A model of cultural evolution in the context of strategic conflict

TL;DR

This paper introduces a mathematical model of cultural evolution in strategic populations, combining individual learning, reproduction, and social transmission, described by a mean-field equation with proven well-posedness.

Contribution

It develops a novel mean-field model for cultural evolution in game-theoretic contexts, including rigorous analysis and illustrative examples.

Findings

Global well-posedness of the evolution equation established

Illustrative examples for classical games provided

Model captures dynamics of cultural trait distribution over time

Abstract

We consider a model of cultural evolution for a strategy selection in a population of individuals who interact in a game theoretic framework. The evolution combines individual learning of the environment (population strategy profile), reproduction, proportional to the success of the acquired knowledge, and social transmission of the knowledge to the next generation. A mean-field type equation is derived that describes the dynamics of the distribution of cultural traits, in terms of the rate of learning, the reproduction rate and population size. We establish global well-posedness of the initial-boundary value problem for this equation and give several examples that illustrate the process of the cultural evolution for some classical games.