Game Theory and the Stock Market
The Nash Equilibrium & Its Stock Price
The article How to Exploit Game Theory for Profit by Aaron Brown makes a unique case for the benefits and disadvantages of using purely game theory to estimate stock purchases and growths. The author introduces the article by describing how game theory can be applied to the market. The article describes how given a simple example such as Company A has a stock for $50 and Company B has a stock for $20, then if Company A offers to give a share of their stock for every two shares of a Company T (target) traded in, B’s shareholders should accept, potentially raising B’s share price if we treat A’s target as B. This would theoretically raise B’s stock price. The author then goes on to mention that this ties into shorting and buying stock, allowing for a potential profit to be generated from interchanging shares using a basic payoff functionality. The simplicity comes from something called risk arbitrage, a state used to describe something without risk. Essentially this payoff functionality assumes no risk will be involved with the stock and simply established basic numbers to make options appealing. Brown then goes on to describe how the complexity for this problem would best be tackled by taking into account the potential decision makers and truly flushing out a game theory problem. Following game theory, we then take each decision maker, such as T’s stockholders, T’s board and management, and A’s management and figure out the decisions and the payoff values for them. This will allow us to find potential Nash Equilibriums and strict Nash Equilibriums within the matrix that can be used to guide decisions.
The second article The Nash equilibrium and it’s stock price by RiskWerk, delves more into a mathematical approach of a way to find a Nash equilibrium. This method involves the usage of trends and tracking stock’s bid and ask prices against each other to formulate the game. This method works by tracking the counter offers to the offers each investor would make, leading to a matrix of bid and ask prices forming the payoff factors for each set. The benefit to this method is that it is largely used to estimate your position agains other investors and can help predict what will happen in different situations based upon what payoff you would receive from what others could potentially do. Another benefit to this method described by RiskWerk is that it can also be tweaked to focus on the improvement of quantity, allowing for somebody to focus more on accumulating more stock rather than just a purely monetary increase.
Following our exploration into game theory and using Nash equilibrium to decide on optimum decisions, it is interesting to see it being played up to such a large economic scale such as the stock market. While using game theory generates a complicated set-up for this, it does reason that if successfully done, a person could use this model to generate a profit from a company and grow their own portfolio. For example, this could help somebody intelligently short/buy stocks in a pattern such that they are increasing their portfolio’s value over time without making completely randomized decisions. This is great because the model’s themselves do not have to be overly complicated to work properly, and in face game theory can benefit from a simplistic model rather than an overly populated one. This allows analysts to better estimate from limited data and help prevent risk and loss in portfolios.