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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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  1. Shurojit Chatterji & Arunava Sen, 2011. "Tops-only domains," Economic Theory, Springer, vol. 46(2), pages 255-282, February.
  2. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
  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. 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.
  5. Ehlers, Lars, 2002. "Multiple public goods and lexicographic preferences: replacement principle," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 1-15, February.
  6. Barbera, Salvador & Dutta, Bhaskar, 1982. "Implementability via protective equilibria," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 49-65, June.
  7. 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.
  8. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
  9. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
  10. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
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  12. Alcalde-Unzu, Jorge & Molis, Elena, 2011. "Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms," Games and Economic Behavior, Elsevier, vol. 73(1), pages 1-16, September.
  13. Sjostrom, Tomas & Yamato, Takehiko & Saijo, Tatsuyoshi, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
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  15. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
  16. 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.
  17. ASWAL, Navin & CHATTERJI, Shurojit & SEN, Arunava, 1999. "Dictatorial domains," CORE Discussion Papers 1999040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  18. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  19. 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.
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  23. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  24. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
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