Firefighting as a game

Carme Álvarez; Maria J. Blesa; Hendrik Molter

doi:10.1007/978-3-319-13123-8_9

Firefighting as a game

Carme Álvarez, Maria J. Blesa, Hendrik Molter

Research output: Contribution to journal › Article › peer-review

Abstract

The Firefighter Problem was proposed in 1995 [16] as a deterministic discrete-time model for the spread (and containment) of a fire. Its applications 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.

In this work, we study the problem from a game-theoretical perspective. Such a context seems very appropriate when applied to large networks, where entities may act and make decisions based on their own interests, without global coordination.

We model the Firefighter Problem as a strategic game where there is one player for each time step who decides where to place the firefighters. We show that the Price of Anarchy is linear in the general case, but at most 2 for trees. We prove that the quality of the equilibria improves when allowing coalitional cooperation among players. In general, we have that the Price of Anarchy is in Θ(n/k) where k is the coalition size. Furthermore, we show that there are topologies which have a constant Price of Anarchy even when constant sized coalitions are considered.

Original language	English
Pages (from-to)	108-119
Number of pages	12
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8882
DOIs	https://doi.org/10.1007/978-3-319-13123-8_9
State	Published - 1 Jan 2014
Externally published	Yes

Keywords

Algorithmic game theory
Coalitions
Firefighter problem
Nash equilibria
Price of anarchy
Spreading models for networks

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-319-13123-8_9

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title = "Firefighting as a game",

abstract = "The Firefighter Problem was proposed in 1995 [16] as a deterministic discrete-time model for the spread (and containment) of a fire. Its applications 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.In this work, we study the problem from a game-theoretical perspective. Such a context seems very appropriate when applied to large networks, where entities may act and make decisions based on their own interests, without global coordination.We model the Firefighter Problem as a strategic game where there is one player for each time step who decides where to place the firefighters. We show that the Price of Anarchy is linear in the general case, but at most 2 for trees. We prove that the quality of the equilibria improves when allowing coalitional cooperation among players. In general, we have that the Price of Anarchy is in Θ(n/k) where k is the coalition size. Furthermore, we show that there are topologies which have a constant Price of Anarchy even when constant sized coalitions are considered.",

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author = "Carme {\'A}lvarez and Blesa, {Maria J.} and Hendrik Molter",

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doi = "10.1007/978-3-319-13123-8_9",

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Firefighting as a game

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