Pareto laws for agent-based wealth distribution models

Abstract

In this thesis, wealth distribution in a closed economic system is examined by studying the simple inclusion process (SIP). The simple inclusion process is a model coming from statistical physics that models the jumping of particles in a graph. In the model particles have attraction among each other and each site also has a characteristic attraction parameter, denoted by the variable α. We regard the simple inclusion process as an agent based model for the economy for which sites represent agents and the particles represent wealth transferring from agent to agent. For the model, invariant measures are found that represent possible long term distributions of wealth in the system. We extend the model by looking at α as a parameter drawn from its own underlying probability distribution, ψ(α). In the view of wealth distribution, α can be seen as the wealth attraction an agent has. We set out to look for conditions on the distribution of α for which we obtain asymptotic power law behaviour of the resulting wealth distribution. It is shown that if a higher-order moment of ψ(α) diverges, the resulting wealth distribution will have a weak asymptotic power law lower bound. By setting stricter conditions on the distribution of α, we obtain that the wealth distribution will be asymptotically equal to a power law.