Convergence of knowledge in a stochastic cultural evolution model with population structure, social learning and credibility biases. (English) Zbl 1462.91016
Summary: 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, Bull. Am. Math. Soc., New Ser. 39, No. 1, 1–49 (2002; Zbl 0983.68162); F. Cucker et al., Found. Comput. Math. 4, No. 3, 315–343 (2004; Zbl 1083.68131)].
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.
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.
MSC:
| 91D10 | Models of societies, social and urban evolution |
| 91D15 | Social learning |
| 60G99 | Stochastic processes |
Keywords:
individual-based model; inhomogeneous Markov chains; convergence to equilibrium; numerical simulations; concentration inequalities; cultural evolution; language evolution; cumulative cultureSoftware:
BoidsReferences:
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