Anja Rey

Bribery in path-disruption games

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 Σ2p, the second level of the polynomial hierarchy, and we suspect it is complete for this class.

Toward the complexity of the existence of wonderfully stable partitions and strictly core stable coalition structures in enemy-oriented hedonic games

We study the computational complexity of the existence and the verification problem for wonderfully stable partitions (WSPE and WSPV) and of the existence problem for strictly core stable coalition structures (SCSCS) in enemy-oriented hedonic games. In this note, we show that WSPV is NP-complete and both WSPE and SCSCS are DP-hard, where DP is the second level of the boolean hierarchy, and we discuss an approach for classifying the latter two problems in terms of their complexity.

Probabilistic path-disruption games

Path-disruption games, recently introduced by Bachrach and Porat [1], are coalitional games played on graphs where one or multiple adversaries each seek to reach a given target vertex from a given source vertex and a coalition of agents seeks to prevent that from happening by blocking every path from the source to the target, for each adversary. We expand their model by allowing uncertainty about the targets. In probabilistic path-disruption games, we assign to each vertex the probability that an adversary wants to reach it. We study the complexity of various problems related to such games.

Path-Disruption Games: Bribery and a Probabilistic Model

Path-disruption games, recently introduced by Bachrach and Porat, are coalitional games played on graphs where one or multiple adversaries each seeks to reach a given target vertex from a given source vertex, while a coalition of agents seeks to prevent that from happening by blocking every path from the source to the target for each adversary. These coalitional games model, for instance, security issues in computer networks. Inspired by bribery in voting, 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 will form that blocks all paths for them. We show that this problem is NP-complete for a single adversary and complete for Σ2P=NPNP

Structural Control in Weighted Voting Games

{\Sigma }^{\mathrm {P}}_{2} = \text {NP}^{\text {NP}}

Structural Control in Weighted Voting Games.

, the second level of the polynomial hierarchy, for the case of multiple adversaries. We also expand the model by allowing uncertainty about the targets: In probabilistic path-disruption games, we assign to each vertex the probability that an adversary wants to reach it, and we study the complexity of problems related to common solution concepts (such as the core and the ε-core) and other properties of such games.

False-name manipulation in weighted voting games is hard for probabilistic polynomial time

Abstract Inspired by the study of control scenarios in elections and complementing manipulation and bribery settings in cooperative games with transferable utility, we introduce the notion of structural control in weighted voting games. We model two types of influence, adding players to and deleting players from a game, with goals such as increasing a given player’s Shapley–Shubik or probabilistic Penrose–Banzhaf index in relation to the original game. We study the computational complexity of the problems of whether such structural changes can achieve the desired effect.

Representing and Solving Hedonic Games with Ordinal Preferences and Thresholds

Inspired by the study of control scenarios in elections and complementing manipulation and bribery settings in cooperative games with transferable utility, we introduce the notion of structural control in weighted voting games. We model two types of influence, adding players to and deleting players from a game, with goals such as increasing a given players Shapley-Shubik or probabilistic Penrose-Banzhaf index in relation to the original game. We study the computational complexity of the problems of whether such structural changes can achieve the desired effect.