Bribe-proof reallocation with single-peaked preferences

We study reallocation rules in the context of a one-good economy consisting of agents with single-peaked preferences and individual endowments. A rule is bribe-proof if no group of agents can compensate one of its subgroups to misrepresent their characteristics (preferences or endowments) in order that each agent is better off after an appropriate redistribution of what the rule reallocates to the group, adjusted by the resource surplus or deficit they all engage in by misreporting endowments. First, we characterize all bribe-proof rules as the class of efficient, (preference and endowment) strategy-proof and weakly replacement monotonic rules, extending the result due to Massó and Neme (Games Econ Behav 61: 331–343, 2007) to our broader framework. Second, we present a full description of the family of bribe-proof rules that in addition are individually rational and peak-only. Finally, we provide two further characterizations of the uniform reallocation rule involving bribe-proofness.

[1]  W. Thomson.  Consistent Allocation Rules , 1996 .

[2]  L. Hurwicz.  On informationally decentralized systems , 1977 .

[3]  William Thomson,et al.  The Replacement Principle in Economies with Single-Peaked Preferences , 1997 .

[4]  Debraj Ray,et al.  Game-Theoretical Applications to Economics and Operations Research , 1997 .

[5]  Andreu Mas-Colell,et al.  Equilibrium Theory with Possibly Satiated Preferences , 1992 .

[6]  W. Thomson.  Fair Allocation Rules , 2011 .

[7]  Jordi Massó,et al.  Bribe-proof rules in the division problem , 2007, Games Econ. Behav..

[8]  Gustavo Bergantiños,et al.  The division problem with voluntary participation , 2011, Social Choice and Welfare.

[9]  Hans Peters,et al.  Reallocation of an infinitely divisible good , 1995 .

[10]  Stephen Ching,et al.  A simple characterization of the uniform rule , 1992 .

[11]  Carmen Herrero.  General allocation problems with single-peaked preferences: path-independence and related topics , 2002 .

[12]  B. Klaus.  The Characterisation of the Uniform Reallocation Rule Without Side Payments , 1997 .

[13]  M. Jackson,et al.  Strategy-Proof Allotment Rules , 1997 .

[14]  Andrew Postlewaite,et al.  Manipulation via Endowments , 1979 .

[15]  H. Peters,et al.  Strategy-proof division with single-peaked preferences and individual endowments , 1995 .

[16]  Bettina Klaus,et al.  Manipulation via Endowments in Exchange Markets with Indivisible Goods , 2006, Soc. Choice Welf..

[17]  James Schummer,et al.  Manipulation through Bribes , 2000, J. Econ. Theory.