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## SANDIA REPORT Modeling Attacker-Defender Interactions in Information Networks Modeling Attacker-Defender Interactions in Information Networks

### Citations

4216 |
Game Theory
- Fudenberg, Tirole
- 1991
(Show Context)
Citation Context .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Aspnes Model with Cost Sharing 15 4 An Attacker-Defender Game 19 References 21 5 List of Figures 2.1 Markov process on a Star Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6 List of Tables 7 8 Chapter 1 Introduction Our general framework for analyzing the behavior of non-cooperative nodes in a network under attack is a game-theoretic model of inoculation against viral infection introduced by Aspnes et al. [1], which we brief y describe (for terminology and concepts of game theory, see [4]). Each “player” in this game is a node in an undirected connected graph G with n nodes. Nodes represent network hosts that might become infected, while edges represent direct communication links through which a virus might spread. Each node has two possible pure strategies: either do nothing, or inoculate itself (i.e. install anti-viral protection). After the nodes have made their choices, an attacker selects one node uniformly at random to infect. Infection then propagates through the graph; a non-inoculated node becomes infected if any of its neighbors are infected. Let I be the set of inoc... |

67 | Inoculation strategies for victims of viruses and the sum-of-squares partition problem
- Aspnes, Chang, et al.
(Show Context)
Citation Context ... . . . . . . . . . . 12 2.2 Adding Propagation Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Aspnes Model with Cost Sharing 15 4 An Attacker-Defender Game 19 References 21 5 List of Figures 2.1 Markov process on a Star Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6 List of Tables 7 8 Chapter 1 Introduction Our general framework for analyzing the behavior of non-cooperative nodes in a network under attack is a game-theoretic model of inoculation against viral infection introduced by Aspnes et al. [1], which we brief y describe (for terminology and concepts of game theory, see [4]). Each “player” in this game is a node in an undirected connected graph G with n nodes. Nodes represent network hosts that might become infected, while edges represent direct communication links through which a virus might spread. Each node has two possible pure strategies: either do nothing, or inoculate itself (i.e. install anti-viral protection). After the nodes have made their choices, an attacker selects one node uniformly at random to infect. Infection then propagates through the graph; a non-inoculated nod... |

18 | Online multicast with egalitarian cost sharing.
- Charikar, Karloff, et al.
- 2008
(Show Context)
Citation Context ...oint is 1 n(1−φλ ) = C . IfC is larger than this, then no node has any incentive to inoculate. 14 Chapter 3 Aspnes Model with Cost Sharing A crucial feature of the Aspnes model is that one node can benef t from another node’s decision to inoculate. We have considered what happens when some nodes seek to avoid the cost of inoculation and force others to inoculate, and how nodes can agree to share costs by taking turns. We now consider a model in which one node can pay part of the cost of another node’s inoculation. Such cost-sharing models of network games have been studied by several authors ([2, 3]), but this idea has not, so far as we are aware, been applied to the Aspnes model previously. Formally, we have the same situation as before, but now the strategy of player i is a vector ai = (ai1 . . .a i n), where aij is the contribution made by node i to the inoculation of node j. Node j will be inoculated if and only if ∑ 1≤i≤n aij ≥C . The individual cost for node i is ∑ 1≤ j≤n aij +L ki n where as before ki is the size of the component κi containing node i (or zero if i is inoculated). We have the following Theorem 3.0.1. Let σ = (a1,a2, . . .an) be an equilibrium in the cost-sharing As... |

14 | Circumventing the price of anarchy: Leading dynamics to good behavior,
- Balcan, Blum, et al.
- 2010
(Show Context)
Citation Context ...oint is 1 n(1−φλ ) = C . IfC is larger than this, then no node has any incentive to inoculate. 14 Chapter 3 Aspnes Model with Cost Sharing A crucial feature of the Aspnes model is that one node can benef t from another node’s decision to inoculate. We have considered what happens when some nodes seek to avoid the cost of inoculation and force others to inoculate, and how nodes can agree to share costs by taking turns. We now consider a model in which one node can pay part of the cost of another node’s inoculation. Such cost-sharing models of network games have been studied by several authors ([2, 3]), but this idea has not, so far as we are aware, been applied to the Aspnes model previously. Formally, we have the same situation as before, but now the strategy of player i is a vector ai = (ai1 . . .a i n), where aij is the contribution made by node i to the inoculation of node j. Node j will be inoculated if and only if ∑ 1≤i≤n aij ≥C . The individual cost for node i is ∑ 1≤ j≤n aij +L ki n where as before ki is the size of the component κi containing node i (or zero if i is inoculated). We have the following Theorem 3.0.1. Let σ = (a1,a2, . . .an) be an equilibrium in the cost-sharing As... |

14 | Guide to preparing SAND reports - Locke - 1998 |