Social Choice and Welfare

, Volume 48, Issue 1, pp 109–131 | Cite as

Efficient, fair, and strategy-proof (re)allocation under network constraints

Original Paper

Abstract

A resource available in different types is to be distributed or redistributed among agents differing in their ability to consume these types. Preferences over consumption levels are not observable but known to be single-peaked. We identify the only strategy-proof and efficient allocation rule satisfying a formulation of “fair net trades” (Schmeidler and Vind in Econometrica 40(4):637–642, 1972). This rule coincides with the “generalized uniform rule” (Thomson in Axiomatic analysis of generalized economies with single-peaked preferences, 1995a) when the resource is available in a single type and with the “egalitarian rule” (Bochet et al. in J Econ Theory 148:535–562, 2013) when there are no individual endowments. Moreover, it coincides with the “uniform rule” (Sprumont in Econometrica 59(2):509–519, 1991) when the resource is available in a single type and there are no individual endowments. This rule belongs to a new class of group strategy-proof rules. Our analysis provides a unified treatment of the applications in Bochet et al. (Theor Econ 7:395–423, 2012, J Econ Theory 148:535–562, 2013).

References

  1. Barberà S, Jackson M, Neme A (1997) Strategy-proof allotment rules. Games Econ Behav 18(1):1–21CrossRefGoogle Scholar
  2. Bochet O, İlkılıç R, Moulin H, Sethuraman J (2012) Balancing supply and demand under bilateral constraints. Theor Econ 7:395–423CrossRefGoogle Scholar
  3. Bochet O, İlkılıç R, Moulin H (2013) Egalitarianism under earmark constraints. J Econ Theory 148:535–562CrossRefGoogle Scholar
  4. Chandramouli S, Sethuraman J (2011) Group strategy-proofness of the egalitarian mechanism for constrained rationing problems. Working paper. arXiv:1107.4566
  5. Ching S (1994) An alternative characterization of the uniform rule. Soc Choice Welf 11(2):131–136CrossRefGoogle Scholar
  6. Foley D (1967) Resource allocation and the public sector. Yale Econ Essays 7:45–98Google Scholar
  7. Fujishige S (2005) Submodular functions and optimization. Annals of discrete mathematics, vol 58. Amsterdam, The NetherlandsGoogle Scholar
  8. Gale D (1957) A theorem on flows in networks. Pac J Math 7(1):1073–1082CrossRefGoogle Scholar
  9. Groenevelt H (1991) Two algorithms for maximizing a separable concave function over a polymatroid feasible region. Eur J Oper Res 54(2):227–236CrossRefGoogle Scholar
  10. Kıbrıs O, Küçükşenel S (2009) Uniform trade rules for uncleared markets. Soc Choice Welf 32:101–121CrossRefGoogle Scholar
  11. Klaus B, Peters H, Strocken T (1998) Strategy-proof division with single-peaked preferences and individual endowments. Soc Choice Welf 15:297–311CrossRefGoogle Scholar
  12. Moulin H (1999) Rationing a commodity along fixed paths. J Econ Theory 84(1):41–72CrossRefGoogle Scholar
  13. Schmeidler D, Vind K (1972) Fair net trades. Econometrica 40(4):637–642CrossRefGoogle Scholar
  14. Schmeidler D (1979) A bibliographical note on a theorem by Hardy, Littlewood, and Polya. J Econ Theory 59(20):125–128CrossRefGoogle Scholar
  15. Sprumont Y (1991) The division problem with single-peaked preferences. Econometrica 59(2):509–519CrossRefGoogle Scholar
  16. Thomson W (1992) Consistency in exchange economies. Working paperGoogle Scholar
  17. Thomson W (1994a) Consistent solutions to the problem of fair division when preferences are single-peaked. J Econ Theory 63(2):219–245CrossRefGoogle Scholar
  18. Thomson W (1994b) Resource-monotonic solutions to the problem of fair division when preferences are single-peaked. Soc Choice Welf 11:205–223Google Scholar
  19. Thomson W (1995a) Axiomatic analysis of generalized economies with single-peaked preferences (revised 2009)Google Scholar
  20. Thomson W (1995b) Population-monotonic solutions to the problem of fair division when preferences are single-peaked. Econ Theory 5(2):229–246CrossRefGoogle Scholar
  21. Thomson W (1997) The replacement principle in economies with single-peaked preferences. J Econ Theory 76(1):145–168CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.University of Southern DenmarkOdenseDenmark

Personalised recommendations