Sharing the cost of a network: core and core allocations

Abstract

Sharing the cost of a network Koster, M.A.L.; Molina, E.; Sprumont, Y.; Tijs, S.H.

Equal-need sharing of a network under connectivity constraints

“…4 See Littlechild and Owen (1973), Koster et al (2001), Wang (2007aWang ( , 2007b need maintenance). Call this the 2*-connectivity constraint.…”

“…12 For instance Thomas (1975). 13 Starting with Littlechild and Owen (1973), and more recently Koster et al (2001), Wang (2007aWang ( , 2007b. In a general problem where the needs of a users can be met by a variety of overlapping subsets of resources, the equalneed and Shapley value solutions are typically different.…”

Cost Sharing in Networks: Some Open Questions

“…The Shapley value simply divides the cost of each edge between all users who need it, namely the users downstream from the source. This model is easily generalized to a tree network connecting all users to the source, with similar properties (Koster et al, 2001;Ni and Wang, 2008). A much broader generalization of the aircraft landing fees model involves a fixed set of abstract nonrival items, and users with single minded needs.…”

“…Recent work on the fixed tree model includes Koster et al [2001] and Ni and Wang [2008], who discuss other core selections alongside the canonical one just described.…”

A network flow approach to cost allocation for rooted trees

“…We apply this algorithm to the egalitarian allocation of our game. The egalitarian allocation of the standard tree game was also investigated by Koster, Molina, Sprumont, and Tijs [10] without reference to the lexicographically optimal flow.…”