IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v226y2013i1p85-93.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712007114
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2012.09.032?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Luciano Andreozzi, 2004. "Rewarding Policemen Increases Crime. Another Surprising Result from the Inspection Game," Public Choice, Springer, vol. 121(1), pages 69-82, October.
    2. 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.
    3. 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.
    4. Luciano Andreozzi, 2008. "Inspection games with long-run inspectors," Department of Economics Working Papers 0821, Department of Economics, University of Trento, Italia.
    5. 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.
    6. 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.
    7. Joseph T. Howson, Jr., 1972. "Equilibria of Polymatrix Games," Management Science, INFORMS, vol. 18(5-Part-1), pages 312-318, January.
    8. Hohzaki, Ryusuke, 2007. "An inspection game with multiple inspectees," European Journal of Operational Research, Elsevier, vol. 178(3), pages 894-906, May.
    9. C. Audet & S. Belhaiza & P. Hansen, 2006. "Enumeration of All the Extreme Equilibria in Game Theory: Bimatrix and Polymatrix Games," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 349-372, June.
    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.
    12. Quintas, L G, 1989. "A Note on Polymatrix Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 261-272.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Hans-Ulrich Küpper & Jan Trockel, 2018. "Editorial," Journal of Business Economics, Springer, vol. 88(7), pages 827-829, September.
    3. Ensthaler, Ludwig & Giebe, Thomas, 2014. "Bayesian optimal knapsack procurement," European Journal of Operational Research, Elsevier, vol. 234(3), pages 774-779.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Deutsch, Yael, 2021. "A polynomial-time method to compute all Nash equilibria solutions of a general two-person inspection game," European Journal of Operational Research, Elsevier, vol. 288(3), pages 1036-1052.
    2. Deutsch, Yael & Goldberg, Noam & Perlman, Yael, 2019. "Incorporating monitoring technology and on-site inspections into an n-person inspection game," European Journal of Operational Research, Elsevier, vol. 274(2), pages 627-637.
    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. Dong, Xiaoqing & Li, Chaolin & Li, Ji & Wang, Jia & Huang, Wantao, 2010. "A game-theoretic analysis of implementation of cleaner production policies in the Chinese electroplating industry," Resources, Conservation & Recycling, Elsevier, vol. 54(12), pages 1442-1448.
    5. 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.
    6. 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.
    7. van den Elzen, A.H., 1996. "Constructive Application of the Linear Tracing Procedure to Polymatrix Games," Research Memorandum 738, Tilburg University, School of Economics and Management.
    8. 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.
    9. Vicki Bier & Naraphorn Haphuriwat, 2011. "Analytical method to identify the number of containers to inspect at U.S. ports to deter terrorist attacks," Annals of Operations Research, Springer, vol. 187(1), pages 137-158, July.
    10. Stamatios Katsikas & Vassili Kolokoltsov & Wei Yang, 2016. "Evolutionary Inspection and Corruption Games," Games, MDPI, vol. 7(4), pages 1-25, October.
    11. Vassili Kolokoltsov, 2017. "The Evolutionary Game of Pressure (or Interference), Resistance and Collaboration," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 915-944, November.
    12. Hunt, Kyle & Zhuang, Jun, 2024. "A review of attacker-defender games: Current state and paths forward," European Journal of Operational Research, Elsevier, vol. 313(2), pages 401-417.
    13. Jann, Ole & Schottmüller, Christoph, 2021. "Regime change games with an active defender," Games and Economic Behavior, Elsevier, vol. 129(C), pages 96-113.
    14. 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.
    15. Naraphorn Haphuriwat & Vicki M. Bier & Henry H. Willis, 2011. "Deterring the Smuggling of Nuclear Weapons in Container Freight Through Detection and Retaliation," Decision Analysis, INFORMS, vol. 8(2), pages 88-102, June.
    16. Renato Soeiro & Alberto A. Pinto, 2022. "A Note on Type-Symmetries in Finite Games," Mathematics, MDPI, vol. 10(24), pages 1-13, December.
    17. Widodo, Erwin & Rochmadhan, Oryza Akbar & Lukmandono, & Januardi,, 2022. "Modeling Bayesian inspection game for non-performing loan problems," Operations Research Perspectives, Elsevier, vol. 9(C).
    18. van den Elzen, A.H., 1996. "Constructive Application of the Linear Tracing Procedure to Polymatrix Games," Other publications TiSEM 7366cd12-e253-4d53-8dea-c, Tilburg University, School of Economics and Management.
    19. Zoroa, N. & Fernández-Sáez, M.J. & Zoroa, P., 2011. "A foraging problem: Sit-and-wait versus active predation," European Journal of Operational Research, Elsevier, vol. 208(2), pages 131-141, January.
    20. Susumu Shikano & Michael F Stoffel & Markus Tepe, 2017. "Information accuracy in legislative oversight: Theoretical implications and experimental evidence," Rationality and Society, , vol. 29(2), pages 226-254, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:226:y:2013:i:1:p:85-93. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.