Abstract
An inspection game models a conflict situation between an inspector and an inspectee. The mathematical analysis aims to determine optimal behaviour of the inspectee. In this paper, the controller’s (inspector) job is to audit a planner’s (inspectee) decision with regard to its optimality and to submit a report to the company’s top managers. Based on Fandel and Trockel (Int J Prod Econ 133:256–261, 2011) this inspection game is discussed here as an infinite two-person game under the aspect of costs minimization. The results show that a higher costs deviation because of a competitive behaviour of the strategic players will decrease their payoffs, so that the optimal cooperative behaviour will finally lead to a better solution for the company with respect to cost minimization as normally expected.
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References
Abreu D, Rubinstein A (1988) The structure of Nash equilibrium in repeated games with finite automata. Econometrica 56: 1259–1281
Arnolds H, Heege F, Tussin W (1996) Materialwirtschaft und Einkauf. Gabler, Wiesb
Avenhaus R (2004) Applications of inspection games. Math Model Anal 9: 179–192
Avenhaus R, von Stengel B, Zamir S (2002) Inspection games. In: Aumann RJ, Hart S (eds) Handbook of game theory with economic applications. North-Holland, Amsterdam 3, pp 1947–1987
Axelrod R, Hamilton WD (1981) The evolution of cooperation. Science 211: 1390–1396
Bierlein D (1969) Auf Bilanzen und Inventuren basierende Safeguards-Systeme. Oper Res Verfahr 8: 36–43
Borch K (1982) Insuring and Auditing the Auditor. In: Deistler M, Fürst E, Schwödiauer G (eds) Games, economic dynamics, time series analysis. Physica, Wien, pp 117–126
Dresher M (1962) A sampling inspection problem in arms control agreements: a game-theoretic analysis. Rand Mem, RAND Corporation, Santa Monica
Ewert R (1993) Rechnungslegung, Wirtschaftsprüfung, rationale Akteure und Märkte: ein Grundmodell zur Analyse der Qualität von Unternehmenspublikationen. Schmalenbachs Z für betrwirtsch Forsch 45: 715–747
Ewert R (2004) Audit Regulation, Audit Quality, and Audit Research in the Post-Enron-Era: An Analysis of Nonaudit Services. In: Leuz C, Pfaff D, Hopwood A (eds) The econ and polit of account. Oxford University Press, Oxford, pp 239–264
Fandel G, Trockel J (2008) Efficient storage under the aspect of conflicting priorities between stockkeeping and controlling. Fifteenth Int Work Semin on Prod Econ, Pre-Prints, Innsbruck 3: 87–100
Fandel G, Trockel J (2011) Optimal lot sizing in a non-cooperative material manager-controller game. Int J Prod Econ 133: 256–261
Fellingham JC, Newman DP (1985) Strategic considerations in auditing. Account Rev 60: 634–650
Friedman JW (1971) A non-cooperative equilibrium for supergames. Rev Econ Stud 38: 1–12
Friehe T (2008) Correlated payoffs in the inspection game: some theory and an application to corruption. Public Choice 137: 127–143
Fudenberg D, Tirole J (2008) Game theory. MIT Press, Cambridge
Nash J (1951) Non-cooperative games. Ann Math 54: 286–295
Paefgen A (2008) Rationalitätsdefizite im Handeln von Controllern: Ausprägungsformen und Gegenmaßnahmen. Gabler, Wiesb
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Fandel, G., Trockel, J. Applying a one-shot and infinite repeated inspection game to materials management. Cent Eur J Oper Res 21, 495–506 (2013). https://doi.org/10.1007/s10100-012-0244-9
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DOI: https://doi.org/10.1007/s10100-012-0244-9