An inspection game with multiple inspectees

Hohzaki, Ryusuke

doi:10.1016/j.ejor.2006.02.015

Cited by 26 publications

(17 citation statements)

References 7 publications

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“…Additionally, while sequential or stochastic multi-stage games have been used to model numerous smuggling problems, each game has a comparatively small number of pure strategies for the smuggler and custom officials. IGs were often modeled as non-cooperative games, with analysis focusing on the inspector's strategy of resource distribution (such as budget and personnel) in order to determine inspection effectiveness, as in Avenhaus and Kilgour (2004) [27] and [114]. That is why we categorize the SG as a game that combines two special strategies and the IG as a game with a special target strategy and a resource-distribution strategy for the searcher.…”

Section: Inspection and Smuggling Gamesmentioning

confidence: 99%

Search Games: Literature and Survey

Hohzaki

2016

JORSJ

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The purpose of this paper is to review literature published to date on search games, almost all of which have originated from search theory. Search theory itself is a research field of operations research that arose from realistic research efforts into air defense operations in England during World War II while the concept of search theory originated in anti-submarine warfare operations conducted by the U.S. Navy against German U-boats during the same war. The search game is an application of game theory to search problems in search theory. Search games have two main players: searchers and targets. There are some models in the search game: binary search game, linear search game, hide-search game, hide-allocation game, evasion-search game, princess-monster game, ambush game, search allocation game, path-constrained search game and search-search game. We fully survey literature on these models. We also outline other games which are closely related to the search game. Search theory has been evolving to be not method-oriented but problem-oriented for practical applications. Therefore we focus on the description of the discovery of problems and their modeling in this paper while we seldom mention the methodologies the authors devised for their search problems.

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Section: Inspection and Smuggling Gamesmentioning

confidence: 99%

Search Games: Literature and Survey

Hohzaki

2016

JORSJ

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“…(ii) Assume there are two pure strategy fixed points p i , p j , i, j ∈ S : i = 0, i < j, both satisfying (22). However, since it is j > i, then from Assumption 1, it is also G(b(ξ j )) ≥ G(b(ξ i )), and since the fine is convex, then from Lemma 1, it is also q i,i+1 ≥ q j−1,j .…”

Section: Theoremmentioning

confidence: 99%

“…Using this inner product notation and substituting (22) into (25), the kinetic equation can be written in a symbolic form:…”

Section: Evolutionary Inspection Game: Continuous Strategy Settingmentioning

confidence: 99%

“…They related the inspector's detection efficiency with the inspection effort through a non-linear detection function and derived results for the inspector's optimum strategy subject to its convexity. Hohzaki [22] moved two steps forward, considering a similar n + 1 players inspection game, where the single inspection authority not only intends to optimally distribute his/her effort among n inspectee countries, but also among l k facilities within each inspectee country k. Hohzaki presents a method of identifying a Nash equilibrium for the game and discusses several properties of the players' optimal strategies.…”

Section: Introductionmentioning

confidence: 99%

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Evolutionary Inspection and Corruption Games

Katsikas

Kolokoltsov

Yang³

2016

Games

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We extend a standard two-person, non-cooperative, non-zero sum, imperfect inspection game, considering a large population of interacting inspectees and a single inspector. Each inspectee adopts one strategy, within a finite/infinite bounded set of strategies returning increasingly illegal profits, including compliance. The inspectees may periodically update their strategies after randomly inter-comparing the obtained payoffs, setting their collective behaviour subject to evolutionary pressure. The inspector decides, at each update period, the optimum fraction of his/her renewable budget to invest on his/her interference with the inspectees' collective effect. To deter the inspectees from violating, he/she assigns a fine to each illegal strategy. We formulate the game mathematically, study its dynamics and predict its evolution subject to two key controls, the inspection budget and the punishment fine. Introducing a simple linguistic twist, we also capture the corresponding version of a corruption game.

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“…3 When randomized audits are desirable, the 4 Such models have been formulated to study financial audits, insurance claim investigations, environmental regulation / pollution control, multilateral treaty monitoring, deterrence theory / law enforcement, optimal tax policy / tax compliance, etc. For example, (a) financial audits: Chatterjee, Morton, and Mukherji [2006] and minor modifications of Newman, Patterson, and Smith [2001] and Patterson and Noel [2003]; (b) insurance claim investigations: Mookherjee and Png [1989] and Picard [1996]; (c) environmental regulation / pollution control: Bontems and Bourgeon [2005] and minor modification of Florens and Foucher [1999]; (d) multilateral treaty monitoring: minor modifications of Avenhaus, von Stengel, and Zamir [2002] and Hohzaki [2007]; (e) deterrence theory / law enforcement: Kaplow and Shavell [1994], Polinsky and Shavell [1998;2000], and Polinsky [2007]; (f) optimal tax policy / tax compliance: Border and Sobel [1987], Sanchez and Sobel [1993], Cremer and Gahvari [1995], Sansing [1993], Rhoades [1997;1999], Mills and Sansing [2000], and Feltham and Paquette [2002].…”

Section: Introductionmentioning

confidence: 99%

Efficient Committed Budget for Implementing Target Audit Probability for Many Inspectees

Yim

2009

Management Science

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Abstract. Strategic models of auditor-inspectee interaction have neglected implementation details in multiple-inspectee settings. With multiple inspectees, the target audit probability derived from the standard analysis can be implemented with sampling plans differing in the budgets committed to support them. Overly-committed audit budgets tie up unneeded resources that could have been allocated for better uses. This paper studies the minimum committed budget required to implement a target audit probability when (i) the audit sample can be contingent on "red flags" due to signals of inspectees' private information (e.g., from self-reporting) and (ii) the number of inspectees is large. It proposes an audit rule called bounded simple random sampling (SRS), which is shown to require no more committed budget to support than two other rules naturally generalized from the one-to-one analysis. When the number of inspectees is large enough, bounded SRS is nearly as good as any efficient audit rule, which demands the lowest committed budget necessary to implement the target audit probability. The results offer insights on how audit sampling plans may be formulated to reduce inefficiency and what budget usage ratios should be expected accordingly. (JEL H26, M42, H72, C72, K34) KEYWORDS: Audit sampling plan, audit budget, tax audit, tax compliance, tax evasion, inspection game, appropriation and rescission.Author's Contacts. Postal: Department of Accountancy, Tilburg University, Warandelaan 2, 5037 AB Tilburg, The Netherlands. Phone: +31 13 466-2489. Fax: +31 13 466-8001. E-mail: andrew.yim@aya.yale.edu .Electronic copy available at: http://ssrn.com/abstract=1401910 Electronic copy available at: http://ssrn.com/abstract=1401910EFFICIENT COMMITTED BUDGET FOR IMPLEMENTING TARGET AUDIT PROBABILITY FOR MANY INSPECTEESAbstract. Strategic models of auditor-inspectee interaction have neglected implementation details in multiple-inspectee settings. With multiple inspectees, the target audit probability derived from the standard analysis can be implemented with sampling plans differing in the budgets committed to support them. Overly-committed audit budgets tie up unneeded resources that could have been allocated for better uses. This paper studies the minimum committed budget required to implement a target audit probability when (i) the audit sample can be contingent on "red flags" due to signals of inspectees' private information (e.g., from self-reporting) and (ii) the number of inspectees is large. It proposes an audit rule called bounded simple random sampling (SRS), which is shown to require no more committed budget to support than two other rules naturally generalized from the one-to-one analysis. When the number of inspectees is large enough, bounded SRS is nearly as good as any efficient audit rule, which demands the lowest committed budget necessary to implement the target audit probability. The results offer insights on how audit sampling plans may be formulated to reduce inefficiency and what budget usage ratios should ...

show abstract

An inspection game with multiple inspectees

Cited by 26 publications

References 7 publications

Search Games: Literature and Survey

Search Games: Literature and Survey

Evolutionary Inspection and Corruption Games

Efficient Committed Budget for Implementing Target Audit Probability for Many Inspectees

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