutually interacting systems, simple models having a rule for additions and deletions of entities are investigated. We found a quite universal lifetime distribution for various kinds of inter-entity interactions, and it is well fitted by a stretched-exponential function with an exponent close to 1/2. We propose a "modified Red-Queen" hypothesis to explain this distribution. We also review empirical studies on the lifetime distribution of social entities, and discussed the applicability of the model.Comment: 10 pages, 6 figures, Proceedings of Social Modeling and Simulations + Econophysics Colloquium 201

Evolution of direct reciprocity in group-structured populations

People tend to have their social interactions with members of their owncommunity. Such group-structured interactions can have a profound impact on thebehaviors that evolve. Group structure affects the way people cooperate, andhow they reciprocate each other's cooperative actions. Past work has shown thatpopulation structure and reciprocity can both promote the evolution ofcooperation. Yet the impact of these mechanisms has been typically studied inisolation. In this work, we study how the two mechanisms interact. Using agame-theoretic model, we explore how people engage in reciprocal cooperation ingroup-structured populations, compared to well-mixed populations of equal size.To derive analytical results, we focus on two scenarios. In the first scenario,we assume a complete separation of time scales. Mutations are rare compared tobetween-group comparisons, which themselves are rare compared to within-groupcomparisons. In the second scenario, there is a partial separation of timescales, where mutations and between-group comparisons occur at a comparablerate. In both scenarios, we find that the effect of population structuredepends on the benefit of cooperation. When this benefit is small,group-structured populations are more cooperative. But when the benefit islarge, well-mixed populations result in more cooperation. Overall, our resultsreveal how group structure can sometimes enhance and sometimes suppress theevolution of cooperation.<br