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Annals of Operations Research

, Volume 237, Issue 1–2, pp 7–26 | Cite as

Multiple agents finitely repeated inspection game with dismissals

  • Yael Deutsch
  • Boaz Golany
Article

Abstract

This paper deals with an inspection game between a single inspector and several independent (potential) violators over a finite-time horizon. In each period, the inspector gets a renewable inspection resource, which cannot be saved and used in future periods. The inspector allocates it to inspect the (potential) violators. Each violator decides in each period whether to violate or not, and in what probability. A violation may be detected by the inspector with a known and positive probability. When a violation is detected, the responsible violator is “dismissed” from the game. The game terminates when all the violators are detected or when there are no more remaining periods. An efficient method to compute a Nash equilibrium for this game is developed, for any possible value of the (nominal) detection probability. The solution of the game shows that the violators always maintain their detection probability below 0.5.

Keywords

Inspection games Repeated games Resource allocation Nash equilibrium 

References

  1. Avenhaus, R., Von Stengel, B., & Zamir, S. (2002). Inspection games. In S. Hart & R. J. Aumann (Eds.), Handbook of game theory, 3, chapter 51 (pp. 1947–1987). Elsevier Science Publishers B.V.Google Scholar
  2. Bakir, N. O. (2011). A Stackelberg game model for resource allocation in cargo container security. Annals of Operations Research, 187(1), 5–22.CrossRefGoogle Scholar
  3. Bier, V. M., (2011). Game-theoretic methods in counterterrorism and security. In Wiley encyclopedia of operations research and management science.Google Scholar
  4. Bier, V. M., & Haphuriwat, N. (2011). Analytical method to identify the number of containers to inspect at US ports to deter terrorist attacks. Annals of Operations Research, 187(1), 137–158.CrossRefGoogle Scholar
  5. Borch, K. (1982). Insuring and auditing the auditor. In M. Deistler, E. Fürst, & G. Schwödiauer (Eds.) Games, economic dynamics, time series analysis, Physica-Verlag, Würzburg, 117–126. Reprinted: K. Borch. 1990. Economics of Insurance, North- Holland, Amsterdam, pp. 350–362.Google Scholar
  6. Borch, K. (1990). Economics of insurance. In Advanced textbooks in economics, 29, North-Holland, Amsterdam.Google Scholar
  7. Casas-Arce, P. (2010). Dismissals and quits in repeated games. Economic theory, 43, 67–80.CrossRefGoogle Scholar
  8. Dechenaux, E., & Samuel, A. (2012). Pre-emptive corruption, hold-up and repeated interactions. Economica, 79, 258–283.CrossRefGoogle Scholar
  9. Deutsch, Y., Golany, B., Goldberg, N., & Rothblum, U. G. (2013). Inspection games with local and global allocation bounds. Naval Research Logistics, 60, 125–140.CrossRefGoogle Scholar
  10. Deutsch, Y., Golany, B., & Rothblum, U. G. (2011). Determining all Nash equilibria in a (bi-linear) inspection game. European Journal of Operational Research, 215(2), 422–430.CrossRefGoogle Scholar
  11. Fukuyama, K., Kilgour, D. M., & Hipel, K. W. (1995). Supplementing review strategies with penalties in environmental enforcement. In Systems, man and cybernetics. IEEE international conference on intelligent systems for the 21st century, vol. 3, pp. 2371–2377.Google Scholar
  12. Golany, B., Goldberg, N., & Rothblum, U. G. (2012). Allocating multiple defensive resources in a zero-sum game setting. Annals of Operations Research, 1–19.Google Scholar
  13. Golany, B., Kaplan, E. H., Marmur, A., & Rothblum, U. G. (2009). Nature plays with dice—terrorists do not: Allocating resources to counter strategic versus probabilistic risks. European Journal of Operational Research, 192, 198–208.CrossRefGoogle Scholar
  14. Heal, G., & Kunreuther, H. (2007). Modeling interdependent risks. Risk Analysis, 27(3), 621–634.CrossRefGoogle Scholar
  15. Rothenstein, D., & Zamir, S. (2002). Imperfect inspection games over time. Annals of Operations Research, 109, 175–192.CrossRefGoogle Scholar
  16. Wu, D. D., Chen, S. H., & Olson, D. L. (2014). Business intelligence in risk management: Some recent progresses. Information Sciences, 256, 1–7.CrossRefGoogle Scholar
  17. Wu, D., & Olson, D. L. (2010). Enterprise risk management: Coping with model risk in a large bank. Journal of the Operational Research Society, 61(2), 179–190.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Faculty of Industrial Engineering and ManagementTechnion, Israel Institute of TechnologyHaifaIsrael

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