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

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?
• No one keeps records or studies the trading of individual unit shares to the minutiae you've laid out in your framework since people buy shares in blocks, which are re-sold/traded on "day2" in many other possible combinations of smaller or bigger blocks. Even if you force such a microscopic analysis, you will likely not find anything meaningful as is the case with all stochastic and highly random phenomena in nature, having no implications on game participants' behavior whatsoever – develarist Nov 20 '20 at 2:26
• I think I know what you might be trying to get at, but the framework proposed right now is far too restrictive and needs to be developed more. Instead of thinking of distributions at individual share prices, just think about downloading stock price data over some given period, and estimating their probability distributions. If you don't already know, financial prices are non-stationary, so you might have to do what all of us have to do which is abandon the study of prices, and instead stare at return distributions. No, data providers do not do probability distributions. You do that yourself – develarist Nov 20 '20 at 2:37
• I don't see why you can't construct this with tick data, but you won't find enough data open-sourced; you will have to pay for it or record it yourself – amdopt Nov 20 '20 at 14:31
• @develarist I found this APP can get distribution infomation support.fututrade.com/hc/en-us/articles/… – maplemaple Dec 2 '20 at 0:04
• @amdopt I found this APP can get distribution infomation support.fututrade.com/hc/en-us/articles/… – maplemaple Dec 2 '20 at 0:05