Dragulescu-Yakovenko model: Boltzmann-Gibbs statistics emerge from random wealth exchange
Parameters
P(w) = (1/T)·exp(−w/T) (Boltzmann-Gibbs)
Gini = 1 − 2∫₀¹ L(x)dx
Gini = 0.000
Mean wealth T = 1.000
Steps: 0
Each step: two random agents exchange a random fraction ε of their combined wealth.
With λ=0 and no saving, the steady state is exactly exponential (Boltzmann-Gibbs).
Saving propensity λ shifts the distribution toward Gamma distributions.
A wealth tax redistributes and reduces the Gini coefficient.