| Below is a repost, but fits very appropriately here, the results are very similar! The pdf pre-dates my small work on this, but you may find the simulation interesting, http://www.cs.toronto.edu/~arnold/research/80-20/ Basically you need two things: 1) Some slight advantage 2) The network effect, that is, for example, the probability of competing depends on the current winnings. (compare with the linked pdf, pg: 548
'Why do we call this a “rich-get-richer” rule? Because the probability that page L experiences an increase in popularity is directly proportional to
L’s current popularity.') 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. 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.More such comparisons can be found at http://www.cs.toronto.edu/~arnold/research/80-20/ 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. When I run this simulation, around 80-90% of top 20% actors lose all wealth in 3 generations. |