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Budget-balance, fairness and minimal manipulability

  • Ehlers, Lars

    ()

    (Departement de Sciences Economiques and CIREQ, Universite de Montreal)

  • Svensson, Lars-Gunnar

    ()

    (Department of Economics, Lund University)

  • Andersson, Tommy

    ()

    (Department of Economics, Lund University)

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. In this context, fairness is incompatible with budget-balance and non-manipulability (Green and Laffont, 1979). Our approach here is to weaken or abandon non-manipulability. We search for the rules which are minimally manipulable among all fair and budget-balanced rules. First, we show for a given preference profile, all fair and budget-balanced rules are either (all) manipulable or (all) non-manipulable. Hence, measures based on counting profiles where a rule is manipulable or considering a possible inclusion of profiles where rules are manipulable do not distinguish fair and budget-balanced rules. Thus, a ``finer'' measure is needed. Our new concept compares two rules with respect to their degree of manipulability by counting for each profile the number of agents who can manipulate the rule. Second, we show that maximally preferred fair allocation rules are the minimally (individually and coalitionally) manipulable fair and budget-balanced allocation rules according to our new concept. Such rules choose allocations with the maximal number of agents for whom the utility is maximized among all fair and budget-balanced allocations.

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Article provided by Econometric Society in its journal Theoretical Economics.

Volume (Year): 9 (2014)
Issue (Month): 3 (September)
Pages:

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Handle: RePEc:the:publsh:1346
Contact details of provider: Web page: http://econtheory.org

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  1. 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.
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  7. ANDERSSON, Tommy & EHLERS, Lars & SVENSSON, Lars-Gunnar, 2012. "(Minimally) 'epsilon'-Incentive Compatible Competitive Equilibria in Economies with Indivisibilities," Cahiers de recherche 2012-03, Universite de Montreal, Departement de sciences economiques.
  8. 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.
  9. Claus-Jochen Haake & Matthias G. Raith & Francis Su, 2000. "Bidding for Envy-Freeness: A Procedural Approach to n-Player Fair Division Problems," Claremont Colleges Working Papers 2000-47, Claremont Colleges.
  10. Azacis, Helmuts, 2008. "Double implementation in a market for indivisible goods with a price constraint," Games and Economic Behavior, Elsevier, vol. 62(1), pages 140-154, January.
  11. Carmen Beviá, 2010. "Manipulation games in economies with indivisible goods," International Journal of Game Theory, Springer, vol. 39(1), pages 209-222, March.
  12. 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.
  13. 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.
  14. Ehlers, Lars & Svensson, Lars-Gunnar & Andersson, Tommy, 2014. "Budget-balance, fairness and minimal manipulability," Theoretical Economics, Econometric Society, vol. 9(3), September.
  15. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  16. Andersson, Tommy & Svensson, Lars-Gunnar, 2008. "Non-manipulable assignment of individuals to positions revisited," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 350-354, November.
  17. Ning Sun & Zaifu Yang, 2003. "A General Strategy Proof Fair Allocation Mechanism," Center for Mathematical Economics Working Papers 346, Center for Mathematical Economics, Bielefeld University.
  18. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
  19. Maus,Stefan & Peters,Hans & Storcken,Ton, 2004. "Minimal Manipulability: Anonymity and Unanimity," Research Memorandum 026, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  20. Sun, Ning & Yang, Zaifu, 2003. "A general strategy proof fair allocation mechanism," Economics Letters, Elsevier, vol. 81(1), pages 73-79, October.
  21. 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.
  22. 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.
  23. 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.
  24. Lars-Gunnar Svensson, 2009. "Coalitional strategy-proofness and fairness," Economic Theory, Springer, vol. 40(2), pages 227-245, August.
  25. 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.
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