×

Cost allocation in spanning network enterprises with stochastic connection costs. (English) Zbl 1045.91006

This paper analyzes the problem of network formation and cost allocation that arises when customers need to be connected to a single service provider through a network and the cost of connections are stochastic. The author shows that how an ‘optimal’ network is determined and the core of the corresponding stochastic spanning tree game is non-empty. For allocating the random costs of an optimal network, the author introduces a two stage bird allocation and shows that it results in a core allocation for stochastic spanning tree games. See also C. G. Bird [Networks 6, 335–350 (1976; Zbl 0357.90083)].

MSC:

91A12 Cooperative games
91A43 Games involving graphs
91A15 Stochastic games, stochastic differential games

Citations:

Zbl 0357.90083
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bird, C., On cost allocation for a spanning tree: A game theoretic approach, Networks, 6, 335-350 (1976) · Zbl 0357.90083
[2] Claus, A., Granot, D., 1976. Game theory application to cost allocation for a spanning tree. Working paper 402, University of British Columbia; Claus, A., Granot, D., 1976. Game theory application to cost allocation for a spanning tree. Working paper 402, University of British Columbia
[3] Claus, A.; Kleitman, D., Cost allocation for a spanning tree, Networks, 3, 289-304 (1973) · Zbl 0338.90031
[4] Dijkstra, E., A note on two problems in connection with graphs, Numer. Math., 1, 269-271 (1959) · Zbl 0092.16002
[5] Goovaerts, M.; De Vylder, F.; Haezendonck, J., Insurance Premiums (1984), North-Holland: North-Holland Amsterdam · Zbl 0532.62082
[6] Granot, D.; Huberman, G., On minimum cost spanning tree games, Math. Programming, 21, 1-18 (1981) · Zbl 0461.90099
[7] Megiddo, N., Computational complexity of the game theory approach to cost allocation for a tree, Math. Oper. Res., 3, 189-196 (1978) · Zbl 0397.90111
[8] Prim, R., Shortest connection networks and some generalizations, Bell Syst. Tech. J., 36, 1389-1401 (1957)
[9] Sharkey, W., Network models in economics, (Moder, J.; Elmaghraby, S., The Handbook of Operations Research (1991), Van Nostrand Reinhold: Van Nostrand Reinhold New York) · Zbl 0861.90023
[10] Suijs, J., Cooperative Decision-Making under Risk (1999), Kluwer Academic: Kluwer Academic Boston · Zbl 0973.90038
[11] Suijs, J.; Borm, P., Stochastic cooperative games: superadditivity, convexity, and certainty equivalents, Games Econ. Behav., 27, 331-345 (1999) · Zbl 0937.91020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.