Eur. Phys. J. B 60, 241-246 (2007)
https://doi.org/10.1140/epjb/e2007-00338-5

Statistical equilibrium in simple exchange games II. The redistribution game

¹ IMEM-CNR, Physics Department, Genoa University, via Dodecaneso 33, 16146 Genoa, Italy
² Department of Advanced Sciences and Technology, Laboratory on Complex Systems, East Piedmont University, Via Bellini 25 g, 15100 Alessandria, Italy
³ Department of Aerospace Engineering, University of Naples “Federico II”, Piazzale Tecchio 80, 80125 Naples, Italy

Corresponding author: ^a garibaldi@fisica.unige.it

Received: 30 July 2007
Revised: 8 October 2007
Published online: 8 December 2007

Abstract

We propose a simple stochastic exchange game mimicking taxation and redistribution. There are g agents and n coins; taxation is modeled by randomly extracting some coins; then, these coins are redistributed to agents following Polya's scheme. The individual wealth equilibrium distribution for the resulting Markov chain is the multivariate symmetric Polya distribution. In the continuum limit, the wealth distribution converges to a Gamma distribution, whose form factor is just the initial redistribution weight. The relationship between this taxation-and-redistribution scheme and other simple conservative stochastic exchange games (such as the BDY game) is discussed.