An incomplete information game modeling to estimate fraud risk by manipulation in stocks

Abstract

Investors can use strategies to mitigate the risk of losses due to price manipulation in stock market investments, which occurs, for example, in speculative movements. In this sense, fraud by manipulation is a complex issue for the audit team, resulting in negative consequences, such as losses for investors and erosion of confidence in the stock market. This research seeks to improve, through the insertion of incomplete information, the estimate of the probability of fraud by manipulation of stock prices established in the framework that connects Game Theory and Detection Software proposed by Bernardino et al. (2021), using the effort/damage ratio of the audit team, the benefit/cost ratio of agents with the potential to manipulate prices and

through the identification of Nash equilibria of an audit game. The results present a mathemat- ical methodology that returns algebraic expressions for the probabilities of fraud, considering

two types of players with different levels of propensity to manipulate asset prices. Additionally,

the method returns expressions for the investigation rates under warning and non-warning sig- nals issued by fraud detection software. This establishes a valuable tool for risk management

in the stock market. The model contributes to a better assessment of investor risk by examining different types of agents with different propensities for fraud, which aligns with the reality of the stock market, in addition to promoting investor understanding and helping them adopt more effective responses to fraudulent behavior.