Tight Samurai Accountant

Abstract: This note applies tightness (Kattwinkel and Preusser (2025)) to the setting of Border and Sobel (1987, "Samurai Accountant: A Theory of Auditing and Plunder"). Border and Sobel characterize efficient mechanisms and argue that efficiency entails no loss of optimality. We characterize tight mechanisms and argue that tightness entails no loss of optimality. We show that tight mechanisms form a subset of efficient mechanisms. Therefore, tightness refines efficiency without loss of optimality. By characterizing tight mechanisms, one can replicate the insights from Border and Sobel (1987) and Chander and Wilde (1998). A novel insight is how and in which order the principal uses different instruments to provide incentives to different agent types. Further, we describe a procedure for constructing efficient mechanisms in a setting with a continuum of types.