A (TU) cooperative game is extendable (Kikuta and Shapley, 1986) if every core allocation of each sub-game can be extended to a core allocation of the game. It is strongly extendable if any minimal vector in the upper core of any of its sub-games can be extended to a core allocation. We prove that strong extendability is equivalent to largeness of the core (Sharkey, 1982). Further, we character...

Weighted voting games are frequently used in decision making. Each voter has a weight and a proposal is accepted if the weight sum of the supporting voters exceeds a quota. One line of research is the efficient computation of so-called power indices measuring the influence of a voter. We treat the inverse problem: Given an influence vector and a power index, determine a weighted voting game suc...

Let a 1 ,. .

The Shapley-Ames Catalog of 1276 galaxies with B < 12.5 is compared with the Sanders et al. all sky sample of the 629 galaxies with 60 μm flux density > 5.24 Jy. The fraction of Shapley-Ames galaxies that are visible in the IR is found to increase from 0.006 for E and E/S0 galaxies to 0.384 for Sc galaxies. The subset of Shapley-Ames galaxies that are detected in the IR has a median blue lumino...

This paper defines a class of cooperative fuzzy games with infinite players, which is monotonically nondecreasing and continuous with respect to each player’s grade of membership. Then, the AumannShapley values for the games with fuzzy coalitions are proposed with the form of Choquet integral. The properties of the Aumann-Shapley values are also shown. Finally, the relationship between the fuzz...

The cocircuit graph of an oriented matroid is the 1-skeleton of the cellular decomposition induced by the Topological Representation Theorem due to Folkman and Lawrence (1978) [J. Folkman, J. Lawrence, Oriented matroids, J. Combin. Theory Ser. B 25 (1978) 199–236]. In this paper we exhibit a characterization of such graphs (for the uniform case) via their natural embedding into Qn—the 1-skeleto...

S. O. Hruszkewycz, C. M. Folkman, M. J. Highland, M. V. Holt, S. H. Baek, S. K. Streiffer, P. Baldo, C. B. Eom, and P. H. Fuoss Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA Center for Nanoscale Materials, Argonne National Laboratory, Argonne, I...

The Shapley Value is arguably the most important normative solution concept in coalitional games. One of its applications is in the domain of networks, where the Shapley Value is used to measure the relative importance of individual nodes. This measure, which is called node centrality, is of paramount significance in many real-world application domains including social and organisational networ...