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Budget-Balance, Fairness and Minimal Manipulability

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  • ANDERSSON, Tommy
  • EHLERS, Lars
  • SVENSSON, Lars-Gunnar

Abstract

A common real-life problem is to fairly allocate a number of indivisible objects and a fixed amount of money among a group of agents. Fairness requires that each agent weakly prefers his consumption bundle to any other agent’s bundle. Under fairness, efficiency is equivalent to budget-balance (all the available money is allocated among the agents). Budget-balance and fairness in general are incompatible with non-manipulability (Green and Laffont, 1979). We propose a new notion of the degree of manipulability which can be used to compare the ease of manipulation in allocation mechanisms. Our measure counts for each problem the number of agents who can manipulate the rule. Given this notion, the main result demonstrates that maximally linked fair allocation rules are the minimally manipulable rules among all budget-balanced and fair allocation mechanisms. Such rules link any agent to the bundle of a pre-selected agent through indifferences (which can be viewed as indirect egalitarian equivalence).

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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2010-09.

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Length: 19 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:mtl:montde:2010-09

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Keywords: Minimal manipulability; fairness; budget-balance; allocation rules.;

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References

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  1. Parag A. Pathak & Tayfun Sönmez, 2011. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation," NBER Working Papers 16783, National Bureau of Economic Research, Inc.
  2. Sun, Ning & Yang, Zaifu, 2003. "A general strategy proof fair allocation mechanism," Economics Letters, Elsevier, vol. 81(1), pages 73-79, October.
  3. Claus-Jochen Haake & Matthias G. Raith & Francis Edward Su, 2002. "Bidding for envy-freeness: A procedural approach to n-player fair-division problems," Social Choice and Welfare, Springer, vol. 19(4), pages 723-749.
  4. Maus, Stefan & Peters, Hans & Storcken, Ton, 2007. "Anonymous voting and minimal manipulability," Journal of Economic Theory, Elsevier, vol. 135(1), pages 533-544, July.
  5. Azacis, Helmuts, 2005. "Double Implementation in a Market for Indivisible Goods with a Price Constraint," Cardiff Economics Working Papers E2005/10, Cardiff University, Cardiff Business School, Economics Section.
  6. Svensson, Lars-Gunnar, 2006. "Coalition Strategy-Proofness and Fairness," Working Papers 2006:10, Lund University, Department of Economics.
  7. Debasis Mishra & Dolf Talman, 2008. "Characterization of the walrasian equilibria of the assignment model," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 08-07, Indian Statistical Institute, New Delhi, India.
  8. ANDERSSON, Tommy & EHLERS, Lars & SVENSSON, Lars-Gunnar, 2010. "Budget-Balance, Fairness and Minimal Manipulability," Cahiers de recherche 18-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Atila Abdulkadiroglu & Tayfun Sonmez & M. Utku Unver, 2002. "Room Assignment-Rent Division: A Market Approach," Game Theory and Information 0202003, EconWPA, revised 26 Sep 2002.
  10. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-54, July.
  11. Stefan Maus & Hans Peters & Ton Storcken, 2007. "Minimal manipulability: anonymity and unanimity," Social Choice and Welfare, Springer, vol. 29(2), pages 247-269, September.
  12. Tadenuma, Koichi & Thomson, William, 1993. "The fair allocation of an indivisible good when monetary compensations are possible," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 117-132, February.
  13. Svensson, Lars-Gunnar, 1991. "Nash Implementation of Competitive Equilibria in a Model with Indivisible Goods," Econometrica, Econometric Society, vol. 59(3), pages 869-77, May.
  14. Andersson, T. & Svensson, L.-G. & Yang, Z., 2010. "Constrainedly fair job assignments under minimum wages," Games and Economic Behavior, Elsevier, vol. 68(2), pages 428-442, March.
  15. Mishra, Debasis & Parkes, David C., 2009. "Multi-item Vickrey-Dutch auctions," Games and Economic Behavior, Elsevier, vol. 66(1), pages 326-347, May.
  16. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  17. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-39, July.
  18. Andersson, Tommy & Svensson, Lars-Gunnar, 2006. "Non-manipulable Assignment of Individuals to Positions Revisited," Working Papers 2006:11, Lund University, Department of Economics, revised 12 Apr 2007.
  19. Ma Jinpeng, 1995. "Stable Matchings and Rematching-Proof Equilibria in a Two-Sided Matching Market," Journal of Economic Theory, Elsevier, vol. 66(2), pages 352-369, August.
  20. Tommy Andersson & Lars Ehlers & Lars-Gunnar Svensson, 2012. "(Minimally) ?-Incentive Compatible Competitive Equilibria in Economies with Indivisibilities," Cahiers de recherche 04-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  21. Flip Klijn, 2000. "An algorithm for envy-free allocations in an economy with indivisible objects and money," Social Choice and Welfare, Springer, vol. 17(2), pages 201-215.
  22. Carmen Beviá, 2010. "Manipulation games in economies with indivisible goods," International Journal of Game Theory, Springer, vol. 39(1), pages 209-222, March.
  23. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
  24. Ning Sun & Zaifu Yang, 2003. "A General Strategy Proof Fair Allocation Mechanism," Working Papers 346, Bielefeld University, Center for Mathematical Economics.
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Citations

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Cited by:
  1. Parag A. Pathak & Tayfun Sönmez, 2011. "School Admissions Reform in Chicago and England: Comparing Mechanisms by their Vulnerability to Manipulation," Boston College Working Papers in Economics 784, Boston College Department of Economics.
  2. Andersson, Tommy & Ehlers, Lars & Svensson, Lars-Gunnar, 2012. "Least Manipulable Envy-free Rules in Economies with Indivisibilities," Working Papers 2012:8, Lund University, Department of Economics, revised 30 Sep 2013.
  3. Andersson, Tommy & Svensson, Lars-Gunnar & Ehlers, Lars, 2010. "Budget-Balance, Fairness and Minimal Manipulability," Working Papers 2010:16, Lund University, Department of Economics, revised 15 Jan 2013.
  4. Tommy Andersson & Lars Ehlers & Lars-Gunnar Svensson, 2012. "(Minimally) ?-Incentive Compatible Competitive Equilibria in Economies with Indivisibilities," Cahiers de recherche 04-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Tommy ANDERSSON & Lars EHLERS, 2013. "An Algorithm for Identifying Agent-k-Linked Allocations in Economies with Indivisibilities," Cahiers de recherche 17-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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