How Should We Face This Cruel World?

Click the image for details. Recently, I saw a very interesting question on Zhihu: There are 100 people in a room, each with 100 yuan, playing a game. In each round, everyone must give 1 yuan randomly to another person. What will the final wealth distribution be among these 100 people? Here are three different answers; please vote. We might as well regard this game as a simplified model of social wealth distribution, simulating the rules of the world. We assume: everyone starts the game at age 18 with an initial capital of 100 yuan, plays once a day, until retirement at 65. "Giving out 1 yuan daily" can be understood as basic daily consumption, and "the probability of gaining wealth is random" is to... well... simplify the model. Based on this, a person plays 17,000 games in a lifetime, i.e., gets 17,000 opportunities for wealth distribution. Now let's answer. Under the above rules, the result after 17,000 rounds is shown below: (Note: 1. In the figure, the horizontal axis labels represent player numbers, and the height changes of the bars reflect changes in that player's wealth. 2. When someone's wealth drops to 0, they do not need to give 1 yuan to others in that round, but they still have a chance to receive money from others.) It can be seen that each player's wealth fluctuates extremely sharply. To describe the overall wealth distribution of society, we also made the following chart sorted by wealth: (Note: In the figure, the horizontal axis labels represent player ranking (not number); the higher the ranking, the more wealth. Initially, everyone's wealth is equal, but as the game progresses, the wealth gap widens.) Yes, wealth distribution is close to a power-law distribution (the conclusion is from program simulation, not mathematical exact solution). In the end, society will have a few rich and many poor:

• The richest person's wealth is about 3.5 times the initial wealth;
• The top 10% rich hold about 30% of the wealth, and the top 20% hold about 50%; 60% of people's wealth will shrink to below 100 yuan. Thus, most people's money goes into the pockets of a few. Even under the fairest rules, the world still shows its cruel side. On this basis, we designed more scenarios and simulated them with programs. Will allowing debt make the world a bit better? In real society, the situation is more complex. For example, when we run out of money, we can borrow from relatives, banks, or investors, and maybe make a comeback. With debt allowed, the game results are as follows (sorted results): The results show:
• At the end of the game, the richest person's wealth is about 4 times the initial wealth;
• The top 10% rich hold about 33% of the wealth, and the top 20% hold about 56%; about 25% of people are in debt, with the highest debt around 200 yuan. Yes. Although debt can give us more leeway when we are desperate, it ultimately makes the poor poorer. Can the underdog really turn the tables? We use the standard deviation of all players' wealth to measure the degree of social wealth polarization, and plot it over time: (Note: The horizontal axis represents the number of game rounds, and the vertical axis represents the standard deviation of social wealth.) It can be seen that the standard deviation changes most drastically in the early game, but after 6000-6500 rounds, the change tends to level off, meaning the overall shape of social wealth distribution stabilizes. According to our set correspondence between game and life, the player's age is 35 at this time. This result tells us that before age 35, the gap between people has fully widened. Further, if a person goes bankrupt at 35, is there still a chance to turn around? In this simulation, 15 people were bankrupt (in debt) at the end of the 35th year, and their subsequent wealth and rankings are shown below: (Note: In the figure, red bars are players bankrupt at 35, green bars are other players. The height changes of red bars on the vertical axis indicate wealth changes, and position changes on the horizontal axis indicate ranking changes.) It can be seen that when these 15 people retire at 65, 7 are still bankrupt; 8 have paid off debts and accumulated wealth, but still far from the rich. It seems that with 35 as the boundary, although after bankruptcy there is still a 50% chance to return to ordinary life, it is quite difficult to achieve a comeback and become rich. So, get rich early; the underdog's comeback is more like a legend. What is the difference between rich second-generation and ordinary people? In real society, everyone's starting point is not the same. There are always rich second-generation or third-generation who have advantages at the start of the wealth game. This should also be considered in our model. To simplify calculations, we assume only two types of players: 90 ordinary players (same settings as above) + 10 rich second-generation players. The rich second-generation players have an initial wealth of 500 yuan, and in each round they need to give out 2 times the money, while their chance of gaining wealth is also 2 times that of ordinary people. The game results are as follows (sorted results): (Note: In the figure, red bars are rich second-generation players, green bars are ordinary players.) Although the distribution shape is basically consistent with the all-ordinary-player result: the top 10 and top 20 rich hold similar proportions of social wealth and debt, but looking closely, all of the top 5 rich and 7 of the top 10 rich are rich second-generation players. We selected 5 from the rich second-generation players (red lines) and 5 from ordinary players (green lines) and plotted their wealth changes: It can be seen that although there are "black sheep" among the rich second-generation, they still have a high probability of maintaining wealth at a high level. The rich second-generation and ordinary people live in two different worlds, with occasional intersections. Yes, ordinary people need extremely good luck to reach the same height as a prodigal rich second-generation. Will taxing the rich change wealth distribution? To ease the contradictions caused by wealth polarization, there are many transfer payment methods in real society, and taxation is one of them. In this round, players' initial wealth is 100 yuan, and in each round, the probability of gaining 1 yuan is equal. But if a selected player's wealth is above 200 yuan in that round, they only get 60% of the gain; the other 40% is equally distributed among all players with wealth below 0 yuan (equivalent to a minimum living allowance for the bankrupt). The simulation results are shown below: It can be seen that under the "tax + minimum living allowance" rule, social wealth distribution is still highly polarized, with the difference being that bankrupts are basically eliminated, and the rich are not as rich. Taxation can ease the polarization of the world, but it is not easy to change the cruel nature of the world (unless transfer payments are greatly strengthened). Will a hardworking life be better? Most of us do not have the luck to get rich overnight, nor a father with a fortune, nor are we willing to rely on minimum living allowances. To change our fate, we can only choose to work harder and strive for a better life. We assume each player's initial wealth is still 100 yuan, but 10 people work twice as hard, gaining a 1% competitive advantage, i.e., their probability of winning gains is 1% higher. What are the simulation results? (Note: In the figure, red bars are the harder-working players, green bars are ordinary players.) It can be seen that the overall distribution shape of social wealth has not changed. However, 9 of the 10 hardworking players entered the top 20 rich! Yes, although the most successful player may not be the hardest worker, most hardworking people do quite well. Thank this cruel world for leaving us a way out. Seeing this, I believe readers already have their own answer to the question: How should we face this cruel world? That is Work hard and persist Source: City Data Group (ID: metrodatateam) -END-