The forensic-type phase: A game-theoretic analysis of fraud detection in auditing

The purpose of this thesis is to examine how the forensic-type phase in auditing affects audit risk with using a stylized game-theoretic analysis. The forensic-type phase is a phase of audits in which the auditors attempt to detect fraud. The main result of this study is that the introduction of the forensic-type phase in an audit does not always reduce audit risk.; The auditor's detection technology in the forensic-type phase is formulated with the cumulative distribution function of an exponential distribution. Then, the phase is added to the standard acceptance sampling game found in Newman and Noel (1989) and Shibano (1990), in which the audit evidence follows distributions showing the strict monotone likelihood ratio property, and the auditor updates the ex post probability of management fraud with Bayes's rule.; The existence of a perfect Bayesian equilibrium is proved. Although the possibility of multiple equilibria is not excluded, a sufficient condition under which the game has a unique equilibrium is identified. The necessary and sufficient condition under which the auditor tries to detect fraud is provided. The range of audit evidence in which the auditor conducts detecting activity is expressed in terms of exogenous parameters such as the auditor's payoffs.; Some results are obtained by comparative statics. The most important result is that audit risk occasionally increases when the forensic-type phase is introduced. To obtain an intuition about general tendencies of the cases that audit risk increases, with the introduction of the forensic-type phase, a Monte Carlo simulation is conducted. The result of the simulation indicates that audit risk tends to increase with the introduction of the forensic-type phase if the manager's additional bonus when he commits fraud and the auditor's penalty for a type I error are large; and/or if the manager's penalty for detected fraud, the manager's penalty for the auditor's rejection and the auditor's penalty for a type II error are small. In general, when the manager has strong incentive to commit fraud and the auditor has strong incentive to avoid false rejection, the introduction of the forensic-type phase tends to increase audit risk.