Proportional rules for state contingent claims

Sinan Ertemel*, Rajnish Kumar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We consider rationing problems where the claims are state contingent. Before the state is realized individuals submit claims for every possible state of the world. A rule distributes resources before the realization of the state of the world. We introduce two natural extensions of the proportional rule in this framework, namely, the ex-ante proportional rule and the ex-post proportional rule, and then we characterize them using standard axioms from the literature.

Original languageEnglish
Pages (from-to)229-246
Number of pages18
JournalInternational Journal of Game Theory
Issue number1
Publication statusPublished - 1 Mar 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.


We characterize the ex-ante proportional rule by NARAI and NARAS combined with Continuity, and No Award for Null Players. To characterize the ex-post proportional rule, we borrow Independence axiom from the Expected Utility Theory. This axiom says that by mixing two lotteries with a third one, the rationing rule remains unaffected by the choice of the third lottery. By replacing NARAS with the Independence Axiom, and adding Symmetry, we obtain the characterization of the ex-post proportional rule. We would like to thank our advisor, Hervé Moulin, for several helpful comments and remarks. Discussions with Anna Bogomolnaia, Youngsub Chun, Ruben Juarez, Juan Moreno-Ternero, Arunava Sen, and William Thomson have been of great help. The valuable comments of the Associate Editor and two anonymous referees have greatly improved our paper. We thank Graham Brownlow and David Seymour for their help with proof-reading. Sinan Ertemel gratefully acknowledges support from “TÜB˙TAK 2232 Grant 115C030”. Rajnish Kumar acknowledges the British Council grant “UGC-UKIERI 2016-17-059”.

FundersFunder number
British CouncilUGC-UKIERI 2016-17-059


    • No advantageous reallocation
    • Proportional rule
    • Rationing
    • State contingent claims


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