IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Two Necessary Conditions for Strategy-Proofness: on What Domains are they also Sufficient?

  • Salvador Barberà
  • Dolors Berga
  • Bernardo Moreno

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 different 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 different conditions that are always related, but not always equivalent to strategy-proofness. We define two very natural conditions that are necessary for strategy-proofness: monotonicity and reshuffling invariance. We remark that they are not always sufficient. Then, we identify a domain condition, called intertwinedness, that ensures the equivalence between our two conditions and that of strategy-proofness. 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 prove that other necessary conditions for strategy-proofness also become equivalent to ours when applied to functions defined on intertwined domains, even if they are not equivalent in general. We also study the relationship between our domain restrictions and others that appear in the literature, proving that we are indeed introducing a novel proposal.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/598.pdf
Download Restriction: no

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 598.

as
in new window

Length:
Date of creation: Dec 2011
Date of revision:
Handle: RePEc:bge:wpaper:598
Contact details of provider: Postal:
Ramon Trias Fargas, 25-27, 08005 Barcelona

Phone: +34 93 542-1222
Fax: +34 93 542-1223
Web page: http://www.barcelonagse.eu
Email:


More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  2. Jaramillo, Paula & Manjunath, Vikram, 2012. "The difference indifference makes in strategy-proof allocation of objects," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1913-1946.
  3. Barbera, S. & Gul, F. & Stacchetti, E., 1992. "Generalized Median Voter Schemes and Committees," UFAE and IAE Working Papers 184.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. Bogomolnaia, Anna & Deb, Rajat & Ehlers, Lars, 2005. "Strategy-proof assignment on the full preference domain," Journal of Economic Theory, Elsevier, vol. 123(2), pages 161-186, August.
  5. Shurojit Chatterji & Arunava Sen, 2009. "Tops-Only Domains," Macroeconomics Working Papers 22064, East Asian Bureau of Economic Research.
    • Shurojit Chatterji & Arunava Sen, 2011. "Tops-only domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 255-282, February.
  6. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
  7. Eiichi Miyagawa, 2001. "Locating libraries on a street," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 527-541.
  8. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  9. 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.
  10. Ehlers, L., 2001. "Multiple Public Goods and Lexicographic Preferences Replacement Principle," Cahiers de recherche 2001-25, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  11. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
  12. ASWAL, Navin & CHATTERJI, Shurojit & SEN, Arunava, 1999. "Dictatorial domains," CORE Discussion Papers 1999040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Navin Aswal & Shurojit Chatterji & Arunava Sen, 2003. "Dictatorial domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(1), pages 45-62, 08.
  13. Ehud Kalai & Eitan Muller, 1977. "Characterization of Domains Admitting Nondictatorial Social Welfare Functions and Nonmanipulable Voting Procedures," Discussion Papers 234, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. ALCALDE-UNZU, Jorge & MOLIS, Elena, 2009. "Exchange of indivisible goods and indifferences: the Top Trading Absorbing Sets mechanisms," CORE Discussion Papers 2009062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Tatsuyoshi Saijo & Tomas Sjostrom & Takehiko Yamato, 2005. "Secure Implementation," Economics Working Papers 0056, Institute for Advanced Study, School of Social Science.
  16. 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).
  17. Shin Sato, 2010. "Circular domains," Review of Economic Design, Springer;Society for Economic Design, vol. 14(3), pages 331-342, September.
  18. Barbera, Salvador & Dutta, Bhaskar, 1982. "Implementability via protective equilibria," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 49-65, June.
  19. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  20. 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).
  21. David Cantala, 2004. "Choosing the level of a public good when agents have an outside option," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 491-514, 06.
  22. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
  23. 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.
  24. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
  25. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  26. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:bge:wpaper:598. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Bruno Guallar)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.