Form of security with a potentially infinite amount of equity for a continous payout for game?
One &quot;natural&quot; approach would be to base the price on the expected discounted revenue stream. Writing $R_t$ as the (random) revenue in period $t$ of one share, this then would be:
$$
p_t = \mathbb{E}\left(\sum_{t = 0}^T \frac{R_t}{(1+r)^t}\right) = \sum_{t = 0}^T \frac{\mathbb{E}(R_t)}{(1+r)^t}.
$$
In addition, you might want to lower this price a bit, especially if the income stream is very volatile and if you would expect that individuals are risk averse.
One thing determine then is the rate $r$. Ideally, this should be set equal to the rate of return of a risk-free asset (if you have this in your game). If the game does not last very long, I guess setting $r = 0$ also makes sense.