Abstract
Bachrach and Porat [1] introduced path-disruption games. In these coalitional games, agents are placed on the vertices of a graph, and one or more adversaries want to travel from a source vertex to a target vertex. In order to prevent them from doing so, the agents can form coalitions, and a coalition wins if it succeeds in blocking all paths for the adversaries. In this paper, we introduce the notion of bribery for path-disruption games. We analyze the question of how hard it is to decide whether the adversaries can bribe some of the agents such that no coalition can be formed that blocks all paths for the adversaries. We show that this problem is NP-complete, even for a single adversary. For the case of multiple adversaries, we provide an upper bound by showing that the corresponding problem is in \(\Sigma_2^p\), the second level of the polynomial hierarchy, and we suspect it is complete for this class.
This work was supported in part by DFG grant RO 1202/12-1 and the European Science Foundation’s EUROCORES program LogICCC.
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Rey, A., Rothe, J. (2011). Bribery in Path-Disruption Games. In: Brafman, R.I., Roberts, F.S., Tsoukiàs, A. (eds) Algorithmic Decision Theory. ADT 2011. Lecture Notes in Computer Science(), vol 6992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24873-3_19
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