Firefighting as a strategic game

The Firefighter Problem was proposed in 1995 as a deterministic discrete-time model for the spread and containment of a fire. The problem is defined on an undirected finite graph G = (V, E), where fire breaks out initially at f nodes. In each subsequent time-step, two actions occur: a certain number...

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Authors: Álvarez Faura, M. del Carme|||0000-0003-2352-0546, Blesa Aguilera, Maria Josep|||0000-0001-8246-9926, Molter, Hendrik
Format: article
Publication Date:2016
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/99674
Online Access:https://hdl.handle.net/2117/99674
https://dx.doi.org/10.1080/15427951.2015.1110542
Access Level:Open access
Keyword:Computer viruses
Game theory
Firefighting problem
Deterministic discrete-time model
Computer viruses spread
Topologies
Virus informàtics
Jocs, Teoria de
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
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oai_identifier_str oai:upcommons.upc.edu:2117/99674
network_acronym_str ES
network_name_str España
repository_id_str
spelling Firefighting as a strategic gameÁlvarez Faura, M. del Carme|||0000-0003-2352-0546Blesa Aguilera, Maria Josep|||0000-0001-8246-9926Molter, HendrikComputer virusesGame theoryFirefighting problemDeterministic discrete-time modelComputer viruses spreadTopologiesVirus informàticsJocs, Teoria deÀrees temàtiques de la UPC::Informàtica::Informàtica teòricaThe Firefighter Problem was proposed in 1995 as a deterministic discrete-time model for the spread and containment of a fire. The problem is defined on an undirected finite graph G = (V, E), where fire breaks out initially at f nodes. In each subsequent time-step, two actions occur: a certain number b of firefighters are placed on nonburning nodes, permanently protecting them from the fire, then the fire spreads to all nondefended neighbors of the nodes on fire. Because the graph is finite, at some point each node is either on fire or saved, and thus the fire cannot spread further. One of the objectives for the problem is to place the firefighters in such a way that the number of saved nodes is maximized. The applications of the Firefighter Problem reach from real fires to the spreading of diseases and the containment of floods. Furthermore, it can be used to model the spread of computer viruses or viral marketing in communication networks. Most research on the problem considers the case in which the fire starts in a single place (i.e., f = 1), and in which the budget of available firefighters per time-step is one (i.e., b = 1). So does the work in this study. This configuration already leads to hard problems and, even in this case, the problem is known to be NP-hard. In this work, we study the problem from a game-theoretical perspective. We introduce a strategic game model for the Firefighter Problem to tackle its complexity from a different angle. We refer to it as the Firefighter Game. Such a game-based context seems very appropriate when applied to large networks where entities may act and make decisions based on their own interests, without global coordination. At every time-step of the game, a player decides whether to place a new firefighter in a nonburning node of the graph. If so, he must decide where to place it. By placing it, the player is indirectly deciding which nodes to protect at that time-step. We define different utility functions in order to model selfish and nonselfish scenarios, which lead to equivalent games. We show that the Price of Anarchy (PoA) is linear for a particular family of graphs, but it is at most two for trees. We also analyze the quality of the equilibria when coalitions among players are allowed. It turns out that it is possible to compute an equilibrium in polynomial time, even for constant-size coalitions. This yields to a polynomial time approximation algorithm for the problem and its approximation ratio equals the PoA of the corresponding game. We show that for some specific topologies, the PoA is constant when constant-size coalitions are considered.Peer ReviewedTaylor & Francis20162016-03-3120172017-01-19journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/99674https://dx.doi.org/10.1080/15427951.2015.1110542reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengMinisterio de Economía y Competitividad http://doi.org/10.13039/501100003329 TIN2013-46181-C2-1-R MODELOS Y METODOS COMPUTACIONALES PARA DATOS MASIVOS ESTRUCTURADOSopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/996742026-05-27T15:37:01Z
dc.title.none.fl_str_mv Firefighting as a strategic game
title Firefighting as a strategic game
spellingShingle Firefighting as a strategic game
Álvarez Faura, M. del Carme|||0000-0003-2352-0546
Computer viruses
Game theory
Firefighting problem
Deterministic discrete-time model
Computer viruses spread
Topologies
Virus informàtics
Jocs, Teoria de
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
title_short Firefighting as a strategic game
title_full Firefighting as a strategic game
title_fullStr Firefighting as a strategic game
title_full_unstemmed Firefighting as a strategic game
title_sort Firefighting as a strategic game
dc.creator.none.fl_str_mv Álvarez Faura, M. del Carme|||0000-0003-2352-0546
Blesa Aguilera, Maria Josep|||0000-0001-8246-9926
Molter, Hendrik
author Álvarez Faura, M. del Carme|||0000-0003-2352-0546
author_facet Álvarez Faura, M. del Carme|||0000-0003-2352-0546
Blesa Aguilera, Maria Josep|||0000-0001-8246-9926
Molter, Hendrik
author_role author
author2 Blesa Aguilera, Maria Josep|||0000-0001-8246-9926
Molter, Hendrik
author2_role author
author
dc.subject.none.fl_str_mv Computer viruses
Game theory
Firefighting problem
Deterministic discrete-time model
Computer viruses spread
Topologies
Virus informàtics
Jocs, Teoria de
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
topic Computer viruses
Game theory
Firefighting problem
Deterministic discrete-time model
Computer viruses spread
Topologies
Virus informàtics
Jocs, Teoria de
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
description The Firefighter Problem was proposed in 1995 as a deterministic discrete-time model for the spread and containment of a fire. The problem is defined on an undirected finite graph G = (V, E), where fire breaks out initially at f nodes. In each subsequent time-step, two actions occur: a certain number b of firefighters are placed on nonburning nodes, permanently protecting them from the fire, then the fire spreads to all nondefended neighbors of the nodes on fire. Because the graph is finite, at some point each node is either on fire or saved, and thus the fire cannot spread further. One of the objectives for the problem is to place the firefighters in such a way that the number of saved nodes is maximized. The applications of the Firefighter Problem reach from real fires to the spreading of diseases and the containment of floods. Furthermore, it can be used to model the spread of computer viruses or viral marketing in communication networks. Most research on the problem considers the case in which the fire starts in a single place (i.e., f = 1), and in which the budget of available firefighters per time-step is one (i.e., b = 1). So does the work in this study. This configuration already leads to hard problems and, even in this case, the problem is known to be NP-hard. In this work, we study the problem from a game-theoretical perspective. We introduce a strategic game model for the Firefighter Problem to tackle its complexity from a different angle. We refer to it as the Firefighter Game. Such a game-based context seems very appropriate when applied to large networks where entities may act and make decisions based on their own interests, without global coordination. At every time-step of the game, a player decides whether to place a new firefighter in a nonburning node of the graph. If so, he must decide where to place it. By placing it, the player is indirectly deciding which nodes to protect at that time-step. We define different utility functions in order to model selfish and nonselfish scenarios, which lead to equivalent games. We show that the Price of Anarchy (PoA) is linear for a particular family of graphs, but it is at most two for trees. We also analyze the quality of the equilibria when coalitions among players are allowed. It turns out that it is possible to compute an equilibrium in polynomial time, even for constant-size coalitions. This yields to a polynomial time approximation algorithm for the problem and its approximation ratio equals the PoA of the corresponding game. We show that for some specific topologies, the PoA is constant when constant-size coalitions are considered.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-03-31
2017
2017-01-19
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/99674
https://dx.doi.org/10.1080/15427951.2015.1110542
url https://hdl.handle.net/2117/99674
https://dx.doi.org/10.1080/15427951.2015.1110542
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://doi.org/10.13039/501100003329 TIN2013-46181-C2-1-R MODELOS Y METODOS COMPUTACIONALES PARA DATOS MASIVOS ESTRUCTURADOS
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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