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,<p><a href="http://www.cs.toronto.edu/~arnold/research/80-20/" rel="nofollow">http://www.cs.toronto.edu/~arnold/research/80-20/</a><p>Basically you need two things:<p>1) Some slight advantage<p>2) The network effect, that is, for example, the probability of competing depends on the current winnings.<p>(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.')<p>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<p><a href="http://www.cs.toronto.edu/~arnold/research/80-20/" rel="nofollow">http://www.cs.toronto.edu/~arnold/research/80-20/</a><p>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:<p>r1) Actors have normally distributed abilities,<p>r2) Actors are chosen randomly based on current winnings, the more you have won, the more you compete,<p>r3) Winner of competition wins one point from the loser,<p>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.<p><pre><code> 4.1% 6.7%
10.8% 11.5%
17.4% 16.0%
24.5% 23.3%
43.3% 45.6%
</code></pre>
Interesting how well the top 3 or 4 quintiles match between the simulation and the real world data.<p>More such comparisons can be found at <a href="http://www.cs.toronto.edu/~arnold/research/80-20/" rel="nofollow">http://www.cs.toronto.edu/~arnold/research/80-20/</a><p>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.<p>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.