Contracts, Cost Sharing and Consistency

23 Pages Posted: 2 Apr 2009 Last revised: 9 Apr 2009

See all articles by Maurice Koster

Maurice Koster

University of Amsterdam - Department of Quantitative Economics (KE)

Date Written: April 1, 2009

Abstract

Under a contract, agents are not only held to honor the allocation as prescribed by a cost sharing mechanism but also a full description of allocated units and costs once production falls short. For agents leaving the cost sharing problem by taking their demanded units and prepaying the corresponding bill, a contract allows for a reformulation of the cost sharing problem to serve the remaining agents. Consistency requires invariance of cost shares relative to any such reduced cost sharing problem. Under consistency, the proportional mechanisms uniquely satisfy additivity and positivity of cost shares. Exchanging positivity by equal treatment characterizes the set of mechanisms which propose proportional shares for only those agents in the maximal indifference set for some preordering on the rest of nonnegative numbers. This includes egalitarian and average cost sharing. The latter is further characterized by the properties linearity. Under R-consistency, a mechanism is supported by at least one reasonable contract which meets upperbounds. The class of additive and R-consistent mechanisms is isomorphic to the class of consistent and monotonic rationing methods. Consequently serial cost sharing is R-consistent, whereas Shapley-Shubik is not. Examples are given how the extensive literature on consistent monotonic rationing can be inferred to study and characterize cost sharing mechanisms.

Keywords: Cost sharing, Consistency, Additivity, Constant returns, Rationing, (Quasi-) Proportional mechanism, Egalitarian mechanism, Serial mechanism, Shapley-Shubik mechanism

JEL Classification: C70, D63, D70

Suggested Citation

Koster, Maurice, Contracts, Cost Sharing and Consistency (April 1, 2009). Available at SSRN: https://ssrn.com/abstract=1371536 or http://dx.doi.org/10.2139/ssrn.1371536

Maurice Koster (Contact Author)

University of Amsterdam - Department of Quantitative Economics (KE) ( email )

Roetersstraat 11
Amsterdam, North-Holland 1018 WB
Netherlands

HOME PAGE: http://www.uva.nl/profiel/k/o/m.a.l.koster/m.a.l.koster.html

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