[aleph_minus_one]

> create a dynamical system model/game-theoretic mode, and try to prove that in the long run everyone doesn't end up broke or a millionaire.

Simply ask yourself which factors in the real world lead or don't lead (depending on your political stance) to this outcome, and you likely have found the relevant factors that you have to include.

[ViscountPenguin]

To be fair, the velocity of money can be be significantly higher in a video game, and you're much less likely to have innovations reshuffling the market. It seems inevitable that extremal states would be more prevalent than real life.

[aleph_minus_one]

With the point "the velocity of money can be be significantly higher in a video game" you actually outlined a serious problem (and a potential solution):

The rest of the in-game economy (including its pricing) doesn't fit the money circulation velocity, thus we get problems.

The famous equation of exchange

> https://en.wikipedia.org/wiki/Equation_of_exchange

gives a rule of thumb how other factors of the in-game economy need to be adjusted if the velocity of money is increased.