Work

Convergence of knowledge in a stochastic cultural evolution model with population structure, social learning and credibility biases

Year: 2020

Type: article

Abstract: Understanding how knowledge emerges and propagates within groups is crucial to explain the evolution of human populations. In this work, we introduce a mathematically oriented model that draws on individual-based approaches, inhomogeneous Markov chains and learning algorithms, such as those introduced in [F. Cucker and S. Smale, On the mathematical foundations of learning, Bull. Amer. Math. Soc. 39 (2002) 1–49; F. Cucker, S. Smale and D. X. Zhou, Modeling language evolution, Found. Comput. Math. 4 (2004) 315–343]. After deriving the model, we study some of its mathematical properties, and establish theoretical and quantitative results in a simplified case. Finally, we run numerical simulations to illustrate some properties of the model. Our main result is that, as time goes to infinity, individuals’ knowledge can converge to a common shared knowledge that was not present in the convex combination of initial individuals’ knowledge.

Source: Mathematical Models and Methods in Applied Sciences

DOI: 10.1142/s0218202520500529

Authors: Sylvain Billiard, Maxime Derex, Ludovic Maisonneuve, Thomas Rey