7 ms·

It should. I suspect this sim is done wrong. If each round is independent and variance is constant the CLT should dominate.

PeterisP 4y ago
This sim is done quite right, with the key part of the article being "This model is the same as in the basic version, but includes basic economics, like debt (whithout interest) and investments that are proportional to the respective wealths of the spending and the receiving player" CLT dominates only if you do the sim wrong by making unrealistic simplifying assumptions (e.g. that each round is independent and variance is constant) that effectively eliminate the main parts of the simulated system and ensure that the simulation gets misleading results.
MontyCarloHall 4y ago
Edit: my post below is not true. The overall distribution is indeed close to Gaussian; see here: https://news.ycombinator.com/item?id=31861089 https://news.ycombinator.com/item?id=31861089 ******* The CLT simply says that the distribution of a sum of random variables will be Gaussian (as the number of random variables being summed tends to infinity). It is not obvious to me that the agent-level difference equations in this simulation would naturally lead to the overall distribution of wealth being a sum of random variables.
- Mattasher 4y ago
  The wealth each "person" has after N rounds is equal to N trials where the expectation is zero each time, and the rounds are independent, at least according to the setup described in the title and first paragraph.
  - MontyCarloHall 4y ago
    That determines the distribution for each individual, not necessarily the entire population. However, I think you are correct and I am wrong about the population level distribution; I wrote and ran the simulation myself and got a Gaussian-looking distribution at the population level.
mellavora 4y ago
Not if growth is cumulative/compounding. Central Limit Theorem assumes additive growth. Do some reading on geometric vs additive means, and on the log-normal distribution for finance.
Applejinx 4y ago
Oh, no, absolutely not. The sim is a proof that even in very primitive economic simulations, Central Limit Theorem absolutely does not apply. 'should' has nothing to do with it. It provably doesn't. Even in the absence of any complicating factors or considerations of value or merit.

PeterisP 4y ago

This sim is done quite right, with the key part of the article being "This model is the same as in the basic version, but includes basic economics, like debt (whithout interest) and investments that are proportional to the respective wealths of the spending and the receiving player" CLT dominates only if you do the sim wrong by making unrealistic simplifying assumptions (e.g. that each round is independent and variance is constant) that effectively eliminate the main parts of the simulated system and ensure that the simulation gets misleading results.

MontyCarloHall 4y ago

Edit: my post below is not true. The overall distribution is indeed close to Gaussian; see here: https://news.ycombinator.com/item?id=31861089 https://news.ycombinator.com/item?id=31861089 ******* The CLT simply says that the distribution of a sum of random variables will be Gaussian (as the number of random variables being summed tends to infinity). It is not obvious to me that the agent-level difference equations in this simulation would naturally lead to the overall distribution of wealth being a sum of random variables.

Mattasher 4y ago
The wealth each "person" has after N rounds is equal to N trials where the expectation is zero each time, and the rounds are independent, at least according to the setup described in the title and first paragraph.
- MontyCarloHall 4y ago
  That determines the distribution for each individual, not necessarily the entire population. However, I think you are correct and I am wrong about the population level distribution; I wrote and ran the simulation myself and got a Gaussian-looking distribution at the population level.

mellavora 4y ago

Not if growth is cumulative/compounding. Central Limit Theorem assumes additive growth. Do some reading on geometric vs additive means, and on the log-normal distribution for finance.

Applejinx 4y ago

Oh, no, absolutely not. The sim is a proof that even in very primitive economic simulations, Central Limit Theorem absolutely does not apply. 'should' has nothing to do with it. It provably doesn't. Even in the absence of any complicating factors or considerations of value or merit.