We investigate the manipulation of power indices in TU-cooperative games by stimulating (subject to a budget constraint) changes in the propensity of other players to participate to the game. We display several algorithms that show that the problem is often tractable for so-called network centrality games and influence attribution games, as well as an example when optimal manipulation is intractable, even though computing power indices is feasible.
First of all, (see e.g. @cite_25 @cite_36 ) is a well-established theme in combinatorial optimization. Our removal model can be seen as a special case of node interdiction.
@cite_36 @cite_25
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A network interdiction problem usually involves two players who compete in a min‐max or max‐min game. One player, the network owner, tries to optimize its objective over the network, for example, as measured by a shortest path, maximum flow, or minimum cost flow. The opposing player, called the interdictor, alters the owner’s network to maximally impair the owner’s objective (e.g., by destroying arcs that maximize the owner’s shortest path). This chapter The field of network interdiction explores techniques for optimally impeding network operations using limited disruption actions. These disruptions may serve to remove network components, decrease arc capacities, or increase cost flows. Network interdiction models and algorithms help to identify vulnerabilities in a complex network without resorting to exhaustively enumerating worst-case scenarios, and can be coupled with fortification models to assess benefits of protecting a network. This article is presented at an introductory level to illustrate the use and breadth of interdiction models, along with a discussion of fortification and design problems. Keywords: interdiction; network; mathematical programming; mathematical models; game theory