Applications of Game Theory in Market Microstructure Modelling

Abstract

We study interactions between the broker and the regulator in the context of front-running in the financial markets. The primary objective is to understand the role of incomplete information and regulators’ beliefs in the broker’s trading behavior. We model the front-running using a sequential game with incomplete information and analyze the perfect Bayesian equilibrium of the game. The equilibrium analysis for different market conditions based on the profitability of the price revealed interesting insights into the broker’s behavior. We show that, when a client order is trend-reversing, the uninformed broker deliberately trades even when the price is not profitable to shape the regulator’s belief away from investigating trading activities. It allows the informed broker to frontrun the market and the broker gets higher expected payoff. We also examine the role of information spread and the regulator’s willingness to investigate the trading in a broker’s optimal strategies. We show that certain equilibria exist only when the information spread is lower or higher compared to the regulator’s investigation threshold. We further show that imperfect investigation leads to decreases in the regulator’s willingness to investigate. The study is helpful in gaining behavioral insights about the broker in the context of front-running and deciding regulatory policies against the front-running.