Egalitarian division under Leontief Preferences

Authors: Jin Li Jingyi Xue

Publish Date: 2012/10/23

Volume: 54, Issue: 3, Pages: 597-622

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Abstract

We consider the problem of fairly dividing l divisible goods among n agents with the generalized Leontief preferences We propose and characterize the class of generalized egalitarian rules which satisfy efficiency group strategyproofness anonymity resource monotonicity population monotonicity envyfreeness and consistency On the Leontief domain our rules generalize the egalitarianequivalent rules with reference bundles We also extend our rules to agentspecific and endowmentspecific egalitarian rules The former is a larger class of rules satisfying all the previous properties except anonymity and envyfreeness The latter is a class of efficient group strategyproof anonymous and individually rational rules when the resources are assumed to be privately ownedWe deeply thank Professor Hervé Moulin for leading us to this topic Our paper is enormously benefited from his invaluable guidance and constant support We very much appreciate the helpful comments from Kazuhiko Hashimoto Antonio Nicolò Szilvia Pápai James Schummer William Thomson and Siyang Xiong We are also very grateful to the anonymous referee for the thoughtful commentsSuppose that xyin mathbbR +l and xy Since succcurlyeq is locally nonsatiated we can find yprime x such that yprime succ y Let U succcurlyeq yprime =a+mathbbR l +ain mathbbR l + Since yprime in U succcurlyeq yprime and xyprime then xge a and thus xin U succcurlyeq yprime Hence xsucccurlyeq yprime succ ySuppose that xin mathbbR +l and U succcurlyeq x=a+mathbbR l + By i forall yin a+mathringmathbbR +lysucc x Now let yin a+partial mathbbR l + Since succcurlyeq is continuous if ysucc x then there exists yprime y such that yprime succ x which contradicts that U succcurlyeq x=a+mathbbR +l Hence I succcurlyeq x=a+partial mathbbR +l square

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