Social Choice and Welfare

, Volume 43, Issue 3, pp 603–633 | Cite as

Asymmetrically fair rules for an indivisible good problem with a budget constraint

  • Paula Jaramillo
  • Çaǧatay Kayı
  • Flip Klijn


We study a particular restitution problem where there is an indivisible good (land or property) over which two agents have rights: the dispossessed agent and the owner. A third party, possibly the government, seeks to resolve the situation by assigning rights to one and compensate the other. There is also a maximum amount of money available for the compensation. We characterize a family of asymmetrically fair rules that are immune to strategic behavior, guarantee minimal welfare levels for the agents, and satisfy the budget constraint.



We would like to thank Tommy Andersson, Vikram Manjunath, William Thomson, and an anonymous referee for detailed comments on an earlier draft of the paper. We also thank the seminar participants at Universidad de Los Andes, Bilkent University, Universidad del Rosario, Maastricht University, UECE Lisbon meeting 2011, JOLATE XII, REES Bilbao, First Caribbean Game Theory Conference, Institute for Economic Analysis (CSIC), GAMES 2012, Latin American Workshop in Economic Theory, and Durham University Business School for valuable discussions. Ç. Kayı gratefully acknowledges the hospitality of Institute for Economic Analysis (CSIC) and financial support from Colciencias/CSIC (Convocatoria No: 506/2010), El Patrimonio Autónomo Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación, Francisco José de Caldas. The first draft of this paper was written while F. Klijn was visiting Universidad del Rosario. He gratefully acknowledges the hospitality of Universidad del Rosario and financial support from CSIC/Colciencias through grant 2010CO0013 and the Spanish Ministry of Economy and Competitiveness through Plan Nacional I+D+i (ECO2011–29847) and the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2011-0075).


  1. Alkan A, Demange G, Gale D (1991) Fair allocation of indivisible goods and criteria of justice. Econometrica 59:1023–1039CrossRefGoogle Scholar
  2. Andersson T, Svensson LG (2008a) Non-manipulable assignment of individuals to positions revisited. Math Soc Sci 56:350–354CrossRefGoogle Scholar
  3. Andersson T, Svensson LG (2008b) Weakly fair allocations and strategy-proofness. Rev Econ Design 11:321–338CrossRefGoogle Scholar
  4. Andersson T, Svensson LG, Yang Z (2010) Constrainedly fair job assignments under minimum wages. Games Econ Behav 68:428–442CrossRefGoogle Scholar
  5. Andersson T, Ehlers L, Svensson LG (2012) (Minimally) \(\varepsilon \)-incentive compatible competitive equilibria in economies with indivisibilities. CIREQ Working Paper Cahier 04–2012Google Scholar
  6. Athanasiou E (2013) A solomonic solution to the problem of assigning a private indivisible object. Games Econ Behav 82:369–387CrossRefGoogle Scholar
  7. Barry M (2011) Land restitution and communal property associations: The Elandskloof case. Land Use Policy 28:139–150Google Scholar
  8. Blacksell M, Born KM (2002) Rural property restitution in Germany’s new Bundesländer: The case of Bergholz. J Rural Stud 18:325–338Google Scholar
  9. Clark EH (1971) Multipart pricing of public goods. Public Choice 11:17–33CrossRefGoogle Scholar
  10. Foley D (1967) Resource allocation and the public sector. Yale Econ Essays 7:45–98Google Scholar
  11. Green J, Laffont JJ (1977) Characterization of satisfactory mechanisms for the revelation of preferences for public goods. Econometrica 45:427–438CrossRefGoogle Scholar
  12. Grover R, Bórquez MF (2004) Restitution and land markets. Mimeo. Oxford Brookes University, OxfordGoogle Scholar
  13. Groves T (1973) Incentives in teams. Econometrica 41:617–631CrossRefGoogle Scholar
  14. Holmström B (1979) Groves’ scheme on restricted domains. Econometrica 47:1137–1144CrossRefGoogle Scholar
  15. Ibáñez AM (2009) El desplazamiento forzoso en Colombia: Un camino sin retorno a la pobreza. Editorial UniandesGoogle Scholar
  16. Kominers SD, Weyl EG (2011) Concordance among holdouts. Discussion Paper, Harvard Institute of Economic ResearchGoogle Scholar
  17. Mishra D, Sarkar S, Sen A (2008) Land deals in Sarkar Raj: Perspectives from mechanism design theory. Mimeo. Indian Statistical InstituteGoogle Scholar
  18. Nisan N (2007) Introduction to mechanism design (for computer scientists). In: Roughgarden T, Tardos E, Vazirani V (eds) Algorithmic game theory. Cambridge University Press, Cambridge, pp 209–241CrossRefGoogle Scholar
  19. Ohseto S (2006) Characterizations of strategy-proof and fair mechanisms for allocating indivisible goods. Econ Theor 29:111–121CrossRefGoogle Scholar
  20. Southern DB (1993) Restitution or compensation: The land question in East Germany. Int Comp Law Q 42:690–697Google Scholar
  21. Sprumont Y (2013) Constrained-optimal strategy-proof assignment: Beyond the Groves mechanisms. J Econ Theory 148:1102–1121Google Scholar
  22. Sun N, Yang Z (2003) A general strategy-proof fair allocation mechanism. Econ Lett 81:73–89CrossRefGoogle Scholar
  23. Svensson LG (1983) Large indivisibles: An analysis with respect to price equilibrium and fairness. Econometrica 51:939–954Google Scholar
  24. Svensson LG (2009) Coalitional strategy-proofness and fairness. Econ Theor 40:227–245CrossRefGoogle Scholar
  25. Tadenuma K, Thomson W (1995) Games of fair division. Games Econ Behav 9:191–204CrossRefGoogle Scholar
  26. van Boven T (2010) The United Nations basic principles and guidelines on the right to a remedy and reparation for victims of gross violations of international human rights law and serious violations of international humanitarian law. United Nations Audiovisual Library of International Law New York, United NationsGoogle Scholar
  27. Vickrey W (1961) Counterspeculation, auctions, and competitive sealed tenders. J Financ 16:8–37CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Facultad de EconomíaUniversidad de Los AndesBogotáColombia
  2. 2.Facultad de EconomíaUniversidad del RosarioBogotáColombia
  3. 3.Institute for Economic Analysis (CSIC) and Barcelona GSEBarcelonaSpain

Personalised recommendations