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Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems

  • KAYI, Cagatay
  • RAMAEKERS, Eve

A set of agents with possibly different waiting costs have to receive the same service one after the other. Efficiency requires to maximize total welfare. Fairness requires to treat equal agents equally. One must form a queue, set up monetary transfers to compensate agents having to wait, and not a priori arbitrarily exclude agents from positions. As one may not know agents' waiting costs, they may have no incentive to reveal them. We identify the only rule satisfying Pareto-efficiency, equal treatment of equals in welfare or symmetry, and strategy-proofness. It satisfies stronger axioms, as no-envy and anonymity. Further, its desirability extends to related problems. To obtain these results, we prove that a rule, single-valued or not, satisfies queue-efficiency and strategy-proofness if and only if it always selects efficient queues and sets transfers à la Groves [Groves, T., 1973. Incentives in teams. Econometrica 41, 617-631]. This holds in other problems, provided the domain of quasi-linear preferences is rich enough.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number -2179.

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Handle: RePEc:cor:louvrp:-2179
Note: In : Games and Economic Behavior, 68, 220-232, 2010
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  1. Pattanaik, Prasanta K., 1973. "On the stability of sincere voting situations," Journal of Economic Theory, Elsevier, vol. 6(6), pages 558-574, December.
  2. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
  3. Manipushpak Mitra, 2000. "Achieving the First Best in Sequencing Problems," Bonn Econ Discussion Papers bgse11_2001, University of Bonn, Germany.
  4. Gardenfors, Peter, 1976. "Manipulation of social choice functions," Journal of Economic Theory, Elsevier, vol. 13(2), pages 217-228, October.
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  6. Chun, Youngsub, 2006. "A pessimistic approach to the queueing problem," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 171-181, March.
  7. Youngsub Chun, 2006. "No-envy in queueing problems," Economic Theory, Springer, vol. 29(1), pages 151-162, September.
  8. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  9. Bossert, Walter, 1989. "On the extension of preferences over a set to the power set: An axiomatic characterization of a quasi-ordering," Journal of Economic Theory, Elsevier, vol. 49(1), pages 84-92, October.
  10. MANIQUET, François & SPRUMONT, Yves, 1998. "Efficient Strategy-Proof Allocation Functions in Linear Production Economies," Cahiers de recherche 9805, Universite de Montreal, Departement de sciences economiques.
  11. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-38, March.
  12. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
  13. Jeroen Suijs, 1996. "On incentive compatibility and budget balancedness in public decision making," Review of Economic Design, Springer, vol. 2(1), pages 193-209, December.
  14. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
  15. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  16. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-46, March.
  17. Feldman, Allan, 1979. "Manipulation and the Pareto rule," Journal of Economic Theory, Elsevier, vol. 21(3), pages 473-482, December.
  18. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
  19. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  20. Carmen Bevia, 1996. "Identical preferences lower bound solution and consistency in economies with indivisible goods," Social Choice and Welfare, Springer, vol. 13(1), pages 113-126, January.
  21. Holmstrom, Bengt, 1979. "Groves' Scheme on Restricted Domains," Econometrica, Econometric Society, vol. 47(5), pages 1137-44, September.
  22. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer, vol. 19(3), pages 569-580.
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