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Avoiding non-optimal management decisions by applying a three-person inspection game

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  • Fandel, G.
  • Trockel, J.

Abstract

An inspection game models a conflict situation between an inspector and an inspectee. The mathematical analysis aims to generate optimal behavior of the inspectee under the assumption that an undesirable action of the inspectee could otherwise be carried out strategically. In this paper the controller’s (inspector’s) particular job is to audit a manager’s (inspectee’s) decision and to submit a report to the company’s top managers for examination. Thus, a conflict as regards the choice of behavioral actions of the manager, the controller and the top management impends. Based on Fandel and Trockel (2011a) this modified inspection game is discussed here for the first time as a three-person game in the context of a manager’s faulty decision that will unnecessarily add to the company’s costs and that the top management understandably wishes to minimize. We will first examine the conditions under which a Nash equilibrium occurs in this three-person game in which poor management, poor monitoring and poor revision coincide. We will then examine the effects that the penalties and bonuses exert on the Nash equilibrium solution. We will find that penalties and bonuses can neutralize each other in their effects on the improved decision making by the manager and the controller.

Suggested Citation

  • Fandel, G. & Trockel, J., 2013. "Avoiding non-optimal management decisions by applying a three-person inspection game," European Journal of Operational Research, Elsevier, vol. 226(1), pages 85-93.
  • Handle: RePEc:eee:ejores:v:226:y:2013:i:1:p:85-93
    DOI: 10.1016/j.ejor.2012.09.032
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    References listed on IDEAS

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    Cited by:

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    2. Benjamin Florian Siggelkow & Jan Trockel & Oliver Dieterle, 2018. "An inspection game of internal audit and the influence of whistle-blowing," Journal of Business Economics, Springer, vol. 88(7), pages 883-914, September.
    3. Puneet Agarwal & Kyle Hunt & Shivasubramanian Srinivasan & Jun Zhuang, 2020. "Fire Code Inspection and Compliance: A Game-Theoretic Model Between Fire Inspection Agencies and Building Owners," Decision Analysis, INFORMS, vol. 17(3), pages 208-226, September.
    4. S. Belhaiza & S. Charrad & R. M’Hallah, 2018. "On the Performance of Managers and Controllers: A Polymatrix Game Approach for the Manager–Controller–Board of Directors’ Conflict," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 584-602, May.
    5. Hans-Ulrich Küpper & Jan Trockel, 2018. "Editorial," Journal of Business Economics, Springer, vol. 88(7), pages 827-829, September.
    6. Robin Christmann & Roland Kirstein, 2023. "You go first!: coordination problems and the burden of proof in inquisitorial prosecution," European Journal of Law and Economics, Springer, vol. 56(2), pages 403-422, October.
    7. Ensthaler, Ludwig & Giebe, Thomas, 2014. "Bayesian optimal knapsack procurement," European Journal of Operational Research, Elsevier, vol. 234(3), pages 774-779.

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