Statistical equilibrium in simple exchange games II. the redistribution game

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.