The last plot isn't found in Pluchino. This shows show the wealth fraction of the 20% richest people varies as a function of time. While the 80:20 rule does emerge, it only happens in quite a narrow window. Had the simulation continued the wealth gap would have been more extreme.
For the slope of the wealth distribution I've taken the comparison figure from Pluchino's single run which has a slope of -1.27 but the slope of the line in mine is -1.33. This isn't a fit to the data, just a comparison with what Pluchino finds after 100 simulations.
Now I can start to see exactly how robust this result is. For example everyone starts with the same wealth, but this isn't realistic. The number of timesteps clearly plays a role and I suspect so too will the size of each timestep. The random walk method for encountering lucky events is completely arbitrary and deserves tinkering with. The assumption that talent can't help you alleviate bad luck is questionable at best, as is the assumption that talent plays no role in the magnitude of the benefit of lucky events. And of course there's no financial contribution directly related to talent here, it's all pure luck. Then there could be the issue of multiple generations and inheritance, etc. etc. etc.
Interesting! But I'm not sure if I have time to catch up.
ReplyDeleteI'm working on it very slowly and intermittently. The next stage is to tidy up the plots and make them look presentable.
ReplyDeleteNow I really need to look into this, because I've put a lot of thought into characterizing skill at games compared to "random" play (a random walk, or a mixed strategy). I think a useful measure of skill is how much a player can improve over random play. In Chess there is no randomness so all the variability in outcomes can be attributed to the skill of the players. In games with some randomness (like dice) then the player's skill only contributes to some of the variability.
ReplyDeleteI'll do some reading tonight! :-)