Bipartite graphs and their applications
Bipartite graphs and their applications
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Inoculation strategies for victims of viruses and the sum-of-squares partition problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A graph-theoretic network security game
WINE'05 Proceedings of the First international conference on Internet and Network Economics
The complexity of uniform Nash equilibria and related regular subgraph problems
Theoretical Computer Science
Game theoretical aspects in modeling and analyzing the shipping industry
ICCL'11 Proceedings of the Second international conference on Computational logistics
The price of defense and fractional matchings
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
A graph-theoretic network security game
WINE'05 Proceedings of the First international conference on Internet and Network Economics
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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Consider an information network with harmful procedures called attackers (e.g., viruses); each attacker uses a probability distribution to choose a node of the network to damage. Opponent to the attackers is the system protector scanning and cleaning from attackers some part of the network (e.g., an edge or a path), which it chooses independently using another probability distribution. Each attacker wishes to maximize the probability of escaping its cleaning by the system protector; towards a conflicting objective, the system protector aims at maximizing the expected number of cleaned attackers. We model this network scenario as a non-cooperative strategic game on graphs. We focus on the special case where the protector chooses a single edge. We are interested in the associated Nash equilibria, where no network entity can unilaterally improve its local objective. We obtain the following results: – No instance of the game possesses a pure Nash equilibrium. –Every mixed Nash equilibrium enjoys a graph-theoretic structure, which enables a (typically exponential) algorithm to compute it. – We coin a natural subclass of mixed Nash equilibria, which we call matching Nash equilibria, for this game on graphs. Matching Nash equilibria are defined using structural parameters of graphs, such as independent sets and matchings. –We derive a characterization of graphs possessing matching Nash equilibria. The characterization enables a linear time algorithm to compute a matching Nash equilibrium on any such graph with a given independent set and vertex cover. – Bipartite graphs are shown to satisfy the characterization. So, using a polynomial-time algorithm to compute a perfect matching in a bipartite graph, we obtain, as our main result, an efficient graph-theoretic algorithm to compute a matching Nash equilibrium on any instance of the game with a bipartite graph.