Emergence and Evolution of Cooperation for Survival: A Continuous Time Model

Abstract

For a large homogeneous population, where individuals rely on the availability of a resource for survival, we introduce a continuous time model for the availability of the resource in time and for each individual. In this framework, cooperation is defined as a mutual insurance mechanism, aimed at covering shortages for group members. We explore essential questions regarding the importance of cooperation: what are the characteristics of populations where cooperation is valuable, versus individualist populations, where cooperation destroys value; how large should be the groups of cooperating entities? In order to answer the latter question, we first characterise the optimal cooperation, which maximises the expected lifetime of entities in the population. Secondly, we explore the same question using a non cooperative stochastic game. This allows to understand to what extent strategic cooperation leads to inefficiencies as compared with optimal cooperation. We complete the theoretical results by suggestive numerical approaches.