Introduction
The Stock market has become much more accessible for small investors through the emergence of online trading. Investors use brokerage firms to purchase quantities of a single stock. There are some brokerage firms that provide little to no investment advice to the investor allowing for their own investment strategies, whereas other brokerage firms provide financial advice through commission with confidential strategies that are not disclosed to the public. That is why there are free commission brokers that allow investors to online trade independently and brokerage firms that take commission and do everything for you. Generally, there are two ways to analyze the stock market. The fundamental approach is to analyze the company’s intrinsic value and the technical approach is to study the historical trading activity of a company.
Motivation
Stock market investment is naturally expressed as a game where the players are brokerage firms, which independently develop investment strategies to attract the investors dollars. Strategies compete against each other in the marketplace and receive payoffs in the form of commission from the investor depending on how well they perform. In general, brokerage firms with poor strategies will lose investments as investors switch to better performing brokerage firms. Thus, stock market investment is essentially a zero-sum game.
Analysis
The game goes as follows, α and ω are brokerage firms. Each individual in the population of α and ω are provided $400 and will use their firm’s investment strategy over a 150 consecutive day period. The bank account balance of each individual in the α population was compared against 10 randomly chosen individuals from the ω population. The individual with the largest bank account wins.
Every time an individual wins against another individual in its tournament set, the winner gets 2% of the loser’s bank account balance. Hence, individuals get paid or have to pay every time they participate in a tournament. This payoff approach to conducting tournaments emulates real-world trading similarly to how commissions and fees are required in each transaction. Firms with lower bank accounts at the end of the trading period have poorer strategies and poor strategies cause investors to move their money elsewhere.
Table II shows the bank account balances for the top five and bottom five trading strategies after completing the 150 days of trading using the training database. Good performing strategies have a higher payoff by taking money out of the bank accounts of poorer performing strategies. This zero-sum game format matches how investors in the real world choose brokerage firms: firms with good strategies attract more investor’s dollars while firms with poorer strategies drive away investor’s dollars.
References
Greenwood, G. ., & Tymerski, R. (2008). A game-theoretical approach for designing market trading strategies. 2008 IEEE Symposium On Computational Intelligence and Games, 316–322. https://doi.org/10.1109/CIG.2008.5035656