Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
ICDCSW '06 Proceedings of the 26th IEEE International ConferenceWorkshops on Distributed Computing Systems
Inoculation strategies for victims of viruses and the sum-of-squares partition problem
Journal of Computer and System Sciences
How Many Attackers Can Selfish Defenders Catch?
HICSS '08 Proceedings of the Proceedings of the 41st Annual Hawaii International Conference on System Sciences
A Network Game with Attackers and a Defender
Algorithmica
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
The price of defense and fractional matchings
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
How many attackers can selfish defenders catch?
Discrete Applied Mathematics
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Consider a network vulnerable to viral infection, where the security software can guarantee safety only to a limited part of it. We model this practical network scenario as a non-cooperative multi-player game on a graph, with two kinds of players, a set of attackers and a protector player, representing the viruses and the system security software, respectively. We are interested in the associated Nash equilibria, where no network entity can unilaterally improve its local objective. We obtain the following results: for certain families of graphs, mixed Nash equilibria can be computed in polynomially time. These families include, among others, regular graphs, graphs with perfect matchings and trees. The corresponding price of anarchy for any mixed Nash equilibria of the game is upper and lower bounded by a linear function of the number of vertices of the graph. (We define the price of anarchy to reflect the utility of the protector). Finally, we introduce a generalised version of the game. We show that the existence problem of pure Nash equilibria here is NP complete.