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Recursive Inspection Games

Wednesday 29 January 2014, 4.30pm - 5.30pm
NAB 5.21, New Academic Building

Prof Bernhard von Stengel

Department of Mathematics, London School of Economics 

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Abstract:

Dresher (1962) described a sequential inspection game where an inspector has to distribute a given number of inspections over a larger number of inspection periods in order to detect an illegal act that an inspectee, who can count the inspector's visits, performs in at most one of these periods. We present an extension of this game where more than one illegal act is allowed. Then, under certain reasonable assumptions for the zero-sum payoffs, the optimal strategy of the inspector does not depend on the number of intended illegal acts. This allows a recursive description. The resulting recursive equation in three variables for the value of the game, which generalizes several other known equations of this kind, is solved explicitly, using numbers similar to binomial  coefficients defined by a "generalized Pascal triangle". We also  extend this approach to non-zero-sum games and, similar to Maschler (1966), "inspector leadership" where the inspector commits to (the same) randomized inspection schedule, but the inspectee acts legally as long as inspections remain. 

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   Bernhard von Stengel