Firewalls and Internet security: repelling the wily hacker
Firewalls and Internet security: repelling the wily hacker
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
ICDCSW '06 Proceedings of the 26th IEEE International ConferenceWorkshops on Distributed Computing Systems
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
A graph-theoretic network security game
WINE'05 Proceedings of the First international conference on Internet and Network Economics
New results on the complexity of uniformly mixed nash equilibria
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Network game with attacker and protector entities
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
On the complexity of uniformly mixed nash equilibria and related regular subgraph problems
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
A graph-theoretic network security game
International Journal of Autonomous and Adaptive Communications Systems
Network Security Validation Using Game Theory
OTM '09 Proceedings of the Confederated International Workshops and Posters on On the Move to Meaningful Internet Systems: ADI, CAMS, EI2N, ISDE, IWSSA, MONET, OnToContent, ODIS, ORM, OTM Academy, SWWS, SEMELS, Beyond SAWSDL, and COMBEK 2009
Strategic multiway cut and multicut games
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
The price of defense and fractional matchings
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
Network games with and without synchroneity
GameSec'11 Proceedings of the Second international conference on Decision and Game Theory for Security
How many attackers can selfish defenders catch?
Discrete Applied Mathematics
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We consider a strategic game with two classes of confronting randomized players on a graph G(V, E): νattackers, each choosing vertices and wishing to minimize the probability of being caught, and a defender, who chooses edges and gains the expected number of attackers it catches. The Price of Defense is the worst-case ratio, over all Nash equilibria, of the optimal gain of the defender over its gain at a Nash equilibrium. We provide a comprehensive collection of trade-offs between the Price of Defense and the computational efficiency of Nash equilibria. – Through reduction to a Two-Players, Constant-Sum Game, we prove that a Nash equilibrium can be computed in polynomial time. The reduction does not provide any apparent guarantees on the Price of Defense. – To obtain such, we analyze several structured Nash equilibria: – In a Matching Nash equilibrium, the support of the defender is an Edge Cover. We prove that they can be computed in polynomial time, and they incur a Price of Defense of α(G), the Independence Number of G. – In a Perfect Matching Nash equilibrium, the support of the defender is a Perfect Matching. We prove that they can be computed in polynomial time, and they incur a Price of Defense of $\frac{|V|}{2}$. – In a Defender Uniform Nash equilibrium, the defender chooses uniformly each edge in its support. We prove that they incur a Price of Defense falling between those for Matching and Perfect Matching Nash Equilibria; however, it is ${\cal NP}$-complete to decide their existence. – In an Attacker Symmetric and Uniform Nash equilibrium, all attackers have a common support on which each uses a uniform distribution. We prove that they can be computed in polynomial time and incur a Price of Defense of either $\frac{|V|}{2}$ or α(G).