International Journal of Game Theory

, Volume 44, Issue 1, pp 195–207 | Cite as

Strategy-proofness versus symmetry in economies with an indivisible good and money

  • Miki Kato
  • Shinji OhsetoEmail author
  • Shohei Tamura


We consider the problem of allocating a single indivisible good among \(n\) agents when monetary transfers are allowed. We study the possibility of constructing strategy-proof, symmetric, and budget balanced mechanisms. We show that there is no strategy-proof, symmetric, and budget balanced mechanism (under the weak domain condition that the set of agent’s possible valuations includes at least \(n+1\) common valuations). Moreover, this result implies that there is no strategy-proof, symmetric, and budget balanced mechanism (i) in the model where agents may have non-quasilinear preferences, and/or (ii) in the unit-demand model with \(n\) heterogeneous indivisible goods.


Strategy-proofness Symmetry Budget balance Indivisible good Monetary transfer 

JEL Classification

C72 D63 D71 D82 



We would like to thank Kazutoshi Ando, an associate editor, and two anonymous referees for helpful suggestions and comments. This research was partially supported by Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science.


  1. Ando K, Kato M, Ohseto S (2008) Strategy-proof and symmetric allocation of an indivisible good. Math Soc Sci 55:14–23CrossRefGoogle Scholar
  2. Ashlagi I, Serizawa S (2012) Characterizing Vickrey allocation rule by anonymity. Soc Choice Welf 38: 531–542Google Scholar
  3. Barberà S (2001) An introduction to strategy-proof social choice functions. Soc Choice Welf 18:619–653CrossRefGoogle Scholar
  4. Barberà S (2012) Strategyproof social choice. In: Arrow KJ, Sen A, Suzumura K (eds) Handbook of social choice and welfare, vol 2. North-Holland, Amsterdam, pp 729–831Google Scholar
  5. Cavallo R (2006) Optimal decision-making with minimal waste: strategyproof redistribution of VCG payments. In: Proceedings of the 5th international conference on autonomous agents and multiagent systems (AAMAS-05), pp 882–889Google Scholar
  6. Chew SH, Serizawa S (2007) Characterizing the Vickrey combinatorial auction by induction. Econ Theory 33:393–406CrossRefGoogle Scholar
  7. Dasgupta P, Hammond P, Maskin E (1979) The implementation of social choice rules: some general results on incentive compatibility. Rev Econ Stud 46:185–216CrossRefGoogle Scholar
  8. Foley D (1967) Resource allocation and the public sector. Yale Econ Essays 7:45–98Google Scholar
  9. Fujinaka Y, Sakai T (2007) Maskin monotonicity in economies with indivisible goods and money. Econ Lett 94:253–258CrossRefGoogle Scholar
  10. Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41:587–601CrossRefGoogle Scholar
  11. Groves T (1973) Incentives in teams. Econometrica 41:617–631CrossRefGoogle Scholar
  12. Hashimoto K, Saitoh H (2010) Domain expansion of the pivotal mechanism. Soc Choice Welf 34:455–470CrossRefGoogle Scholar
  13. Holmström B (1979) Groves’ scheme on restricted domains. Econometrica 47:1137–1144CrossRefGoogle Scholar
  14. Miyagawa E (2001) House allocation with transfers. J Econ Theory 100:329–355CrossRefGoogle Scholar
  15. Moulin H (2009) Almost budget-balanced VCG mechanisms to assign multiple objects. J Econ Theory 144:96–119CrossRefGoogle Scholar
  16. Muller E, Satterthwaite MA (1977) The equivalence of strong positive association and strategy-proofness. J Econ Theory 14:412–418CrossRefGoogle Scholar
  17. Ohseto S (1999) Strategy-proof allocation mechanisms for economies with an indivisible good. Soc Choice Welf 16:121–136CrossRefGoogle Scholar
  18. Ohseto S (2000) Strategy-proof and efficient allocation of an indivisible good on finitely restricted preference domains. Int J Game Theory 29:365–374CrossRefGoogle Scholar
  19. Ohseto S (2004) Implementing egalitarian-equivalent allocation of indivisible goods on restricted domains. Econ Theory 23:659–670CrossRefGoogle Scholar
  20. Ohseto S (2006) Characterizations of strategy-proof and fair mechanisms for allocating indivisible goods. Econ Theory 29:111–121CrossRefGoogle Scholar
  21. Pápai S (2003) Groves sealed bid auctions for heterogeneous objects with fair prices. Soc Choice Welf 20:371–385CrossRefGoogle Scholar
  22. Pazner EA, Schmeidler D (1978) Egalitarian equivalent allocations: a new concept of economic equity. Q J Econ 92:671–687Google Scholar
  23. Porter R, Shoham Y, Tennenholtz M (2004) Fair imposition. J Econ Theory 118:209–228CrossRefGoogle Scholar
  24. Saitoh H, Serizawa S (2008) Vickrey allocation rule with income effect. Econ Theory 35:391–401CrossRefGoogle Scholar
  25. Sakai T (2008) Second price auctions on general preference domains: two characterizations. Econ Theory 37:347–356CrossRefGoogle Scholar
  26. Sakai T (2013a) An equity characterization of second price auctions when preferences may not be quasilinear. Rev Econ Des 17:17–26Google Scholar
  27. Sakai T (2013b) Axiomatizations of second price auctions with a reserve price. Int J Econ Theory 9:255–265CrossRefGoogle Scholar
  28. Satterthwaite MA (1975) Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10:187–217CrossRefGoogle Scholar
  29. Schummer J (2000) Eliciting preferences to assign positions and compensation. Games Econ Behav 30: 293–318Google Scholar
  30. Sprumont Y (1995) Strategyproof collective choice in economic and political environments. Can J Econ 28:68–107CrossRefGoogle Scholar
  31. Sprumont Y (2013) Constrained-optimal strategy-proof assignment: beyond the Groves mechanisms. J Econ Theory 148:1102–1121Google Scholar
  32. Svensson L-G (2009) Coalitional strategy-proofness and fairness. Econ Theory 40:227–245CrossRefGoogle Scholar
  33. Svensson L-G, Larsson B (2002) Strategy-proof and nonbossy allocation of indivisible goods and money. Econ Theory 20:483–502CrossRefGoogle Scholar
  34. Takamiya K (2001) Coalition strategy-proofness and monotonicity in Shapley-Scarf housing markets. Math Soc Sci 41:201–213CrossRefGoogle Scholar
  35. Vickrey W (1961) Counterspeculation, auctions, and competitive sealed tenders. J Financ 16:8–37CrossRefGoogle Scholar
  36. Yengin D (2012) Egalitarian-equivalent Groves mechanisms in the allocation of heterogeneous objects. Soc Choice Welf 38:137–160CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Tohoku Seikatsu Bunka CollegeSendaiJapan
  2. 2.Faculty of EconomicsTohoku UniversitySendaiJapan

Personalised recommendations