Abstract
We present a new model for cost sharing in minimum cost spanning tree problems to allow planners to identify how many agents merge. Under this new framework, in contrast to the traditional model, there are rules that satisfy the property of Merge-proofness. Furthermore, strengthening this property and adding some others, such as Population Monotonicity and Solidarity, makes it possible to define a unique rule that coincides with the weighted Shapley value of an associated cost game.
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Notes
For example, assuming all the costs are different.
For example, charging all the cost to the merging agents.
Charging all the cost to the merging agents will clearly not satisfy Core Selection.
In the context of pricing traffic demand in a spanning network, Moulin (2014) also finds the weighted Shapley value of a cooperative game to satisfy the so-called routing-proofness. This property is related to Split-proofness, preventing agents gaining advantage by claiming to be several different users along a path.
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Acknowledgments
We are grateful to Gustavo Bergantiños, Anna Bogomolnaia and an anonymous referee for helpful comments. Usual disclaimer applies. We also thank participants at several seminars and conferences at U. Vigo, MINES ParisTech, Technical University of Lisbon, U. Barcelona, U. York, U. Granada, Boston College and U.P. Navarra.
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Financial support by the Spanish Ministerio de Ciencia e Innovación (ECO2011-23460), Ministerio de Economía y Competitividad (ECO2014-52616-R), Apoyo a la Investigación de la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia (Ref. 19320/PI/14), and Xunta de Galicia (GRC 2015/014, 10PXIB362299PR and EM2013/013) is gratefully acknowledged.
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Gómez-Rúa, M., Vidal-Puga, J. A monotonic and merge-proof rule in minimum cost spanning tree situations. Econ Theory 63, 813–826 (2017). https://doi.org/10.1007/s00199-016-0996-x
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DOI: https://doi.org/10.1007/s00199-016-0996-x
Keywords
- Minimum cost spanning tree problems
- Cost sharing
- Core Selection
- Cost Monotonicity
- Merge-proofness
- Weighted Shapley value