Overview

In the mid-1990s, political scientist Robert Axelrod proposed a model of cultural dissemination, in which agents interact locally according to the principles of homophily and social influence, aiming to answer the question: 'If people interact with each other and, through interaction, become more similar, why are there cultural differences in our society?' Each agent is considered an element of a matrix and is modelled by a list of F cultural characteristics, each assuming q possible states. The initial cultural identities of each agent are defined randomly with equal probability for the q^F different identities. However, in the one-dimensional model with F=q=2, Monte Carlo simulations show convergence to monocultural configurations in about 30% of the initial condition choices, while the exact analytical results indicate that monocultural convergence should always occur. In this book, we show that the discrepancy between the simulations and the exact results occurs due to the non-commutativity of the thermodynamic limit, in which the size of the network tends to infinity, and the asymptotic time limit.

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