Abstract.
We provide a direct proof of a representation theorem for additive cost sharing methods as sums of path methods. Also, by directly considering the paths that generate some common additive cost sharing methods (Aumann-Shapley, Shapley Shubik, and Serial Cost) we show that they are consistent. These results follow directly from a simple sufficient condition for consistency: being generated by an associative path. We also introduce a new axiom, dummy consistency, which is quite mild. Using this, we also show that the Aumann-Shapley and Serial Cost methods are the unique (additive) consistent extension of their restriction on all two agent problems, while the Shapley-Shubik method has multiple consistent extensions but a unique anonymous scale invariant one.
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I would like to thank Rich Mclean for many detailed comments and suggestions, Ori Haimanko for pointing out an error in an earlier version of this paper, Hervé Moulin, Yves Sprumont, Yuntong Wang for helpful comments and an anonymous referee for many useful comments. This paper contains results from two previous working papers: “Paths in Additive Cost Sharing” and “Weak and Strong Consistency in Additive Cost Sharing”.
Received: November 2001/Revised: January 2004
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Friedman, E. Paths and consistency in additive cost sharing. Int J Game Theory 32, 501–518 (2004). https://doi.org/10.1007/s001820400173
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DOI: https://doi.org/10.1007/s001820400173