Mathematical Models of Cooperation, Consensus, and Collective Computation

Abstract

Social systems occur at all levels of biological organization. A full understanding of the evolution and maintenance of sociality requires that we study how groups can maintain cohesion, despite conflicts of interest between their members, and how collective phenomena emerge out of individuals' behaviors. In this thesis, I develop and study a set of mathematical models to answer these questions. Each model is inspired and grounded by a particular empirical system, but their generality allows me to identify common principles that underlie sociality across systems. First, by extending a standard model of indirect reciprocity, I find that cooperation can be maintained by discriminators that observe themselves more frequently than they observe other types of individuals, even if they have limited and imperfect information. Second, by studying a model of opinion dynamics driven by environmental information, I find that the evolutionarily stable strategy for gathering social information depends on the content of the information, and only when individuals are trying to learn about certain properties of the environment do they construct an optimal interaction network. Third, I develop a set of measures to quantify the degree of consensus in an interaction network about individuals' values. I find that a global property of the interaction network is informative about individuals' functions in three empirical systems: a subordination-signaling network in macaques, a physicist collaboration network, and a gene interaction network. Fourth, I use a model of stochastic decision-making to describe the development of the signaling network. I find that conflicts of interest can incentivize the group to make more accurate decisions and that the skewness of the distribution of power that emerges is most strongly affected by the costs of waiting for a decision. A similar stochastic model has previously been applied to neural decision-making, which suggests that there are common principles of collective computation across systems.