This is a continuing part of my talent-luck simulator and a quest for a dramatic speedup (see link at end for details; I don't want to do a detailed intro each time). The standard model consists of static agent objects and mobile event objects. When then intersect, the event is said to occur - that is, agent's wealth either increases or decreases. Then the events are moved around by a fixed amount in a random direction, the timestep is increased, and so on until the end. The left hand plot shows the position of the event objects over time.
My idea for a faster method was to measure the mean and standard deviation of how frequently events occur and use this to generate a distribution of the number of agents who experience events at any moment. This distribution is well-approximated by a Gaussian so that seems reasonable. It also allows the same agent to experience multiple events per timestep, just as in the random walk method (with some subtleties).
So this sort-of works. It's is about 100 times faster than the random-walk method because instead of having to evaluate the exact separation of all agents from all events (though this can be significantly optimised), only the agents who experience events (typically around 40) have to be evaluated and the distance calculation isn't necessary. The basics come out the same, but it gives significantly different results to the random-walk : the final inequality and total wealth levels are significantly lower with the faster method. I've found that this is in excellent agreement with simply positioning the events at random locations for each timestep, which is shown in the right hand plot.
These two distributions are, of course, quite different. The random walk method produces a random spatial distribution of events each time, if you consider each timestep independently. The problem is that each timestep is not independent. The position of the events thus depends very strongly on where they were before : they are spatially random, but not temporally random. So - and here I'm speculating but only slightly - this means agents have a higher chance of multiple encounters with the same event, even though fewer events occur overall.
I haven't decided if I should call it quits and stick with the random walk method or not. There's nothing particularly special about either, except that the random walk was used in the original paper. It might be interesting to try and modify the faster method to give a closer agreement, perhaps by measuring the number of repeat events with the random walk, but I'm not sure it would be worth the effort.
So far I've found that :
- The original model shows that strong inequality can be due to luck more than talent. A Gaussian distribution of talent leads to a power law of wealth because of chance.
- ... but that's only because it minimises the role of talent. When talent is given a greater importance in determining what the events do, the same wealth distributions result but now there's a very clear correlation with talent and money. Again, a Gaussian distribution of talent leads to a power law of wealth even though talent is critical to success.
- The model is strongly dependent on the random walk method used.
As always, code and more details here :
https://repl.it/@RhysTaylor1/TalentVersusLuck
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