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Two necessary conditions for strategy-proofness: On what domains are they also sufficient?

  • Barberà, Salvador
  • Berga, Dolors
  • Moreno, Bernardo

A social choice function may or may not satisfy a desirable property depending on its domain of definition. For the same reason, different conditions may be equivalent for functions defined on some domains, while not in other cases. Understanding the role of domains is therefore a crucial issue in mechanism design. We illustrate this point by analyzing the role of two conditions, monotonicity and reshuffling invariance, that are always necessary, but not always sufficient for strategy-proofness. We identify domains, that we call intertwined, ensuring the equivalence between these two conditions and that of strategy-proofness for whatever functions are defined on them. We prove that some important domains are intertwined: those of single-peaked preferences, both with public and private goods, and also those arising in simple models of house allocation. We also discuss the relationship between our conditions on functions and domains with others considered in the literature.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 75 (2012)
Issue (Month): 2 ()
Pages: 490-509

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Handle: RePEc:eee:gamebe:v:75:y:2012:i:2:p:490-509
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  2. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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  7. Salvador Barbera, 1995. "Strategy-Proof Allotment Rules," Discussion Papers 1142, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2009. "Individual versus group strategy-proofness: when do they coincide?," UFAE and IAE Working Papers 761.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  9. Ehlers, L., 2001. "Multiple Public Goods and Lexicographic Preferences Replacement Principle," Cahiers de recherche 2001-25, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  10. ALCADE-UNZU, Jorge & MOLIS, Elena, . "Exchange of indivisible goods and indifferences: the top trading absorbing sets mechanisms," CORE Discussion Papers RP -2331, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Paula Jaramillo & Vikram Manjunath, 2011. "The Difference Indifference Makes in Strategy-Proof Allocation of Objects," DOCUMENTOS CEDE 008746, UNIVERSIDAD DE LOS ANDES-CEDE.
  12. Eiichi Miyagawa, 2001. "Locating libraries on a street," Social Choice and Welfare, Springer, vol. 18(3), pages 527-541.
  13. Kalai, Ehud & Muller, Eitan, 1977. "Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures," Journal of Economic Theory, Elsevier, vol. 16(2), pages 457-469, December.
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  15. Barbera, S. & Sonnenschein, H., 1988. "Voting By Quota And Committee," UFAE and IAE Working Papers 95-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  16. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  17. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  18. Carmen Bevi? & Salvador Barber?, . "Self-Selection Consistent Functions," UFAE and IAE Working Papers 468.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  19. David Cantala, 2004. "Choosing the level of a public good when agents have an outside option," Social Choice and Welfare, Springer, vol. 22(3), pages 491-514, 06.
  20. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
  21. Shin Sato, 2010. "Circular domains," Review of Economic Design, Springer, vol. 14(3), pages 331-342, September.
  22. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
  23. Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990. "Voting by Committees," Cowles Foundation Discussion Papers 941, Cowles Foundation for Research in Economics, Yale University.
  24. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
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  26. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
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