Wealth Distribution Model

Abstract

Purpose of this project is to simulate money exchanges between people using a very simplified model that only takes into account random interactions. First, the study will address a fair game, i.e. a game in which every agent has the same probability of winning or losing as compared to the other one. Calling α the initial capital of each agent, this analysis will provide a theoretically predicted exponential trend with both parameters ≃ α−1. Unfortunately, this trend seems very unlikely. We’ll try to improve the model introducing the so-called preferential attachment, that means that the probability to win will be proportional to the amount of money possessed. This will provide a power trend with constant ≃ −2, that can be connected to a Zipf’s law, that most countries seem to follow. For last, we’ll try to expand again the model introducing a new parameter intended to represent the saving tendency of each agent. This will result in two main trends, one exponential on lower capitals and one power at higher capitals, in good agreement with real data.