Addressing Problem Size in Stackelberg Security Games.

In this thesis we present algorithmic and modeling contributions for Stackelberg games that help address challenges due to problem size. Stackelberg games consider that one player, called leader, commits a strategy first and the other player, named follower, observes this strategy and plays a best r...

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Detalhes bibliográficos
Autor: Bucarey López, Víctor
Formato: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2017
País:Chile
OAI Identifier:oai:repositorio.anid.cl:10533/209821
Acesso em linha:https://hdl.handle.net/10533/209821
Access Level:acceso abierto
Palavra-chave:Ingeniería y Tecnología
Otras Ingenierías y Tecnologías
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dc.title.es_CL.fl_str_mv Addressing Problem Size in Stackelberg Security Games.
dc.title.none.fl_str_mv Addressing problem size in stackelberg security games.
title Addressing Problem Size in Stackelberg Security Games.
spellingShingle Addressing Problem Size in Stackelberg Security Games.
Bucarey López, Víctor
Ingeniería y Tecnología
Otras Ingenierías y Tecnologías
Otras Ingenierías y Tecnologías
title_short Addressing Problem Size in Stackelberg Security Games.
title_full Addressing Problem Size in Stackelberg Security Games.
title_fullStr Addressing Problem Size in Stackelberg Security Games.
title_full_unstemmed Addressing Problem Size in Stackelberg Security Games.
title_sort Addressing Problem Size in Stackelberg Security Games.
dc.creator.none.fl_str_mv Bucarey López, Víctor
author Bucarey López, Víctor
author_facet Bucarey López, Víctor
author_role author
dc.contributor.advisor.none.fl_str_mv Ordoñez Pizarro, Fernando
dc.contributor.institution.es_CL.fl_str_mv UNIVERSIDAD DE CHILE
dc.subject.oecd1n.es_CL.fl_str_mv Ingeniería y Tecnología
topic Ingeniería y Tecnología
Otras Ingenierías y Tecnologías
Otras Ingenierías y Tecnologías
dc.subject.oecd2n.es_CL.fl_str_mv Otras Ingenierías y Tecnologías
dc.subject.oecd3n.es_CL.fl_str_mv Otras Ingenierías y Tecnologías
description In this thesis we present algorithmic and modeling contributions for Stackelberg games that help address challenges due to problem size. Stackelberg games consider that one player, called leader, commits a strategy first and the other player, named follower, observes this strategy and plays a best response. In this thesis we address the problem size that arises due to large leader action space, or because the interaction between the leader and the follower is evolving over time. In the last case, we model this interaction as a stochastic game. In Chapter 1, we present a situation where a defender, the leader in the Stackelberg game, has to pair up resources to do patrol labor. In this case the set of pure strategies is exponentially large. We show a mixed integer programming formulation with polynomial number of variables and an exponentially sized set of constraints that can be separated in polynomial time. Moreover, we design sampling methods to retrieve implementable strategies for the defender. We show a case study in border patrolling labor of Carabineros de Chile. We show that our model with the cut-generation scheme outperforms other models, scaling up to large size instances. In Chapter 2 we show a method to scale up an algorithm to compute optimal strategies in the context of opportunistic crime modelling, via a multi-layer clustering. Inside each cluster the algorithm can scale up in reasonable times. This methodology can be adapted to any problem where geographical aspects are important and the number of targets is large. In Chapter 3 we face the problem of computing stationary policies that form a strong Stackelberg equilibrium in stochastic games. We find a family of instances where both, Value Iteration and Policy iteration converge to a strong Stackelberg equilibrium. We show via a counterexample that this is not always possible. Also, we show computationally that Value Iteration applied to security games instances seem to always converge to a unique strong Stackelberg equilibrium. Finally, we study mathematical programming formulations to compute a Stackelberg equilibrium in stochastic games. Finally, in Chapter 4 we study a dynamic game, where a central agency aim to avoid the overexploitation of water, controlling the marginal cost of water extraction in agriculture. We model this situation as a stochastic game where the leader is the central agency and the followers are farmers who seek to maximize an instantaneous reward function at each period. In our setting, the leader maximizes the total discounted reward of the whole set of farmers. We find that we can achieve better levels of water in the steady-state by controlling the marginal cost. Finally, we propose a robust optimization approach to include uncertainty in our model.
publishDate 2017
dc.date.issued.es_CL.fl_str_mv 2017
dc.date.accessioned.none.fl_str_mv 2018-04-11T19:16:16Z
2022-08-18T00:44:40Z
dc.date.available.none.fl_str_mv 2018-04-11T19:16:16Z
2022-08-18T00:44:40Z
dc.type.none.fl_str_mv Tesis Doctorado
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status_str publishedVersion
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dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10533/209821
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url https://hdl.handle.net/10533/209821
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spelling UNIVERSIDAD DE CHILEBucarey López, Víctor2017https://hdl.handle.net/10533/209821http://purl.org/coar/access_right/c_abf2Otras Ingenierías y TecnologíasOtras Ingenierías y TecnologíasIngeniería y TecnologíaAddressing Problem Size in Stackelberg Security Games.Ordoñez Pizarro, FernandoUNIVERSIDAD DE CHILEChileBucarey López, Víctor2018-04-11T19:16:16Z2022-08-18T00:44:40Z2018-04-11T19:16:16Z2022-08-18T00:44:40Z2017In this thesis we present algorithmic and modeling contributions for Stackelberg games that help address challenges due to problem size. Stackelberg games consider that one player, called leader, commits a strategy first and the other player, named follower, observes this strategy and plays a best response. In this thesis we address the problem size that arises due to large leader action space, or because the interaction between the leader and the follower is evolving over time. In the last case, we model this interaction as a stochastic game. In Chapter 1, we present a situation where a defender, the leader in the Stackelberg game, has to pair up resources to do patrol labor. In this case the set of pure strategies is exponentially large. We show a mixed integer programming formulation with polynomial number of variables and an exponentially sized set of constraints that can be separated in polynomial time. Moreover, we design sampling methods to retrieve implementable strategies for the defender. We show a case study in border patrolling labor of Carabineros de Chile. We show that our model with the cut-generation scheme outperforms other models, scaling up to large size instances. In Chapter 2 we show a method to scale up an algorithm to compute optimal strategies in the context of opportunistic crime modelling, via a multi-layer clustering. Inside each cluster the algorithm can scale up in reasonable times. This methodology can be adapted to any problem where geographical aspects are important and the number of targets is large. In Chapter 3 we face the problem of computing stationary policies that form a strong Stackelberg equilibrium in stochastic games. We find a family of instances where both, Value Iteration and Policy iteration converge to a strong Stackelberg equilibrium. We show via a counterexample that this is not always possible. Also, we show computationally that Value Iteration applied to security games instances seem to always converge to a unique strong Stackelberg equilibrium. Finally, we study mathematical programming formulations to compute a Stackelberg equilibrium in stochastic games. Finally, in Chapter 4 we study a dynamic game, where a central agency aim to avoid the overexploitation of water, controlling the marginal cost of water extraction in agriculture. We model this situation as a stochastic game where the leader is the central agency and the followers are farmers who seek to maximize an instantaneous reward function at each period. In our setting, the leader maximizes the total discounted reward of the whole set of farmers. We find that we can achieve better levels of water in the steady-state by controlling the marginal cost. 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