Int J Game Theory (2018) 47:229–246
Proportional rules for state contingent claims
· Rajnish Kumar
Accepted: 29 June 2017 / Published online: 10 July 2017
© Springer-Verlag GmbH Germany 2017
Abstract 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 extensionsof 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.
Keywords Rationing · Proportional rule · State contingent claims · No advantageous
JEL Classiﬁcation C71 · D63 · D81
The rationing problem is arguably the simplest model of distributive justice. The
problem involves a resource that is to be divided among individuals each of whom
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
Grant 115C030”. Rajnish Kumar acknowledges the British Council grant “UGC-UKIERI 2016-17-059”.
Department of Economics, Istanbul Technical University, Maçka, 34367 Istanbul, Turkey
Queen’s Management School, Queen’s University Belfast, Riddel Hall, 185-Stranmillis Road,
Belfast BT9 5EE, UK