Game theory has various applications related to economics. There are many popular concepts in game theory that we might have heard about before, such as the Nash equilibrium.
Today, many of us have tried investing into trading markets, such as the stock market, futures market and options market. We may or may not truly understand the market operation rule but it is well known that the market price to a great extend depends on the demand and supply. Also, the market is relatively stable, and the market price will be kept in an equilibrium unless some big news comes out and consequently the price fluctuates and finally hits a new balance. How does the market keep the balance? One of the tools used is the order book, which is an electronic list of buying and selling orders. Investors will send electronic messages to the order book. The messages will contain a side (“buy” or “sell”), a price and a quantity. There is a matching engine in the order book, and if a new order matches the order book, the transaction will take place. All the orders in the order book are pending orders, which means that investors can withdraw the order at any time before the transaction happens. In finance and economics there are many papers studying the relationship between order-book volume and the trend of the market price. I am very excited to get the summer research opportunity to use the game-theory approach to study how the order-book volume will influence the trading strategy for each investor to influence the market price.
Most of the investors have some common trading behaviours. Individual investors tend to trade small quantities with a high frequency. Institutional investors tend to trade large quantities with a relatively low frequency. In some way, we can assume the investors in the same group are identical. That’s why we introduce mean-field game approach to model the order-book dynamics. The identical investor’s assumption can satisfy the assumptions in the mean-field game. The mean-field game is used when the number of players is substantial, so that it would be difficult to analyse the individually optimal strategy based on all the other players’ strategies. ‘Mean’ is the average strategy that we use to determine the optimal personal strategy.
The first part of my AMSI Vacation Research Scholarship project is to learn some interesting concepts in game theory. The first part is both relaxing and exciting, the text book is understandable and I can learn new things every day. The second part focuses on using the mean-field game approach to model the order book in the market, which is challenging yet interesting as well. The gain of my summer research is not only the new knowledge, more importantly, I have a much clearer idea about how academic research is undertaken, consequently strengthening my belief that I will pursue further academic study.
Lachapelle, A, Lasry, J-M, Lehalle, C-A, & Lions, P-L 2016, ‘Efficiency of the price formation process in presence of high frequency participants: a mean field game analysis’, Mathematics and Financial Economics, vol. 10, pp. 223-262.
Yueyi Sun was one of the recipients of a 2017/18 AMSI Vacation Research Scholarship.