A Retail Trader Versus Hedge Funds: A Proposed Payoff Matrix

Summary

The document sketches a two-player game between a retail trader and a hedge fund, framing their trading choices as a game-theory assignment to be expressed through linear programming. The retail trader can buy or short, while the fund can buy or sell. The proposed payoff table assigns gains when both choose the same direction and losses when they take opposing positions, using separate payoff amounts for the two aligned outcomes.

This is only an initial setup, not a solved model or a validated representation of market behavior. The stated rules say decisions are made simultaneously, yet also suggest each player can access the other’s decision at the same time, leaving the information structure unclear. The table’s payoff notation is also ambiguous, and it does not explain how price changes, investment size, or the opponent’s payoff are determined. No equilibrium analysis or linear-programming solution is provided.

Key ideas

• The proposed example models trading choices as a two-player game between a retail trader and a hedge fund.
• The retail trader chooses to buy or short, while the fund chooses to buy or sell.
• The payoff table assigns gains to matching directions and losses to opposing directions.
• The simultaneous-choice rules conflict with the suggestion that each player can see the other’s decision.
• The document provides no market model, equilibrium analysis, or linear-programming solution.

Tags

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


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












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}

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.