The Core of an Extended Tree Game: A New Characterisation
Cost allocation problems on networks can be interpreted as cooperative games on a graph structure. In the classical standard tree game, the cost of a service delivered, by a source has to be allocated between homogeneous users at the vertices. But, modern networks have also the capacity to supply different (levels of) services. For example, a cable network that provides diff erent television standards. Users that choose different levels of service can not be treated equally. The extended tree game accounts for such differences between users. Here, players are characterised by their level of demand, consequently the implications on the cost structure of the problem can be considered. We show how an ET-game can be formulated as the sum of unanimity games. This observation enables us to directly calculate the weighted Shapley values and to identify the core of an ET-game.
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- repec:ner:tilbur:urn:nbn:nl:ui:12-80718 is not listed on IDEAS
- Borm, P.E.M. & Hamers, H.J.M. & Hendrickx, R.L.P., 2001.
"Operations Research Games : A Survey,"
2001-45, Tilburg University, Center for Economic Research.
- Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 9(2), pages 139-199, December.
- Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer, vol. 21(1), pages 27-39.
- René Brink & Gerard Laan & Valeri Vasil’ev, 2007. "Component efficient solutions in line-graph games with applications," Economic Theory, Springer, vol. 33(2), pages 349-364, November.
- Monderer, Dov & Samet, Dov, 2002. "Variations on the shapley value," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 54, pages 2055-2076 Elsevier.
- Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
- Sharkey, W.W., 1991. "Network Models in Economics," Papers 69, Bell Communications - Economic Research Group.
- Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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