How can I know the distribution of how many shares were bought in specific price?

Question

Given a stock and any time $t$, is there a way to find the distribution $f_t$ $$f_t: \text{price}\ p \rightarrow \text{in current time $t$, how many shares were bought in price $p$}$$

For example, a stock has 3 shares labeled as ($s1$, $s2$, $s3$).

In day1, ($s1$, $s2$, $s3$) are bought at price $\\\$1$, $f_{t_1}(1) = 3$ and all other $f_{t_1}(x) = 0$ for $x != 1$;

In day2, $s2$, $s3$ were sold at $\\\$2.5$, then $f_{t_2}(1) = 1$, $f_{t_2}(2.5) = 2$, $f_{t_2}(x) = 0$ for $x != 1, 2.5$;

I want to model stock as a game theory problem: every player as $(\text{number of shares}, \text{average cost})$ or $(0\ \text{shares})$, therefore given a specific player, its strategy will depend on personal state and the environment $f_t$ (encoding the information of all other players).

My questions:

1. Is there any terminology for this $f_t$? Or is there any research in this area? Thank you so much.
2. Where can I find the information of $f_t$ for a given stock? If there is no direct source, is there a way to derive this $f_t$ from open source?