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Sharing the cost of redundant items. (English) Zbl 1302.91117

Summary: We ask how to share the cost of finitely many public goods (items) among users with different needs: some smaller subsets of items are enough to serve the needs of each user, yet the cost of all items must be covered, even if this entails inefficiently paying for redundant items. Typical examples are network connectivity problems when an existing (possibly inefficient) network must be maintained.
We axiomatize a family cost ratios based on simple liability indices, one for each agent and for each item, measuring the relative worth of this item across agents, and generating cost allocation rules additive in costs.

MSC:

91B32 Resource and cost allocation (including fair division, apportionment, etc.)
91B18 Public goods
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References:

[1] Ball, M. O., Computing network reliability, Operations Res., 27, 832-838 (1979) · Zbl 0412.90030
[2] Dubey, P., The Shapley value as aircraft landing fees - revisited, Manage. Sci., 28, 869-874 (1982) · Zbl 0487.90093
[3] Holler, M.; Owen, G., Power Indices and Coalition Formation (2001), Kluwer
[4] Jackson, M., Social and Economic Networks (2008), Princeton University Press · Zbl 1149.91051
[5] Littlechild, S. C.; Thompson, G. F., Aircraft landing fees: a game theoretic approach, Bell J. Econ., 8, 186-204 (1977)
[6] Moulin, H., Axiomatic cost and surplus sharing, Ch. 6, (Arrow; Sen; Suzumura, Handbook of Social Choice and Welfare, vol. 1 (2002), Elsevier)
[7] Moulin, H., Cost sharing in networks: some open questions, Int. Game Theory Rev., 15, 134-144 (2013)
[8] Moulin, H.; Laigret, F., Equal-need sharing of a network under connectivity constraints, Games Econ. Behav., 72, 314-320 (2011) · Zbl 1236.91094
[9] Peleg, B.; Sudhölter, P., Introduction to the Theory of Cooperative Games (2007), Springer · Zbl 1193.91002
[10] Shapley, L., A value for \(n\)-person games, Ann. Math. Stud., 28, 307-318 (1953) · Zbl 0050.14404
[11] Thomson, W., Consistency and its converse: an introduction, Rev. Econ. Design, 15, 4, 257-291 (2011) · Zbl 1233.91163
[12] Thomson, W., Cost allocation and airport problems (2007), University of Rochester, Working paper
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