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Firefighting as a Game

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Book cover Algorithms and Models for the Web Graph (WAW 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8882))

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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 \(\Theta (\frac{n}{k})\) 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.

This work was supported by grants TIN2013-46181-C2-1-R, TIN2012-37930 and grant TIN2007-66523 of the Spanish Government, and project 2014-SGR1034 of the Generalitat de Catalunya.

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Authors and Affiliations

  1. ALBCOM Research Group, Computer Science Department, Universitat Politècnica de Catalunya, BarcelonaTech, 08034, Barcelona, Spain

    Carme Àlvarez, Maria J. Blesa & Hendrik Molter

Authors
  1. Carme Àlvarez
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  2. Maria J. Blesa
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  3. Hendrik Molter
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Corresponding author

Correspondence to Hendrik Molter .

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Editors and Affiliations

  1. Ryerson University, Toronto, Ontario, Canada

    Anthony Bonato

  2. University of California San Diego, La Jolla, California, USA

    Fan Chung Graham

  3. Ryerson University, Toronto, Ontario, Canada

    Paweł Prałat

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Àlvarez, C., Blesa, M.J., Molter, H. (2014). Firefighting as a Game. In: Bonato, A., Graham, F., Prałat, P. (eds) Algorithms and Models for the Web Graph. WAW 2014. Lecture Notes in Computer Science(), vol 8882. Springer, Cham. https://doi.org/10.1007/978-3-319-13123-8_9

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  • DOI: https://doi.org/10.1007/978-3-319-13123-8_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13122-1

  • Online ISBN: 978-3-319-13123-8

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