Rationing a Commodity Along Fixed Paths

A private commodity is divided among agents with single peaked preferences over their share. A rationing method elicits individual peaks (demands); if the commodity is overdemanded (resp. underdemanded), no agent receives more (resp. less) than his peak. A fixed path rationing method allocates an overdemanded "good" along a path independent of individual demands, except that an agent receives exactly his demand if it is below the path-generated share. An underdemanded "bad" is allocated along another such path, except that an agent who demands more than his path-generated share receives exactly his peak. We consider four properties of allocation mechanisms: efficiency, strategyproofness, resource monotonicity, and consistency. Together, these axioms characterize precisely the set of fixed path rationing methods. The result holds when the commodity is infinitely divisible and when it comes in indivisible units.

[1]  Barry O'Neill,et al.  A problem of rights arbitration from the Talmud , 1982, Math. Soc. Sci..

[2]  H. Peyton Young,et al.  On Dividing an Amount According to Individual Claims or Liabilities , 1987, Math. Oper. Res..

[3]  M. Jackson,et al.  A characterization of strategy-proof social choice functions for economies with pure public goods , 1994 .

[4]  William Thomson,et al.  Resource-monotonic solutions to the problem of fair division when preferences are single-peaked , 1994 .

[5]  Yves Sprumont.  The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule , 1991 .

[6]  B. Peleg,et al.  Strategy-proof voting schemes with continuous preferences , 1990 .

[7]  J. Benassy,et al.  The economics of market disequilibrium , 1982 .

[8]  H. Moulin.  Priority Rules and Other Asymmetric Rationing Methods , 2000 .

[9]  H. Moulin.  On strategy-proofness and single peakedness , 1980 .

[10]  H. Peyton Young,et al.  Equity - in theory and practice , 1994 .

[11]  W. Thomson.  Population-monotonic solutions to the problem of fair division when preferences are single-peaked , 1995 .

[12]  H. Moulin,et al.  Can everyone benefit from growth?: Two difficulties , 1988 .

[13]  R. Aumann,et al.  Game theoretic analysis of a bankruptcy problem from the Talmud , 1985 .

[14]  M. Jackson,et al.  Strategy-Proof Exchange , 1995 .

[15]  Salvador Barberà,et al.  Sur les fonctions de choix non manipulables , 1996 .

[16]  Gérard P. Cachon,et al.  Capacity Choice and Allocation: Strategic Behavior and Supply Chain Performance , 1999 .

[17]  S. Ching.  An alternative characterization of the uniform rule , 1994 .

[18]  William Thomson,et al.  Axiomatic Analysis of Resource Allocation Problems , 1997 .

[19]  W. Thomson.  The Consistency Principle , 1989 .

[20]  T. Ichiishi,et al.  Game Theory and Applications , 1990 .

[21]  Tayfun Sönmez,et al.  Consistency, monotonicity, and the uniform rule , 1994 .

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

[23]  William Thomson,et al.  Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked , 1994 .