Talent-luck : changing the starting distributions

Talent versus luck : the story continues...

I added a couple of new sections, hope the links work, let's see..
https://docs.google.com/document/d/1TD1PCW1IG2BlBQ27GPe5Nqi5phjg4qXwhpgEfJAgbBw/edit#heading=h.oa3a1zrn8fhn

https://docs.google.com/document/d/1TD1PCW1IG2BlBQ27GPe5Nqi5phjg4qXwhpgEfJAgbBw/edit#heading=h.1rdxtmtmxpl4

(They do, but give it a second to load properly)

So far I've tried adjusting the effects of talent, the movement of the events, and the initial distribution of talent. All of these turn out to be rather important, and unlike the original claims, it can be shown that a Gaussian distribution of talent can transform into a power law distribution of wealth. I wondered just how strong this could be, if it could overcome initial disadvantages from an unfair wealth distribution. Thus far the wealth has always been initially uniform, so here I tried using an initial power law.

Admittedly I did this in a lazy and somewhat contrived way. I let the simulation run once, then reset the counter, move the agents to new random positions and run it again. As found at great length, the positions do matter : the random walk of the events meant that repeat encounters with the same events can be very significant. So moving the agents puts them in entirely new locations far from the places where fortunes were won and lost. However, any subtle trends between talent and wealth (which are present, albeit weakly) are likely to continue to be enhanced.

What happens is the agents who finish the first run as very wealthy continue to amass even more wealth. The most talented agents show a lot more fluctuation. But this doesn't seem to be due to resetting their position : the same thing happens if the standard conditions are used but allowed to run for longer. I think this is because the chance of multiple repeat encounters (which can have dramatic effects) is just low enough that they're unlikely to happen during the standard 80 timesteps but fairly probable over 160. Individuals who have much higher wealth than the rest become more probable the longer the simulation goes on, and they can dominate the end results.

More interesting might be to start with a wealth distribution that's completely "wrong", that is, give most of the money to the stupid people and start with the geniuses in poverty. It would be fun to see if altering the effects of talent can be sufficient to overcome initial disadvantages.

In the second new section, I tried allowing talent to control the reward/loss level of events, rather than the levels being fixed at doubling or halving wealth as before. Now agents can only double their wealth if their talent is maximum (1.0) and only halve it if it's zero. This gives the most talented people a much greater share of the wealth, despite, quite interestingly, there still being no obvious trend in the talent-money plot (which now has a weird fan-shaped structure which for some reason I found absurd).

Next up I think will be to allow talent to vary, i.e. agents to gain the benefit of experience.