In this paper we develop a unified framework for the study of additive cost sharing methods. We show that any additive cost sharing method satisfying the dummy axiom can be generated by a (possibly infinite) convex combination of path generated methods. We also show that the set of scale invariant cost sharing methods can be generated by the set of scale invariant paths and the set of demand monotonic methods by the set of demand monotonic paths, both of which we construct. We first apply these results to the study a strict version of marginality, and show that none of the standard methods satisfy this requirement. We construct two new methods, which are generated by infinite sums of paths, and show that these satisfy strict marginality. We then note that the minimum of any concave functional over the set of cost sharing methods, either general, scale invariant, or demand monotonic, must be path generated, and therefore can be computed using techniques from the theory of optimal control. This allows us to provide a new characterization of the Random Order methods as the methods which minimize a lexicographic function of agents' payments according for supermodular cost functions. It may also lead to new characterizations of other interesting methods.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number
199706.
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.: