Mathematical Modeling of the Stock Market

Game Theory is used on many occasions to help us understand interactions between decision-makers. The famous Nash equilibrium is a steady state in a model that shows the interaction of different players, in which no player can do better by choosing a different action if the actions of the other players do not change. These two concepts can be applied to numerous situations that vary in types of players, but for our research, we are focusing on businesses in the stock market. The main objective is to use Game Theory to analyze data collected from the stock market, model our findings, predict decisions made by businesses, and understand what scenarios will produce a stable stock market. We will provide a thorough analysis of the stock market behavior between the three leading competitors in technology: Apple, Microsoft, and Google. To begin, we will use the website Nasdaq, a detailed online record of the stock market, to record the daily price of stock and share volume for each company. We will analyze the trend of the data through statistical models and R, a popular programming language used in statistics. The findings from this analysis will be used to construct our Game Theory model, which we analyze through Nash equilibriums. As a result, we should be able to evaluate the stability of the stock market and discuss the relationships between our companies. More specifically, we expect to find the impact changes in the stock market have on each business and predict the behavior, or the best next move, they should have