Wealth distribution simulation experiment
A very interesting simulation experiment on wealth distribution.
The experiment goes like this:
There were 100 people in the room, each with $100, and they were playing a game.
In each round of the game, everyone has to take out a dollar and randomly give it to another person, what is the wealth distribution of the last 100 people?
Here are three different answers, guess which one?
We might as well think of this game as a simplified model of the distribution of wealth in society, thus simulating the laws of the world.
Hypothesis: Everyone starts playing the game at the age of 18 with an initial capital of $100, once a day, until retirement at age 65.
"Taking out a dollar a day" can be understood as a basic daily consumption, and "the probability of acquiring wealth is random" in order to... Simplify the model.
Based on this calculation, people play 17,000 games in their lifetime, that is, they get 17,000 opportunities to distribute wealth.
Under the above rules, the result of the game running 17000 times is shown in the following figure:
When someone's wealth value drops to 0 yuan, he does not need to give 1 yuan to others in that round, but still has the opportunity to get the money given by others.
The horizontal axis label in the image above represents the player's sort, and the higher the sort, the more wealth there is.
Initially, everyone's wealth value is equal, and as the game progresses, the wealth value gap becomes wider and wider.
If indebtedness is allowed, that is, you can borrow money from friends, relatives, banks, investors, etc., the chart will become the following pattern:
Yes, with or without allowing indebtedness, the distribution of wealth is close to a power law distribution:
- The wealth value of the richest person is about 4 times the initial wealth;
- The top 10% of the wealthy own about 33% of the wealth;
- The top 20% of the wealthy own about 56% of the wealth;
- About 25% of the people are saddled with debt, with the maximum debt being about 200 yuan;
In this way, most people's money ran into the pockets of a small number of people.
Even under the fairest rules, the world is still showing its cruel side.
Borrowing, while giving us more leeway when we are desperate, can ultimately make the poor poorer.
Will the rich second generation take advantage of the average player?
In the real world, there are always some rich second generations and rich third generations, who take advantage of the wealth game at the beginning.
This should also be taken into account in our model.
To simplify the calculation, suppose there are only two types of players: 90 regular players + 10 rich second-generation players.
The initial wealth of the rich second generation player is 500 yuan. The result of the game is shown in the following figure (the red pillar is for the rich second generation player, and the green column is for the normal player):
Although this distribution pattern is basically the same as the result of all ordinary players, on closer inspection, 7 of the top 10 are rich second generation, and top 5 are all rich second generation.
Although there are also "losers" among the rich second generation players, they still have a high probability of maintaining their wealth value at a high level.
The rich second generation and ordinary people live in two worlds, and occasionally intersect.
Yes, ordinary people need excellent luck to reach the same heights as the second generation of the losers.
What can you do if you want to change your destiny?
Again, it's that mathematical model, now suppose that the initial wealth per player is still $100, but 10 people are doubly hard, hard working, and studying harder than others, thus gaining a 1% competitive advantage.
That is, the probability of winning the profit is 1% higher than others, what will the simulation result be? (The red pillar is for the harder player, and the green pillar is for the normal player.) ）
It can be seen that there has been no change in the overall distribution of social wealth.
However, 9 out of 10 hard-working players have made it into the rich top 20!
As long as you work harder than others, you may be able to fight a story of Jedi Strikes Back.
Thanks to this cruel world there is still a way to live.
Effort is not the point,
And it's not hard to make an effort,
Who hasn't tried?
But why are so many people,
So far from success?