An example that mixes the stock market, game theory and linear programing

Question

First of all i am not entirely sure if this is the correct place to discuss this problem but i shall give it a try.

I'm currently doing an assignment for a degree in Linear Programing. My objective was to apply game theory in the stock market and then solve it using tools from linear programing, and this is where i fing myself stuck because i am not to produce a good enough example and i cant find a good example either. Can someone help me?

My attempt: Retail trader vs Hedge funds

The ideia here is that the Hedge funds have such a big impact in a share price that we can consider that a Retail is playing against the Hedges funds.

Rules of the game:

• Both players must invest their money;
• The Reatil trader had the option to buy or short and the Hedge fund has the option to buy or to sell;
• Both players have acess to the ther player decision at the same time;
• If Retail trader decides to buy and the hedge fund buys too, then the Retail trader wins x;
• If the Retail trader decides to short and the hedge fund sell, then the Retail trader gains y;
• If the Retail trader decides to buy and the hedge fund sells, then the Retail trader loses z;
• If the Retail tradet decides to sell and the hedge fund buys, the Retail tradet loses z too;

We can construct the following table

\begin{align} &|Buys\:|Sells\:\:|\\ Buys&| \:\:\:x\frac14\:\:\:|-z\frac14 |\\ Shorts&|-z\frac14\:|\:\:\:\:y\:\:\:\:| \end{align}