# Bayesian Dynamics of Growth, Inequality, and Co-Adaptation in Noisy Environments

## Abstract

Adaptation is a fundamental mechanism of growth. Scientists have developed statistical models in numerous contexts to characterize growth and its emergent behaviors, such as inequality, competition, and cooperation. However, we still lack a general adaptive mechanism that explains the emergence of growth in uncertain environments, preventing systematic exploration of the origins of agent heterogeneities. In this talk, I demonstrate a theory of statistical growth among agents adapting to their environments. I show that the average growth rate of agents' resources is governed by the information they hold about their environment. It follows that the learning process can attenuate growth rate disparities, reducing inequality in the long run. Second, I show how groups that optimally combine complementary information about resources maximize their effective growth rate. I show that these advantages are quantified by the information synergy embedded in the conditional probability of environmental states given agentsâ€™ signals, such that groups with a greater diversity of signals maximize their collective information. Then, using simple, pairwise agent interactions, I show how agent preferences converge when driven by observation of each other's behaviors. These results demonstrateÂ how the formal properties of information underlie the statistical dynamics of many complex processes across biological and social phenomena. The talk concludes with an outlook on how machine learning methods can guide the development of mechanics for signal selection, partner selection, and learning under uncertainty to rewards.