It should be fairly anti-symmetric, since the dynamics of losing are similar to those of winning. So instead of exponential looking, it's shaped like exp(rank) - exp(-rank). (just confirmed this with a quick simulation)

With participants able to go into debt indefinitely, the process becomes a random walk.

The result should be each participant being up or down from 0 at a rate of proportionated sqrt of t, the number of iterations of the system. Implying a wealth distribution which would become ever-more skewed over time.

Is that what "skewed" means? To my mind a widening bell curve which remained symmetric (which is what we're talking about, right?) would not be "skewed".

Over time, the average participant would have either far more coins in credit than they began with or be in debt for far more coins than they started with.

Whether you have what statistician call "skewed" or not, you have what most people would call skewed, unequal, extreme.

"Varied" or "widely distributed" seem like better terms. To my mind, "skew" is what we have in the original problem (with a zero-bound) - it only describes asymmetric distributions.

Removing the boundary doesn't really make sense -- if you allow people to go into negative dollars but still be able to give a dollar each tick, then there's no longer a finite amount of money in the system.

Sure there is, it's just effectively a zero interest debt instrument. Imagine that everyone is exchanging IOUs, instead of physical dollars.

You misunderstand. The parent meant that the amount is infinite, so the property that eventually every state will happen is no longer there.

Wow, a mathematical explanation of how uncapped debt reduces wealth mobility.

You're kidding, right? No way a generic observation about a markov chain (which doesn't even model interest) implies that "uncapped debt reduces wealth mobility".

So, with typical debt, interest rates are higher for debt than for savings. Does seem that a) removing the cap, and b) introducing interest on savings < debt would trap some people in poverty?

IOUs are money, in a model this simple.