The impact of randomness on the distribution of wealth: Some economic aspects of the Wright–Fisher diffusion process

Nicolas Bouleau and Christophe Chorro

Physica A: Statistical Mechanics and its Applications, 2017, vol. 479, issue C, 379-395

Abstract: In this paper we consider some elementary and fair zero-sum games of chance in order to study the impact of random effects on the wealth distribution of N interacting players. Even if an exhaustive analytical study of such games between many players may be tricky, numerical experiments highlight interesting asymptotic properties. In particular, we emphasize that randomness plays a key role in concentrating wealth in the extreme, in the hands of a single player. From a mathematical perspective, we interestingly adopt some diffusion limits for small and high-frequency transactions which are otherwise extensively used in population genetics. Finally, the impact of small tax rates on the preceding dynamics is discussed for several regulation mechanisms. We show that taxation of income is not sufficient to overcome this extreme concentration process in contrast to the uniform taxation of capital which stabilizes the economy and prevents agents from being ruined.

Keywords: Wealth distribution; Fair zero-sum games; Wright–Fisher diffusions; Inequalities; Impact of modes of taxation (search for similar items in EconPapers)
JEL-codes: C32 C63 D31 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:479:y:2017:i:c:p:379-395

DOI: 10.1016/j.physa.2017.03.017

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