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


  • Fandel, G.
  • Trockel, J.


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

    1. Quintas, L G, 1989. "A Note on Polymatrix Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 261-272.
    2. Luciano Andreozzi, 2004. "Rewarding Policemen Increases Crime. Another Surprising Result from the Inspection Game," Public Choice, Springer, vol. 121(1), pages 69-82, October.
    3. Avenhaus, Rudolf & Canty, Morton & Marc Kilgour, D. & von Stengel, Bernhard & Zamir, Shmuel, 1996. "Inspection games in arms control," European Journal of Operational Research, Elsevier, vol. 90(3), pages 383-394, May.
    4. Deutsch, Yael & Golany, Boaz & Rothblum, Uriel G., 2011. "Determining all Nash equilibria in a (bi-linear) inspection game," European Journal of Operational Research, Elsevier, vol. 215(2), pages 422-430, December.
    5. Luciano Andreozzi, 2008. "Inspection games with long-run inspectors," Department of Economics Working Papers 0821, Department of Economics, University of Trento, Italia.
    6. Hohzaki, Ryusuke & Maehara, Hiroki, 2010. "A single-shot game of multi-period inspection," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1410-1418, December.
    7. Fandel, Günter & Trockel, Jan, 2011. "Optimal lot sizing in a non-cooperative material manager-controller game," International Journal of Production Economics, Elsevier, vol. 133(1), pages 256-261, September.
    8. Hohzaki, Ryusuke, 2007. "An inspection game with multiple inspectees," European Journal of Operational Research, Elsevier, vol. 178(3), pages 894-906, May.
    9. R Hohzaki & R Masuda, 2012. "A smuggling game with asymmetrical information of players," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(10), pages 1434-1446, October.
    10. Avenhaus, Rudolf & Canty, Morton John, 2005. "Playing for time: A sequential inspection game," European Journal of Operational Research, Elsevier, vol. 167(2), pages 475-492, December.
    11. Yasuhiro Ohta, 2008. "On the Conditions under which Audit Risk Increases with Information," European Accounting Review, Taylor & Francis Journals, vol. 17(3), pages 559-585.
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    Cited by:

    1. Avenhaus, Rudolf & Krieger, Thomas, 2013. "Distributing inspections in space and time – Proposed solution of a difficult problem," European Journal of Operational Research, Elsevier, vol. 231(3), pages 712-719.
    2. 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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