Skip to main content
SpringerLink
Log in

Implementation of solutions to the problem of fair division when preferences are single-peaked

  • Original Paper
  • Published:
Review of Economic Design Aims and scope Submit manuscript

Abstract

We consider the problem of fairly allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. We address the issue of (Nash)-implementability of solutions to this problem. As the lack of monotonicity of preferences often causes solutions to violate no veto power, the classic Maskin-type theorems cannot be invoked. Instead, we show that more powerful theorems due to Danilov-Yamato and Sjöström can help settle implementation questions for most of the central fairness concepts, generally in the positive.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barberà S, Jackson M, Neme A (1997) Strategy-proof allotment rules. Games Econ Behav 18: 1–21

    Article  Google Scholar 

  • Bochet O, Sakai T (2009) Secure implementation in allotment economies, mimeo. Games Econ Behav (forthcoming)

  • Ching S (1992) A simple characterization of the uniform rule. Econ Lett 40: 57–60

    Article  Google Scholar 

  • Ching S (1994) An alternative characterization of the uniform rule. Soc Choice Welf 11: 131–136

    Article  Google Scholar 

  • Ching S, Serizawa S (1988) A maximal domain for the existence of strategy-proof rules. J Econ Theory 78: 157–166

    Article  Google Scholar 

  • Chun Y (2006) The separability principle in economies with single-peaked preferences. Soc Choice Welf 26: 239–253

    Article  Google Scholar 

  • Dagan N (1996) A note on Thomson’s characterization of the uniform rule. J Econ Theory 69: 255–261

    Article  Google Scholar 

  • Danilov V (1992) Implementation via Nash equilibria. Econometrica 60: 43–56

    Article  Google Scholar 

  • Doghmi A, Ziad A (2008a) Reexamination of Maskin’s theorem on Nash implementability. Econ Lett 100: 150–152

    Article  Google Scholar 

  • Doghmi A, Ziad A (2008b) Nash implementation in exchange economies with single-peaked preferences. Econ Lett 100: 157–160

    Article  Google Scholar 

  • Ehlers L (2002) Resource-monotonic allocation when preferences are single-peaked. Econ Theory 20: 113–131

    Article  Google Scholar 

  • Fleurbaey M, Maniquet F (1997) Implementability and horizontal equity require no-envy. Econometrica 65: 1215–1219

    Article  Google Scholar 

  • Foley D (1967) Resource allocation and the public sector. Yale Econ Essays 7: 45–98

    Google Scholar 

  • Geanakoplos J, Nalebuff B (1988) On a fundamental conflict between equity and efficiency. Discussion Paper

  • Gensemer S, Hong L, Kelly JS (1996) Division rules and migration equilibria. J Econ Theory 69: 104–116

    Article  Google Scholar 

  • Herrero C, Villar A (2000) An alternative characterization of the equal-distance rule for allocation problems with single-peaked preferences. Econ Lett 66: 311–317

    Article  Google Scholar 

  • Hurwicz L (1978) The interaction between information and incentives in organizations. In: Krippendorff K (eds) Communication and control in society. Scientific Publishers Inc., NY, pp 123–147

  • Hurwicz L (1979) On allocations attainable through Nash equilibria. In: Laffont JJ (eds) Aggregation and revelation of preferences. North-Holland, pp 397–419

  • Kar A, (2008) Allocating multiple estates among agents with single-peaked preferences. Soc Choice Welf 31: 641–666

    Article  Google Scholar 

  • Kesten O (2006) More on the uniform rule: characterizations without Pareto optimality. Math Soc Sci 51: 192–200

    Article  Google Scholar 

  • Klaus B (1997) Fair allocation and reallocation: an axiomatic study. Maastricht University Dissertation

  • Klaus B (2006) A note on the separability principle in economies with single-peaked preferences. Soc Choice Welf 26: 255–261

    Article  Google Scholar 

  • Klaus B, Peters H, Storcken T (1997) Reallocation of an infinitely divisible good. Econ Theory 10: 305–333

    Article  Google Scholar 

  • Maskin E (1999) Nash equilibrium and welfare optimality. Rev Econ Stud 66: 83–114

    Article  Google Scholar 

  • Massó J, Neme A (2001) Maximal domain of preferences in the division problem. Games Econ Behav 37: 367–381

    Article  Google Scholar 

  • Moulin H (1993) On the fair and coalitionproof allocation of private goods. In: Binmore K, Kirman A, Tani P (eds) Frontiers of game theory. MIT Press, Cambridge, pp 151–163

    Google Scholar 

  • Repullo R (1987) A simple proof of Maskin’s theorem on Nash implementation. Soc Choice Welf 4: 39–41

    Article  Google Scholar 

  • Saijo T (1988) Strategy space reduction in Maskin’s theorem: sufficient conditions for Nash implementation. Econometrica 56: 693–700

    Article  Google Scholar 

  • Saijo T, Sjöström T, Yamato T (2007) Secure implementation. Theor Econ 2: 203–229

    Google Scholar 

  • Sjöström T (1991) On the necessary and sufficient conditions for Nash implementation. Soc Choice Welf 8: 333–340

    Article  Google Scholar 

  • Sönmez T (1994) Consistency, monotonicity and the uniform rule. Econ Lett 46: 229–235

    Article  Google Scholar 

  • Sprumont Y (1991) The division problem with single-peaked preferences: a characterization of the uniform allocation rule. Econometrica 89: 509–519

    Article  Google Scholar 

  • Thomson W (1990) Manipulation and implementation of solutions to the problem of allocation when preferences are single-peaked. mimeo (unpublished)

  • Thomson W (1994a) Consistent solutions to the problem of fair division when preferences are single-peaked. J Econ Theory 63: 219–245

    Article  Google Scholar 

  • Thomson W (1994b) Resource-monotonic solution to the problem of fair division when preferences are single-peaked. Soc choice Welf 11: 205–223

    Google Scholar 

  • Thomson W (1995) Population-monotonic solutions to the the problem of fair division when preferences are single-peaked. Econ Theory 5: 229–246

    Article  Google Scholar 

  • Thomson W (1996) Concepts of implementation. Jpn Econ Rev 47: 133–143

    Article  Google Scholar 

  • Thomson W (1997) The replacement principle in private good economies with single-peaked preferences. J Econ Theory 76: 145–168

    Article  Google Scholar 

  • Varian H (1974) Equity, envy, and efficiency. J Econ Theory 9: 63–91

    Article  Google Scholar 

  • Vind K (1972) Lecture notes in mathematical economics. Stanford University, Mimeo

    Google Scholar 

  • Yamato T (1992) On sufficient conditions for Nash implementation. Games Econ Behav 4: 484–492

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Rochester, Rochester, NY, USA

    William Thomson

Authors
  1. William Thomson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to William Thomson.

Additional information

This paper is based on Sect. 4 of Thomson (1990). I thank the NSF for its support under grant No. SES 0214691, and Rajeev Bhattacharya, Hervé Moulin, Ken-Ichi Shimomura and Takehiko Yamato, and in particular Eun Jeong Heo, Tarık Kara, Vikram Manjunath, Rodrigo Velez, Ayşe Yazıcı, and a referee for their comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Thomson, W. Implementation of solutions to the problem of fair division when preferences are single-peaked. Rev Econ Design 14, 1–15 (2010). https://doi.org/10.1007/s10058-009-0092-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10058-009-0092-9

Keywords

JEL Classification

Search

Navigation