Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Inspection Games

  • Rudolf Avenhaus
  • Morton J. Canty
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_287-4



In an inspection game, deterrence is said to be achieved by a Nash equilibrium in which the inspectee behaves legally, or in accordance with the agreed rule.

Extensive form

The extensive form of a noncooperative game is a graphical representation which describes a succession of moves by different players, including chance moves, and which can handle quite intricate information patterns.

Inspector leadership

Leadership in inspection games is a strategic concept by which, through persuasive announcement of her strategy, the inspector can achieve deterrence.

Mixed strategy

A mixed strategy for a player in a noncooperative game is a probability distribution over that player’s pure strategies.

Nash equilibrium

A Nash equilibrium in a noncooperative game is a specification of strategies for all players with the property that no player has an incentive to deviate unilaterally from her specified strategy. A solutionof a noncooperative game is a Nash equilibrium which is...


Nash Equilibrium International Atomic Energy Agency Mixed Strategy Pure Strategy Equilibrium Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.


  1. Avenhaus R (1997) Entscheidungstheoretische Analyse der Fahrgast-Kontrollen. Der Nahverkehr 9:27Google Scholar
  2. Avenhaus R, Canty MJ (1989) Re-examination of the IAEA formula for stratified attribute sampling. In: Proceedings of the 11th ESARDA symposium, JRC, Ispra, pp 351–356Google Scholar
  3. Avenhaus R, Canty MJ (1996) Compliance quantified. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  4. Avenhaus R, Canty MJ (2005) Playing for time: a sequential inspection game. Eur J Oper Res 167(2):474–492MathSciNetCrossRefzbMATHGoogle Scholar
  5. Avenhaus R, Jaech JL (1981) On subdividing material balances in time and/or space. J Inst Nucl Manag IV(3):24–33Google Scholar
  6. Avenhaus R, Okada A, Zamir S (1991) Inspector leadership with incomplete information. In: Selten R (ed) Game equilibrium models, vol IV. Springer, Heidelberg, pp 319–361CrossRefGoogle Scholar
  7. Avenhaus R, Canty MJ, Kilgour DM, von Stengel B, Zamir S (1996) Inspection games in arms control. Eur J Oper Res 90:383–394CrossRefzbMATHGoogle Scholar
  8. Avenhaus R, von Stengel B, Zamir S (2002) Inspection games. In: Aumann R, Hart S (eds) Handbook of game theory. Elsevier, Amsterdam, pp 1947–1987Google Scholar
  9. Baiman S (1982) Agency research in managerial accounting: a survey. J Account Lit 1:154–213Google Scholar
  10. Baston VJ, Bostock FA (1991) A remark on the customs smuggler game. Nav Res Logist 41:287–293MathSciNetGoogle Scholar
  11. Bierlein D (1968) Direkte Überwachungssysteme. Oper Res Verfahr 6:57–68zbMATHGoogle Scholar
  12. Bierlein D (1969) Auf Bilanzen und Inventuren basierenden Safeguards-Systeme. Oper Res Verfahr 6:36–43zbMATHGoogle Scholar
  13. Borch K (1990) Economics of insurance. North-Holland, AmsterdamGoogle Scholar
  14. Cavasoglu H, Raghunatahan S (2004) Configuration of detection software: a comparison of decision and game theory. Decis Anal 1:131–148CrossRefGoogle Scholar
  15. Cook J, Nadeau L, Thomas LC (1997) Does cooperation in auditing matter? A comparison of a non-cooperative and a cooperative game model of auditing. Eur J Oper Res 103:470–482CrossRefzbMATHGoogle Scholar
  16. Derman C (1961) On minimax surveillance schedules. Nav Res Logist 8:415–419CrossRefzbMATHGoogle Scholar
  17. Diamond H (1982) Minimax policies for unobservable inspections. Math Oper Res 7(1):139–153MathSciNetCrossRefzbMATHGoogle Scholar
  18. Dresher M (1962) A sampling inspection problem in arms control agreements: a game theoretical analysis. Memorandum RM-2972-ARPA. RAND Corporation, Santa MonicaGoogle Scholar
  19. Dye RA (1986) Optimal monitoring policies in agencies. RAND J Econ 17:339–350CrossRefGoogle Scholar
  20. Ferguson TS, Melolidakis C (1998) On the inspection game. Nav Res Logist 45:327–334MathSciNetCrossRefzbMATHGoogle Scholar
  21. Garnaev AY (1991) A generalized inspection game. Nav Res Logist 28:171–188MathSciNetGoogle Scholar
  22. Goutal P, Garnaev A, Garnaeva G (1997) On the infiltration game. Int J Game Theory 26(2):215–221MathSciNetCrossRefzbMATHGoogle Scholar
  23. Höpfinger E (1971) A game-theoretic analysis of an inspection problem, University of Karlsruhe (unpublished manuscript)Google Scholar
  24. Höpfinger E (1974) Zuverlässige Inspektionsstrategien. Z Wahrscheinlichkeitstheorie Verw Geb 31:35–46CrossRefzbMATHGoogle Scholar
  25. Hozaki R, Kuhdoh D, Komiya T (2006) An inspection game: taking account of fulfillment probabilities of players. Nav Res Logist 53:761–771MathSciNetCrossRefGoogle Scholar
  26. IAEA (1972) The structure and content of agreements between the agency and states required in connection with the treaty on the non-proliferation of nuclear weapons. IAEA, Vienna, INF/CIRC 153 (corrected)Google Scholar
  27. IAEA (1997) Model protocol additional to the agreement(s) between state(s) and the international atomic energy agency for the application of safeguards. IAEA, Vienna, INF/CIRC 140Google Scholar
  28. Kanodia CS (1985) Stochastic and moral hazard. J Account Res 23:175–293CrossRefGoogle Scholar
  29. Kilgour DM (1992) Site selection for on-site inspection in arms control. Arms Control 13:439–462CrossRefGoogle Scholar
  30. Krieger T (2008) On the asymptotic behavior of a discrete time inspection game. Math Model Anal 13(1):37–46MathSciNetCrossRefzbMATHGoogle Scholar
  31. Kuhn HW (1953) Extensive games and the problem of information. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games, vol II. Princeton University Press, Princeton, pp 193–216Google Scholar
  32. Maschler M (1966) A price leadership method for solving the inspector’s non-constant-sum game. Nav Res Logist 13:11–33CrossRefzbMATHGoogle Scholar
  33. Maschler M (1967) The inspector’s non-constant-sum-game: its dependence on a system of detectors. Nav Res Logist 14:275–290CrossRefzbMATHGoogle Scholar
  34. Morris P (1994) Introduction to game theory. Springer, New YorkCrossRefzbMATHGoogle Scholar
  35. Nash JF (1951) Non-cooperative games. Ann Math 54:286–295MathSciNetCrossRefzbMATHGoogle Scholar
  36. O’Neill B (1994) Game theory models of peace and war. In: Aumann R, Hart S (eds) Handbook of game theory. Elsevier, Amsterdam, pp 995–1053Google Scholar
  37. Ostrom E, Gardner R, Walker J (1994) Rules, games and common pool resources. University of Michigan Press, Ann ArborCrossRefGoogle Scholar
  38. Owen G (1968) Game theory. W. B. Saunders, PhiladelphiazbMATHGoogle Scholar
  39. Pavlovic L (2002) More on the search for an infiltrator. Nav Res Logist 49:1–14MathSciNetCrossRefzbMATHGoogle Scholar
  40. Rinderle K (1996) Mehrstufige sequentielle Inspektionsspiele mit statistischen Fehlern erster und zweiter Art. Kovac, HamburgGoogle Scholar
  41. Rohatgi VK (1976) An introduction to probability theory and mathematical statistics. Wiley, New YorkzbMATHGoogle Scholar
  42. Rothenstein D, Zamir S (2002) Imperfect inspection games over time. Ann Oper Res 109:175–192MathSciNetCrossRefzbMATHGoogle Scholar
  43. Sakaguchi M (1994) A sequential game of multi-opportunity infiltration. Math Jpn 39:157–166MathSciNetzbMATHGoogle Scholar
  44. Schelling TC (1960) The strategy of conflict. Harvard University Press, Cambridge, MAzbMATHGoogle Scholar
  45. Simaan M, Cruz JB (1973) On the Stackelberg strategy in nonzero-sum games. J Optim Theory Appl 11(5):533–555MathSciNetCrossRefzbMATHGoogle Scholar
  46. von Neumann J, Morgenstern O (1947) Theory of games and economic behavior. Princeton University Press, PrincetonzbMATHGoogle Scholar
  47. von Stackelberg H (1934) Marktform und Gleichgewicht. Springer, ViennaGoogle Scholar
  48. von Stengel B (1991) Recursive inspection games, Report No. S 9106. Computer Science Faculty, Armed Forces University MunichGoogle Scholar
  49. Stewart KB (1971) A cost-effectiveness approach to inventory verification. In: Proceedings of the IAEA symposium on safeguards techniques, vol II. International Atomic Energy Agency, Vienna, pp 387–409Google Scholar
  50. Thomas MU, Nisgav Y (1976) An infiltration game with time-dependent payoff. Nav Res Logist 23:297–320CrossRefzbMATHGoogle Scholar
  51. Wilks TJ, Zimbelman MF (2004) Using game theory and strategic reasoning concepts to prevent and detect fraud. Account Horiz 18(3):173–184CrossRefGoogle Scholar
  52. Wölling A (2002) Das Führerschaftsprinzip bei Inspektionsspielen. Kovac, HamburgGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Armed Forces University MunichNeubibergGermany
  2. 2.Institute for Chemistry and Dynamics of the GeosphereForschungszentrum JülichJülichGermany