One of the fundamental research challenges in network science is the centrality analysis, i.e., identifying the nodes that play the most important roles in the network. In this paper, we focus on the game-theoretic approach to centrality analysis. While various centrality indices have been proposed based on this approach, it is still unknown what distinguishes this family of indices from the more classical ones. In this paper, we answer this question by providing the first axiomatic characterization of game-theoretic centralities. Specifically, we show that every centrality can be obtained following the game-theoretic approach, and show that two natural classes of game-theoretic centrality can be characterized by two intuitive properties pertaining to Myerson's notion of Fairness.

Algorithms for NP-complete problems often have different strengths andweaknesses, and thus algorithm portfolios often outperform individualalgorithms. It is surprisingly difficult to quantify a component algorithm's contributionto such a portfolio. Reporting a component's standalone performance wronglyrewards near-clones while penalizing algorithms that have small but distinctareas of strength. Measuring a component's marginal contribution to an existingportfolio is better, but penalizes sets of strongly correlated algorithms,thereby obscuring situations in which it is essential to have at least onealgorithm from such a set. This paper argues for analyzing component algorithmcontributions via a measure drawn from coalitional game theory---the Shapleyvalue---and yields insight into a research community's progress over time. Weconclude with an application of the analysis we advocate to SAT competitions,yielding novel insights into the behaviour of algorithm portfolios, theircomponents, and the state of SAT solving technology.

We propose a novel representation for coalitional games with externalities, called Partition Decision Trees. This representation is based on rooted directed trees, where non-leaf nodes are labelled with agents' names, leaf nodes are labelled with payoff vectors, and edges indicate membership of agents in coalitions. We show that this representation is fully expressive, and for certain classes of games significantly more concise than an extensive representation. Most importantly, Partition Decision Trees are the first formalism in the literature under which most of the direct extensions of the Shapley value to games with externalities can be computed in polynomial time.

Solution concepts from cooperative game theory, such as the Shapley value or the Banzhaf index, have recently been advocated as interesting extensions of standard measures of node centrality in networks. While this direction of research is promising, the computation of game-theoretic centrality can be challenging. In an attempt to address the computational issues of game-theoretic network centrality, we present a generic framework for constructing game-theoretic network centralities. We prove that all extensions that can be expressed in this framework are computable in polynomial time. Using our framework, we present the first game-theoretic extensions of weighted and normalized degree centralities, impact factor centrality,distance-scaled and normalized betweenness centrality,and closeness and normalized closeness centralities.

We introduce a new representation scheme for coalitional games, called coalition-flow networks (CF-NETs), where the formation of effective coalitions in a task-based setting is reduced to the problem of directing flow through a network. We show that our representation is intuitive, fully expressive, and captures certain patterns in a significantly more concise manner compared to the conventional approach. Furthermore, our representation has the flexibility to express various classes of games, such as characteristic function games, coalitional games with overlapping coalitions, and coalitional games with agent types. As such, to the best of our knowledge, CF-NETs is the first representation that allows for switching conveniently and efficiently between overlapping/non-overlapping coalitions, with/without agent types. We demonstrate the efficiency of our scheme on the coalition structure generation problem, where near-optimal solutions for large instances can be found in a matter of seconds.