OPTIMAL STRATEGIES IN "LOCKS, BOMBS AND TESTING" (LBT) PROBLEM FOR THE CASE OF INDEPENDENT PROTECTION

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Liu, L. (2019). OPTIMAL STRATEGIES IN "LOCKS, BOMBS AND TESTING" (LBT) PROBLEM FOR THE CASE OF INDEPENDENT PROTECTION. Unc Charlotte Electronic Theses And Dissertations.
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Abstract

This thesis constructs a Defense/Attack resource allocation model. Defender uses "locks" to protect their boxes from Attacker, and Attacker uses "bombs" to destroy as many boxes as possible. The first models of such type were given by E. Borel (1921). Later such models were extensively analyzed at the initial stage of Game Theory development under the general title (Colonel) Blotto game. Previous LBT model focuses on violence patterns produced by attackers with different levels of capacity to see whether rebel capacity influences how rebels fight (the attack timing). We sought to extend this problem into a situation with an extra setting where rebels can test vulnerability of boxes before placing bombs. In previous problem the goal was to find violence patterns produced by rebels. Here, we are interested in the optimal strategy of placing bombs. Further, our problem discusses the optimal strategy for defenders to allocate locks even when attackers have already applied their best strategy for placing bombs.After posing the basic problem we then examine several specific cases with dependent and independent, identical and non-identical, locks distribution in valued boxes by using Bayes' Posterior distribution and Monte Carlo simulations.

Details
Author

Liu, Li

Title

OPTIMAL STRATEGIES IN "LOCKS, BOMBS AND TESTING" (LBT) PROBLEM FOR THE CASE OF INDEPENDENT PROTECTION

Physical Description

1 online resource (68 pages) : PDF

Date

2019

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

This thesis constructs a Defense/Attack resource allocation model. Defender uses "locks" to protect their boxes from Attacker, and Attacker uses "bombs" to destroy as many boxes as possible. The first models of such type were given by E. Borel (1921). Later such models were extensively analyzed at the initial stage of Game Theory development under the general title (Colonel) Blotto game. Previous LBT model focuses on violence patterns produced by attackers with different levels of capacity to see whether rebel capacity influences how rebels fight (the attack timing). We sought to extend this problem into a situation with an extra setting where rebels can test vulnerability of boxes before placing bombs. In previous problem the goal was to find violence patterns produced by rebels. Here, we are interested in the optimal strategy of placing bombs. Further, our problem discusses the optimal strategy for defenders to allocate locks even when attackers have already applied their best strategy for placing bombs.After posing the basic problem we then examine several specific cases with dependent and independent, identical and non-identical, locks distribution in valued boxes by using Bayes' Posterior distribution and Monte Carlo simulations.

Genre

doctoral dissertations

Subjects--Topics

Mathematics
Statistics
Operations research

Degree

Ph.D.

Keywords

Blotto Game
Defense/Attack Model
Game Theory
Search
Testing

Subject Area

Applied Mathematics

Advisor(s)

Sonin, Isaac

Committee Members

Zhang, Zhiyi
Zhou, Qingning
Chiang, I-Hsuan Ethan

Degree Note

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2019.

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Rights Holder Information

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Identifier

Liu_uncc_0694D_12182

Permalink

http://hdl.handle.net/20.500.13093/etd:2157