Finding Even Cycles Even Faster
SIAM Journal on Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The economics of information security investment
ACM Transactions on Information and System Security (TISSEC)
Why Information Security is Hard-An Economic Perspective
ACSAC '01 Proceedings of the 17th Annual Computer Security Applications Conference
Near rationality and competitive equilibria in networked systems
Proceedings of the ACM SIGCOMM workshop on Practice and theory of incentives in networked systems
ICDCSW '06 Proceedings of the 26th IEEE International ConferenceWorkshops on Distributed Computing Systems
Secure or insure?: a game-theoretic analysis of information security games
Proceedings of the 17th international conference on World Wide Web
Predicted and observed user behavior in the weakest-link security game
UPSEC'08 Proceedings of the 1st Conference on Usability, Psychology, and Security
A Network Game with Attackers and a Defender
Algorithmica
A graph-theoretic network security game
International Journal of Autonomous and Adaptive Communications Systems
The Price of Stability for Network Design with Fair Cost Allocation
SIAM Journal on Computing
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
Network games with and without synchroneity
GameSec'11 Proceedings of the Second international conference on Decision and Game Theory for Security
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In a distributed system with attacks and defenses, both attackers and defenders are self-interested entities. We assume a reward-sharing scheme among interdependent defenders; each defender wishes to (locally) maximize her own total fair share to the attackers extinguished due to her involvement (and possibly due to those of others). What is the maximum amount of protection achievable by a number of such defenders against a number of attackers while the system is in a Nash equilibrium? As a measure of system protection, we adopt the Defense-Ratio (Mavronicolas et al., 2008) [20], which provides the expected (inverse) proportion of attackers caught by the defenders. In a Defense-Optimal Nash equilibrium, the Defense-Ratio matches a simple lower bound. We discover that the existence of Defense-Optimal Nash equilibria depends in a subtle way on how the number of defenders compares to two natural graph-theoretic thresholds we identify. In this vein, we obtain, through a combinatorial analysis of Nash equilibria, a collection of trade-off results: *When the number of defenders is either sufficiently small or sufficiently large, Defense-Optimal Nash equilibria may exist. The corresponding decision problem is computationally tractable for a large number of defenders; the problem becomes NP-complete for a small number of defenders and the intractability is inherited from a previously unconsidered combinatorial problem in Fractional Graph Theory. *Perhaps paradoxically, there is a middle range of values for the number of defenders where Defense-Optimal Nash equilibria do not exist.