Title: A dynamic defender-attacker optimization model; modeling different attackers as exogenous forces
Language: English
Authors: Wanek, Roman 
Qualification level: Diploma
Keywords: Verteidiger; Angreifer; Terror; Pontryagins-Maximumsprinzip; nichtlinear; Kontrolltheorie
defender; attacker; terror; security; Pontryagins-Maximum-Principle; nonlinear; optimal-control
Advisor: Tragler, Gernot
Assisting Advisor: Grass, Dieter
Issue Date: 2011
Number of Pages: 83
Qualification level: Diploma
Abstract: 
Basierend auf Ideen eines spieltheoretischen Modells, das in der Arbeit "The Timing and Deterrence of Terrorist Attacks" von Kjell Hausken und Jun Zhuang präsentiert wird, wird in dieser Diplomarbeit ein nichtlineares Optimierungsproblem formuliert dessen Hintergrund ein aktueller Konflikt in Kolumbien ist. In diesem Modell muss sich der repräsentative Agent entscheiden wieviel von seinem Budget er für den Sicherheitslevel einer Anlage, die er zu verteidigen versucht, ausgibt und wieviel er direkt in den Wert derselbigen investiert. Der zweite Spieler des spieltheoretischen Modells wird als exogene Kraft in Form von "Reaktionsfuntionen" modelliert und das Modell mit dem Pontryagin'schen Maximumsprinzip gelöst, wobei es das Ziel dieser Arbeit ist zu untersuchen wie sich verschiedene Arten von Angreifern auf die Resultate auswirken.

Based on the ideas of a game theoretical model presented in the paper "The Timing and Deterrence of Terrorist Attacks" by Kjell Hausken and Jun Zhuang, in this thesis a nonlinear optimal control model is formulated, which is linked to an ongoing conflict in Colombia. In this framework the decision maker has to decide wether to invest a normalised budget into the security level of an asset he tries to defend against an attacker or directly into the asset in form of repairs or upgrades. The second player of the game theoretical model will be modeled as an exogenous force in form of a "reaction function". This nonlinear optimal control model then will be solved by applying Pontryagin's Maximum Principle.
The main goal of this thesis is to analyse how different kinds of attackers affect the model results and optimal solutions. In a first step simple, strictly monotone and strictly convex (concave) reaction functions will be applied. For a given set of parameters values, which will model a well organised attacker, the problem will be solved and a sensitivity analysis will be carried out. In an extension, more complex, convex-concave (concave-convex) reaction functions will be used and it will be analysed how they affect the model outcome.
URI: https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-51102
http://hdl.handle.net/20.500.12708/10057
Library ID: AC07811717
Organisation: E105 - Institut für Wirtschaftsmathematik 
Publication Type: Thesis
Hochschulschrift
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