Recursive Inspection Games

• 成果类型: Article
• 署名作者: von Stengel, Bernhard
• 署名单位: University of London; London School Economics & Political Science
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0762
• 发表日期: 2016
• 页码: 935-952
• 关键词: time

摘要

We consider a sequential inspection game where an inspector uses a limited number of inspections over a larger number of time periods to detect a violation (an illegal act) of an inspectee. Compared with earlier models, we allow varying rewards to the inspectee for successful violations. As one possible example, the most valuable reward may be the completion of a sequence of thefts of nuclear material needed to build a nuclear bomb. The inspectee can observe the inspector, but the inspector can only determine if a violation happens during a stage where he inspects, which terminates the game; otherwise the game continues. Under reasonable assumptions for the payoffs, the inspector's strategy is independent of the number of successful violations. This allows to apply a recursive description of the game, even though this normally assumes fully informed players after each stage. The resulting recursive equation in three variables for the equilibrium payoff of the game, which generalizes several other known equations of this kind, is solved explicitly in terms of sums of binomial coefficients. We also extend this approach to nonzero-sum games and inspector leadership where the inspector commits to (the same) randomized inspection schedule, but the inspectee acts legally (rather than mixes as in the simultaneous game) as long as inspections remain.