### Abstract

In order to design robust networks, first, one has to be able to measure robustness of network topologies. In [1], a game-theoretic model, the network blocking game, was proposed for this purpose, where a network operator and an attacker interact in a zero-sum game played on a network topology, and the value of the equilibrium payoff in this game is interpreted as a measure of robustness of that topology. The payoff for a given pair of pure strategies is based on a loss-in-value function. Besides measuring the robustness of network topologies, the model can be also used to identify critical edges that are likely to be attacked. Unfortunately, previously proposed loss-in-value functions are either too simplistic or lead to a game whose equilibrium is not known to be computable in polynomial time. In this paper, we propose a new, linear loss-in-value function, which is meaningful and leads to a game whose equilibrium is efficiently computable. Furthermore, we show that the resulting game-theoretic robustness metric is related to the Cheeger constant of the topology graph, which is a well-known metric in graph theory.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 152-170 |

Number of pages | 19 |

Volume | 7638 LNCS |

DOIs | |

Publication status | Published - 2012 |

Event | 3rd International Conference on Decision and Game Theory for Security, GameSec 2012 - Budapest, Hungary Duration: Nov 5 2012 → Nov 6 2012 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7638 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 3rd International Conference on Decision and Game Theory for Security, GameSec 2012 |
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Country | Hungary |

City | Budapest |

Period | 11/5/12 → 11/6/12 |

### Fingerprint

### Keywords

- adversarial games
- blocking games
- Cheeger constant
- computational complexity
- game theory
- network robustness

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 7638 LNCS, pp. 152-170). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7638 LNCS). https://doi.org/10.1007/978-3-642-34266-0_9

**Linear loss function for the network blocking game : An efficient model for measuring network robustness and link criticality.** / Laszka, Aron; Szeszlér, Dávid; Buttyán, L.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 7638 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7638 LNCS, pp. 152-170, 3rd International Conference on Decision and Game Theory for Security, GameSec 2012, Budapest, Hungary, 11/5/12. https://doi.org/10.1007/978-3-642-34266-0_9

}

TY - GEN

T1 - Linear loss function for the network blocking game

T2 - An efficient model for measuring network robustness and link criticality

AU - Laszka, Aron

AU - Szeszlér, Dávid

AU - Buttyán, L.

PY - 2012

Y1 - 2012

N2 - In order to design robust networks, first, one has to be able to measure robustness of network topologies. In [1], a game-theoretic model, the network blocking game, was proposed for this purpose, where a network operator and an attacker interact in a zero-sum game played on a network topology, and the value of the equilibrium payoff in this game is interpreted as a measure of robustness of that topology. The payoff for a given pair of pure strategies is based on a loss-in-value function. Besides measuring the robustness of network topologies, the model can be also used to identify critical edges that are likely to be attacked. Unfortunately, previously proposed loss-in-value functions are either too simplistic or lead to a game whose equilibrium is not known to be computable in polynomial time. In this paper, we propose a new, linear loss-in-value function, which is meaningful and leads to a game whose equilibrium is efficiently computable. Furthermore, we show that the resulting game-theoretic robustness metric is related to the Cheeger constant of the topology graph, which is a well-known metric in graph theory.

AB - In order to design robust networks, first, one has to be able to measure robustness of network topologies. In [1], a game-theoretic model, the network blocking game, was proposed for this purpose, where a network operator and an attacker interact in a zero-sum game played on a network topology, and the value of the equilibrium payoff in this game is interpreted as a measure of robustness of that topology. The payoff for a given pair of pure strategies is based on a loss-in-value function. Besides measuring the robustness of network topologies, the model can be also used to identify critical edges that are likely to be attacked. Unfortunately, previously proposed loss-in-value functions are either too simplistic or lead to a game whose equilibrium is not known to be computable in polynomial time. In this paper, we propose a new, linear loss-in-value function, which is meaningful and leads to a game whose equilibrium is efficiently computable. Furthermore, we show that the resulting game-theoretic robustness metric is related to the Cheeger constant of the topology graph, which is a well-known metric in graph theory.

KW - adversarial games

KW - blocking games

KW - Cheeger constant

KW - computational complexity

KW - game theory

KW - network robustness

UR - http://www.scopus.com/inward/record.url?scp=84869464435&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-34266-0_9

DO - 10.1007/978-3-642-34266-0_9

M3 - Conference contribution

AN - SCOPUS:84869464435

SN - 9783642342653

VL - 7638 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 152

EP - 170

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -