Firefighting as a Game

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8882)

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.

Keywords

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

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Carme Àlvarez
    • 1
  • Maria J. Blesa
    • 1
  • Hendrik Molter
    • 1
  1. 1.ALBCOM Research Group, Computer Science DepartmentUniversitat Politècnica de Catalunya, BarcelonaTechBarcelonaSpain

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