Game Theory and the Stock Market

Game theory, the study of rational beings interacting in situations having a linkage is often thought to be an independent niche that economists and psychologists study. This often involves taking strategic decisions for oneself while being mindful of the options available at hand and the possible decisions that others might take. We see that such scenarios arise in another established system, the stock market. However, we are yet to see how far it is inter-related.


As individual investors, some aspects of the game theory could be applied while participating in the stock market. Technical analysis is used to evaluate price movements and observe patterns based on statistical historic data to find trading opportunities in the market. Equity analysts don’t limit their research to the technical or the fundamental analysis however, retail investors often take short term decisions based on such patterns. When retail investors are put against large institutional investors, the expected returns for the individuals depends on the decisions made by a large number of players in the market.


Just like the possibilities table constructed in the game theory, the stock market will involve sell/buy calls between the retail players and the equity research firms/banks. The individuals make a call based on the expected values they earn/lose when all the possibilities are considered, bearing in mind the price movements based on such decisions. This explains how ‘GameStop’ prices short squeezed and increased exponentially in a short amount of time; a large number of retail investors when made decisions in unison were able to inflate the price of a fundamentally weak company, causing volatile changes in the market.


The Zero-Sum postulate in game theory explains the phenomenon in which the net change in the benefits or wealth of all the players in the market sums up to zero. The ‘futures and options’ market is often considered to be the outcome of this theory, as one investor’s loss is another investor’s gain. However, investing on a long-term basis results in a ‘positive sum’ or a ‘negative sum’ phenomenon, allowing for wealth accumulation and subsequent improvement in future production, savings and investments. This means that all the market players could be ‘winners’ or ‘losers’ in the long run.


Intra-day trading on the other hand is to a large extent, a ‘zero-sum’ game. Everyone wants to buy a rising stock before everybody else, a key aspect of decision making in the game theory. The payment of GST, brokerage and securities transaction charges add to the losses of individuals, taking it further away from being a ‘zero-sum’ game.


Traders believe that in order to make the best use of game theory, they need to decipher what the ‘dominant strategy’ in the stock market could be for them. A ‘dominant strategy’ is one that leads to the highest payoff accounting for all other possible decisions that a player could make. This however is never possible, just like how a ‘nash equilibrium’ point is not seen in the stock market (a ‘nash equilibrium’ point is where the players wouldn’t want to change their decisions as their outcome will not be affected by the other party’s decision at that point). Hence, we find a greater degree of volatility and uncertainty in the stock market, even during a short period of six months.


The stock market may not completely fit the game theory narrative, however there are certain strategies that the traders must be aware of to survive this game. A ‘sentiment game’ is played in the stock market, with information available to the public being a key factor that affects trades. When an institution such as Eqwires research analyst posts information for the public, all investors know that the information is available to all other investors. Even though a certain trader may not necessarily agree with the analysis, they’ll have to go ahead with the larger market sentiment at least in the short-run period.


All of this can be narrowed down to the ability to gather signals and market information while anticipating and assimilating decisions other players in the market will take. While the stock market doesn’t exactly fit in the game theory definition, an investor can build ‘dominant strategies’ to make a marginally larger amount of profit than the other investors or reduce the losses on their bets.


References:

- https://www.investopedia.com/terms/z/zero-sumgame.asp

- https://medium.com/swlh/an-informational-introduction-to-game-theory-and-the-stock-market-1b97d6a7b30d

- Game theory models in finance (Franklin Allen and Stephen Morris)

- https://www.investopedia.com/articles/investing/111113/advanced-game-theory-strategies-decisionmaking.asp

- https://www.businessinsider.com/ben-hunt-on-the-sentiment-game-2013-11?IR=T

- https://www.csse.uwa.edu.au/cig08/Proceedings/papers/8011.pdf