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Following my post of yesterday evening, Alex (@AlexSablay) suggested me to look at the Boltzman-Gibbs distribution (e.g. in Yakovenko &#38; Rosser (2009)). There are indeed interesting ideas, and it looks it is more or less what we tried to do in our previous postAgain, I found that article hard to read, but at some point, it looks like they mention that the limiting distribution could be a discrete version that tends to the exponential distribution when the size of the population tends to infinity. Here we have 2000 people, so it should be possible to see it..If we go for 100,000 rounds, the range of wealth isso it is still hard to say about the upper bound... For the distribution of the wealth, at the end we obtain the following histogramand the empirical cumulative distribution function isHere the red line is the exponential distribution...So, indeed, it seems that there is a limiting distribution, and it is the exponential one... And the good thing with stable distributions is that they are some sort of fixed point : if we start with that distribution, we should not move (too much) from is. For instance, if we start with an exponential distributionx = rexp(n,1/init)x = x*init/mean(round(x))x = round(x)the range of the wealth remains very stableas well as the density (again, it is a (symmetric)-kernel based estimate, with a multiplicative bias in 0, and some negative values)If we plot Lorenz curve, we can see that inequalities do not change hereIn that case, it is well known that the Lorenz curve is [latex]u\mapsto u+(1-u)\log(1-u)[/latex] and Gini coefficient is exactly [latex]1/2[/latex].