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Game Theoretic Analysis of Discovery Sampling for Internal Fraud Control Auditing

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  • DAVID R. FINLEY

Abstract

. A strategic internal auditing model is developed to analyze the use of discovery sampling to deter or detect abstraction of assets by an auditee. The analysis develops a game in which the auditee chooses the fraud level and an auditor chooses an effort level (sample size). The auditee seeks to maximize expected successful fraud net of a fixed sanction for detected fraud. The auditor seeks to minimize expected costs from sampling and fraud losses. Both simultaneous play and commitment versions of the game are analyzed. For each version, pure strategies are optimal. In comparison with simultaneous play, the commitment version equilibrium results in greater audit effort and less fraud by the auditee. Comparative statics showing effects of sanction level and recovery rates are derived. For simultaneous play, optimal monitoring effort decreases with the sanction level and increases with the recovery rate; for the commitment version, these effects are reversed. The analysis demonstrates the sensitivity of results to the audit effort communication arrangement and to the specific audit objective of fraud detection. Résumé. L'auteur élabore un modèle stratégique de vérification interne permettant d'analyser l'utilisation du sondage de dépistage dans le but d'empêcher ou de détecter l'abstraction d'éléments d'actif par l'entité vérifiée. Il élabore, dans son analyse, un jeu dans lequel l'entité vérifiée choisit l'importance de la fraude et le vérificateur choisit l'envergure du travail de vérification (taille de l'échantillon). L'entité vérifiée cherche à maximiser le montant de la fraude qu'elle arrive à dissimuler, diminué d'une pénalité établie au préalable s'appliquant aux fraudes détectées. Le vérificateur cherche à minimiser les coûts prévus des sondages et des pertes attribuables aux fraudes. L'auteur analyse la version du jeu où les protagonistes agissent simultanément de même que celle où le vérificateur s'engage au préalable. Pour chaque version, les stratégies pures sont optimales. Par comparaison à la version simultanée, la situation d'équilibre de la version de l'engagement préalable donne lieu à un travail de vérification d'envergure plus grande et une fraude de moindre importance de la part de l'entité vérifiée. Des statistiques comparatives montrant les effets du niveau de pénalité et des taux de récupération sont dérivées. Dans le cas de la version de l'action simultanée des protagonistes, le travail de contrôle optimal diminue avec le niveau de sanction et augmente avec le taux de récupération; dans le cas de l'engagement préalable du vérificateur, les résultats sont inverses. L'analyse démontre la sensibilité des résultats à l'entente relative à la communication de l'envergure du travail de vérification et à l'objectif précis de la vérification consistant à détecter la fraude.

Suggested Citation

  • David R. Finley, 1994. "Game Theoretic Analysis of Discovery Sampling for Internal Fraud Control Auditing," Contemporary Accounting Research, John Wiley & Sons, vol. 11(1), pages 91-114, June.
  • Handle: RePEc:wly:coacre:v:11:y:1994:i:1:p:91-114
    DOI: 10.1111/j.1911-3846.1994.tb00438.x
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    References listed on IDEAS

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    1. Dennis H. Caplan & Michael Kirschenheiter, 2000. "Outsourcing and Audit Risk for Internal Audit Services," Contemporary Accounting Research, John Wiley & Sons, vol. 17(3), pages 387-428, September.
    2. J. Reed Smith & Samuel L. Tiras & Sansakrit S. Vichitlekarn, 2000. "The Interaction between Internal Control Assessment and Substantive Testing in Audits for Fraud," Contemporary Accounting Research, John Wiley & Sons, vol. 17(2), pages 327-356, June.
    3. Rudolf Avenhaus & D. Marc Kilgour, 2004. "Efficient distributions of arms‐control inspection effort," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(1), pages 1-27, February.
    4. Davis, Jon S. & Pesch, Heather L., 2013. "Fraud dynamics and controls in organizations," Accounting, Organizations and Society, Elsevier, vol. 38(6), pages 469-483.

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