Abstract
In this paper we present an axiomatic characterization of the weighted Shapley value of the optimistic TU game associated with a minimum cost spanning tree problem. This characterization is based on two monotonicity properties, population monotonicity (if a new agent joint the society nobody is worse off) and the strong cost monotonicity (if the connection cost between any pair of agents increases nobody is better off), and weighted share of extra costs (the extra costs should be divided proportionally to the weights of the agents).
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References
Bergantiños G., Lorenzo L. (2004). A non-cooperative approach to the cost spanning tree problem. Math Methods Oper Res 59: 393–403
Bergantiños, G., Lorenzo-Freire, S.: “Optimistic” weighted Shapley rules in minimum cost spanning tree problems. Eur J Oper Res (forthcoming). Available at http://webs.uvigo.es/gbergant/papers/optShapley.pdf (2007)
Bergantiños, G., Vidal-Puga, J.J.: A fair rule in cost spanning tree problems. J Econ Theory (forthcoming). Available at http://econwpa.wustl.edu:80/eps/game/papers/0504/0504001.pdf (2006a)
Bergantiños, G., Vidal-Puga, J.J.: The optimistic TU game in minimum cost spanning tree problems. Int J Game Theory (forthcoming). Available at http://econwpa.wustl.edu:80/eps/game/papers/0509/ 0509001.pdf (2006b)
Bergantiños, G., Vidal-Puga, J.J.: Several approaches to the same rule in cost spanning tree problems. Mimeo. Available at http://webs.uvigo.es/gbergant/papers/cstapproaches.pdf (2006c)
Bird C.G. (1976). On cost allocation for a spanning tree: a game theoretic approach. Networks 6: 335–350
Chun Y. (2006). No-envy in queueing problems. Econ Theory 29: 152–162
Dominguez D., Thomson W. (2006). A new solution to the problem of adjudicating conflicting claims. Econ Theory 28: 283–307
Dutta B., Kar A. (2004). Cost monotonicity, consistency and minimum cost spanning tree games. Games Econ Behav 48: 223–248
Feltkamp V., Tijs S., Muto S. (1994). On the irreducible core and the equal remaining obligation rule of minimum cost extension problems. Mimeo, Tilburg University
Granot D., Huberman G. (1981). Minimum cost spanning tree games. Math Program 21: 1–18
Granot D., Huberman G. (1984). On the core and nucleolus of the minimum cost spanning tree games. Math Program 29: 323–347
Kalai E., Samet D. (1987). On weighted Shapley values. Int J Game Theory 16: 205–222
Kar A. (2002). Axiomatization of the Shapley value on minimum cost spanning tree games. Games Econ Behav 38: 265–277
Kruskal J. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem. Proc Am Math Soc 7: 48–50
Owen G. (1968). A note on the Shapley value. Manage Sci 14: 731–732
Prim R.C. (1957). Shortest connection networks and some generalizations. Bell Syst Technol J 36: 1389–1401
Shapley, L.S.: Additive and non-additive set functions. PhD Thesis, Department of Mathematics, Princeton University (1953a)
Shapley L.S. (1953b). A value for n-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the Theory of Games II. Princeton, Princeton University Press, pp 307–317
Tauman Y., Watanabe N. (2007). The Shapley value of a patent licensing game: the asymptotic equivalence to non-cooperative results. Econ Theory 30: 135–149
Tijs S., Branzei R., Moretti S., Norde H. (2006). Obligation rules for minimum cost spanning tree situations and their monotonicity properties. Eur J Oper Res 175: 121–134
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Bergantiños, G., Lorenzo-Freire, S. A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems. Economic Theory 35, 523–538 (2008). https://doi.org/10.1007/s00199-007-0248-1
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DOI: https://doi.org/10.1007/s00199-007-0248-1