Retention of cultural identity in a swarm of diverse agents

Abstract

We propose a simple lattice model to understand the dynamics of culture retention over time. In this work, we represent the cultural identity as a set of zeroes and ones I_j = |I_1j , I_{2j ,} . . . , I_Lj i, with each I_lj representing the absence or presence of the cultural element l (e.g. customs, traditions) in an individual agent j or collectively (entire swarm of agents, when j = 0). We place ns agents in a lattice, each with an information set whose components are determined by an initial error rate q₀ common to all. The agents are allowed to move with global probability rate m and a global copy probability rate c (probability per iteration). We investigate the effects of m and c on the probability Φ(t) that the swarm still retains complete collective information (I_l = 1 ∀ l ∈ [1, L]) and the error rate q(t) at some generation t in the future.