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Hitting a path: a generalization of weighted connectivity via game theory

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  • Dávid Szeszlér

    (Budapest University of Technology and Economics)

Abstract

Applying game-theoretical tools for measuring the reliability of a network has become very common. The basic idea is very natural: analyzing an appropriately defined attacker–defender game might give rise to a relevant security metric. In this paper we consider a very natural set of games: the Defender chooses a path P between two given nodes and the Attacker chooses a network element a (that is, an edge or a node). In all cases, the Attacker has to pay a given cost of attack c(a); if, however, a is on P then he also gains a given profit of d(a). We determine the value of various versions of this game and show that the thus arising reliability metrics provide a generalization of weighted connectivity of graphs. We also prove that the values of the games and optimum mixed strategies for both players can be computed in strongly polynomial time.

Suggested Citation

  • Dávid Szeszlér, 2019. "Hitting a path: a generalization of weighted connectivity via game theory," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 72-85, July.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:1:d:10.1007_s10878-018-0366-7
    DOI: 10.1007/s10878-018-0366-7
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    References listed on IDEAS

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    1. Alan Washburn & Kevin Wood, 1995. "Two-Person Zero-Sum Games for Network Interdiction," Operations Research, INFORMS, vol. 43(2), pages 243-251, April.
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