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Secure implementation in Shapley–Scarf housing markets

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Abstract

This paper considers the object allocation problem introduced by Shapley and Scarf (1974). We study secure implementation (Saijo, Sjostrom, and Yamato, 2007), that is, double implementation in dominant strategy and Nash equilibria. We prove that (i) an individually rational solution is securely implementable if and only if it is the no-trade solution, (ii) a neutral solution is securely implementable if and only if it is a serial dictatorship, and (iii) an efficient solution is securely implementable if and only if it is a sequential dictatorship. Furthermore, we provide a complete characterization of securely implementable solutions in the two-agent case.
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  • Yuji Fujinaka & Takuma Wakayama, 2011. "Secure implementation in Shapley–Scarf housing markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 147-169, September.
    • Handle: RePEc:spr:joecth:v:48:y:2011:i:1:p:147-169
    DOI: 10.1007/s00199-010-0538-x
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    1. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 265-280, October.
    2. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
    3. Hervé Moulin & Scott Shenker, 2001. "Strategyproof sharing of submodular costs:budget balance versus efficiency," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 511-533.
    4. Bochet, Olivier & Sakai, Toyotaka, 2010. "Secure implementation in allotment economies," Games and Economic Behavior, Elsevier, vol. 68(1), pages 35-49, January.
    5. Hiroki Saitoh & Shigehiro Serizawa, 2008. "Vickrey allocation rule with income effect," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(2), pages 391-401, May.
    6. Lars Ehlers & Bettina Klaus, 2007. "Consistent House Allocation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(3), pages 561-574, March.
    7. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    8. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(2), pages 457-488.
    9. Sonmez, Tayfun & Utku Unver, M., 2005. "House allocation with existing tenants: an equivalence," Games and Economic Behavior, Elsevier, vol. 52(1), pages 153-185, July.
    10. Lars-Gunnar Svensson, 2009. "Coalitional strategy-proofness and fairness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(2), pages 227-245, August.
    11. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
    12. , & , & ,, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
    13. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    14. Takamiya, Koji, 2001. "Coalition strategy-proofness and monotonicity in Shapley-Scarf housing markets," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 201-213, March.
    15. Chen, Yan & Sonmez, Tayfun, 2004. "An experimental study of house allocation mechanisms," Economics Letters, Elsevier, vol. 83(1), pages 137-140, April.
    16. Lars Ehlers & Bettina Klaus, 2004. "Resource-monotonicity for house allocation problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 545-560, August.
    17. Fujinaka, Yuji & Wakayama, Takuma, 2008. "Secure implementation in economies with indivisible objects and money," Economics Letters, Elsevier, vol. 100(1), pages 91-95, July.
    18. Cason, Timothy N. & Saijo, Tatsuyoshi & Sjostrom, Tomas & Yamato, Takehiko, 2006. "Secure implementation experiments: Do strategy-proof mechanisms really work?," Games and Economic Behavior, Elsevier, vol. 57(2), pages 206-235, November.
    19. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    20. Lars-Gunnar Svensson & Bo Larsson, 2002. "Strategy-proof and nonbossy allocation of indivisible goods and money," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(3), pages 483-502.
    21. Mizukami, Hideki & Wakayama, Takuma, 2007. "Dominant strategy implementation in economic environments," Games and Economic Behavior, Elsevier, vol. 60(2), pages 307-325, August.
    22. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-479, June.
    23. Sonmez, Tayfun, 1996. "Implementation in generalized matching problems," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 429-439.
    24. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
    25. Bird, Charles G., 1984. "Group incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 14(4), pages 309-313.
    26. Shinji Ohseto, 2004. "Implementing egalitarian-equivalent allocation of indivisible goods on restricted domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 659-670, March.
    27. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 557-567.
    28. Shinji Ohseto, 2000. "Strategy-proof and efficient allocation of an indivisible good on finitely restricted preference domains," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 365-374.
    29. Manipushpak Mitra, 2001. "Mechanism design in queueing problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(2), pages 277-305.
    30. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    31. Yan Chen & Tayfun Sönmez, 2002. "Improving Efficiency of On-Campus Housing: An Experimental Study," American Economic Review, American Economic Association, vol. 92(5), pages 1669-1686, December.
    32. Toyotaka Sakai, 2008. "Second price auctions on general preference domains: two characterizations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(2), pages 347-356, November.
    33. Takamiya, Koji, 2009. "Preference revelation games and strong cores of allocation problems with indivisibilities," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 199-204, January.
    34. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
    35. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    36. Szilvia Pápai, 2001. "Strategyproof and Nonbossy Multiple Assignments," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(3), pages 257-271, July.
    37. Ehlers, Lars & Klaus, Bettina & Papai, Szilvia, 2002. "Strategy-proofness and population-monotonicity for house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 329-339, November.
    38. Schummer, James, 2000. "Eliciting Preferences to Assign Positions and Compensation," Games and Economic Behavior, Elsevier, vol. 30(2), pages 293-318, February.
    39. Miyagawa, Eiichi, 2002. "Strategy-Proofness and the Core in House Allocation Problems," Games and Economic Behavior, Elsevier, vol. 38(2), pages 347-361, February.
    40. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
    41. Shinji Ohseto, 2006. "Characterizations of strategy-proof and fair mechanisms for allocating indivisible goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 111-121, September.
    42. Bettina Klaus & Eiichi Miyagawa, 2002. "Strategy-proofness, solidarity, and consistency for multiple assignment problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 421-435.
    43. Miyagawa, Eiichi, 2001. "House Allocation with Transfers," Journal of Economic Theory, Elsevier, vol. 100(2), pages 329-355, October.
    44. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
    45. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    46. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
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    Cited by:

    1. Nishizaki, Katsuhiko, 2018. "Secure implementability under Pareto-efficient rules in linear production economies with classical preferences," Research in Economics, Elsevier, vol. 72(3), pages 379-383.
    2. Kazuhiko Hashimoto, 2018. "Strategy-proofness and identical preferences lower bound in allocation problem of indivisible objects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 1045-1078, June.
    3. Rodrigo A. Velez & Alexander L. Brown, 2019. "Empirical strategy-proofness," Papers 1907.12408, arXiv.org, revised Jul 2020.
    4. Harless, Patrick & Phan, William, 2022. "Efficient mixtures of priority rules for assigning objects," Games and Economic Behavior, Elsevier, vol. 132(C), pages 73-89.
    5. Katsuhiko Nishizaki, 2013. "An impossibility theorem for secure implementation in discrete public good economies," Economics Bulletin, AccessEcon, vol. 33(1), pages 300-308.
    6. Fujinaka, Yuji & Miyakawa, Toshiji, 2020. "Ex-post incentive compatible and individually rational assignments in housing markets with interdependent values," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 157-164.
    7. Katsuhiko Nishizaki, 2014. "An equivalence of secure implementability and full implementability in truthful strategies in pure exchange economies with Leontief utility functions," Review of Economic Design, Springer;Society for Economic Design, vol. 18(1), pages 73-82, March.
    8. Bochet, Olivier & Sakai, Toyotaka, 2010. "Secure implementation in allotment economies," Games and Economic Behavior, Elsevier, vol. 68(1), pages 35-49, January.
    9. Hagiwara Makoto, 2023. "Double Implementation in Dominant Strategy Equilibria and Ex-Post Equilibria with Private Values," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 23(2), pages 663-678, June.

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    More about this item

    Keywords

    Secure implementation; Sequential dictatorship; Strict core; Strategy-proofness; Shapley–Scarf housing markets; C72; C78; D61; D63; D71;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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