[arnold8020]

I was wondering about this in the context of the 80-20 rule, and believe I have a simple answer. Basically you need two things: 1) Some slight advantage 2) The network effect, that is, the probability of competing depends on the current winnings.

If you have these two things, you get 80-20 like distributions, you get the explanation for why winners keep winning. If you are interested, you can find my simulation and analysis at

http://www.cs.toronto.edu/~arnold/research/80-20/

Kind of shocking how well this works. The intuition is, why has coke won, well they had some initial advantage, and so they won a bit. Now that they have won a bit, they can finance themselves into more competition. For example, they can place themselves into more stores, into more restaurants etc. Now they get a chance to compete more.

[static_noise]

Your rules are basically "the winner takes it all in the long run". This is similar to reality but real actors can disappear. Individuals have a limited lifespan. Their offspring have slightly different abilities. Corporations/Nations/Organizations are run by individuals (chosen not randomly) and may face technological/political challenges but here it's not clear that these structures need to disappear.

Do you see a good way to factor in these things?

[arnold8020]

Interesting that you see it as 'winner takes all'. Wondering why you say that. The simulation can be run in various ways. When I run with rules:

r1) Actors have normally distributed abilities,

r2) Actors are chosen randomly based on current winnings, the more you have won, the more you compete,

r3) Winner of competition wins one point from the loser,

You get interesting results, for example, in the two columns below, the left is Household income in 1970 broken into quintiles. The right column is simulation results.

    4.1%                         6.7%

   10.8%                        11.5%

   17.4%                        16.0%

   24.5%                        23.3%

   43.3%                        45.6%

Interesting how well the top 3 or 4 quintiles match between the simulation and the real world data.

If you run the simulation with different rules, the real world quintiles do not match the simulation quintiles nearly as well. You can tweak the simulation to see this as well.

The simulation can be tweaked to handle cases such as inheritance, so an actor with different ability inherits the wealth of a past actor. It would be interesting to see how many generations it takes to loose the wealth to test the adage that wealthy families loose their wealth in 3 generations.

https://www.theglobeandmail.com/globe-investor/globe-wealth/...

Ill try it and get back to you.

[arnold8020]

I modified the simulation as follows:

I allowed it to evolve for a single generation, enough time for the top 20% of the population to have 80% of the wealth. I now choose a random sample from the top 20% of the population to follow, lets call them T20.

I now repeatedly

1) pass the wealth of all actors to actors with new, random abilities

2) let the new actors compete for a generation (the same number of competitions we used above)

Result: After 3 generations of steps 1 and 2 above, 80% of T20 has lost almost all their wealth, 10% has lost 75% of their wealth, 10% has done really well, growing it by a factor of 8, due to capable ancestors for three generations.

Amazing, it matches the statistics in https://www.theglobeandmail.com/globe-investor/globe-wealth/...