International Journal of Game Theory

, Volume 39, Issue 1–2, pp 209–222 | Cite as

Manipulation games in economies with indivisible goods

Article

Abstract

In this paper we study the strategic aspects of the No-Envy solution for the problem of allocating a finite set of indivisible goods among a group of agents when monetary compensations are possible. In the first part of the paper we consider the case where each agent receives, at most, one indivisible good. We prove that the set of equilibrium allocations of any direct revelation game associated with a subsolution of the No-Envy solution coincides with the set of envy-free allocations for the true preferences. Under manipulation all the subsolutions of the No-Envy solution are equivalent. In the second part of the paper, we allow each agent to receive more than one indivisible good. In this situation the above characterization does not hold any more. We prove that any Equal Income Walrasian allocation for the true preferences can be supported as an equilibrium allocation of any direct revelation game associated with subsolutions of the No-Envy solution, but also non-efficient allocations can be supported.

Keywords

Indivisible goods Envy-freeness Direct revelation games 

JEL Classification

C72 D63 D71 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdulkadiroğlu A, Sönmez T, Ünver MU (2004) Room assignment-rent division: a market approach. Soc Choice Welf 22: 515–538CrossRefGoogle Scholar
  2. Alkan A, Demange G, Gale D (1991) Fair allocation of indivisible goods and criteria of justice. Econometrica 63: 1023–1039CrossRefGoogle Scholar
  3. Āzacis H (2008) Double implementation in a market for indivisible goods with a price constraint. Games Econ Behav 62: 140–154CrossRefGoogle Scholar
  4. Barberà S, Jackson M (1995) Strategy-proof exchange. Econometrica 63: 51–87CrossRefGoogle Scholar
  5. Beviá C (1996) Identical preferences lower bound solution and consistency in economies with indivisible goods. Soc Choice Welf 13: 113–126CrossRefGoogle Scholar
  6. Beviá C (1998) Fair allocation in a general model with indivisible goods. Rev Econ Des 3: 195–213Google Scholar
  7. Beviá C, Quinzii M, Silva JA (1999) Buying several indivisible goods. Math Soc Sci 37: 1–23CrossRefGoogle Scholar
  8. Foley D (1967) Resource allocation and the public sector. Yale Econ Essays 7: 45–98Google Scholar
  9. Fujinaka Y, Sakai T (2007) The manipulability of fair solutions in assignment of an indivisible object with monetary transfers. J Public Econ Theory 9: 993–1011CrossRefGoogle Scholar
  10. Henry C (1970) Indivisibilite´ dans une Economie d’Echanges. Econometrica 38(3): 542–558CrossRefGoogle Scholar
  11. Hurwicz L (1972) On informationally decentralized systems. In: McGuire CB, Radner R (eds) Decision and organization. North-Holland, Amsterdam, pp 297–336Google Scholar
  12. Hurwicz L (1979) On the interactions between information and incentives in organizations. In: Krippendorf K (eds) communication and control in society. Scientific Publishers, New York, pp 123–147Google Scholar
  13. Moulin H (1990) Fair division under joint ownership: recent results and open questions. Sco Choice Welf 7: 149–170CrossRefGoogle Scholar
  14. Otani Y, Sicilian J (1982) Equilibrium allocations of Walrasian preferences games. J Econ Theory 27: 47–68CrossRefGoogle Scholar
  15. Roth AE (1984) Misrepresentation and stability in the marriage problem. J Econ Theory 34: 383–387CrossRefGoogle Scholar
  16. Svensson LG (1983) Large indivisibles: an analysis with respect to price equilibrium and fairness. Econometrica 51: 939–954CrossRefGoogle Scholar
  17. Tadenuma K, Thomson W (1995) Games of fair division. Games Econ Behav 9: 191–204CrossRefGoogle Scholar
  18. Thomson W (1979) The equilibrium allocations of Walras and Lindahl manipulation games. University of Minnesota, Center for Economic Research, Discussion paper No. 790-111 (1995)Google Scholar
  19. Thomson W (1984) The manipulability of resource allocation mechanisms. Rev Econ Stud 51(3): 447–460CrossRefGoogle Scholar
  20. Thomson W (1987) The vulnerability to manipulate behavior of economic mechanisms design to select equitable and efficient outcomes. In: Groves T, Radner R, Reiter S (eds) Information, incentives and economic mechanisms. University of Minnesota Press, pp 375–396Google Scholar
  21. Thomson W (2007) Fair allocation rules. Rochester Center for economic research working paper no. 539Google Scholar
  22. Zhou L (1991a) Inefficiency of strategy-proof allocation mechanisms in pure exchange economies. Soc Choice Welf 8: 247–254CrossRefGoogle Scholar
  23. Zhou L (1991b) Stable matchings and equilibrium outcomes of the Gale–Shapley algorithm for the marriage problem. Econ Lett 36: 25–29CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Departament d’Economia i d’Història Econòmica and CODEUniversitat Autònoma de BarcelonaBarcelonaSpain

Personalised recommendations