Social Choice and Welfare

, Volume 28, Issue 3, pp 421–437 | Cite as

Bargaining over a finite set of alternatives

Original Paper

Abstract

We analyze bilateral bargaining over a finite set of alternatives. We look for "good" ordinal solutions to such problems and show that Unanimity Compromise and Rational Compromise are the only bargaining rules that satisfy a basic set of properties. We then extend our analysis to admit problems with countably infinite alternatives. We show that, on this class, no bargaining rule choosing finite subsets of alternatives can be neutral. When rephrased in the utility framework of Nash (1950), this implies that there is no ordinal bargaining rule that is finite-valued.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anbarcı N(2005) Finite alternating-move arbitration schemes and the equal area solution. Theory Decis (forthcoming)Google Scholar
  2. Brams S, Kilgour DM (2001) Fallback bargaining. Group Decis Negoti 10:287–316CrossRefGoogle Scholar
  3. Hurwicz L, Sertel MR (1997) Designing mechanisms, in particular for electoral systems: the majoritarian compromise. Department of Economics, Boğaziçi University, İstanbul (preprint)Google Scholar
  4. Kalai E, Smorodinsky M (1975) Other solutions to Nash’s bargaining problem. Econometrica 43:513–518CrossRefGoogle Scholar
  5. Kalai E (1977) "Proportional solutions to bargaining situations: interpersonal utility comparisons. Econometrica 45:1623–1630CrossRefGoogle Scholar
  6. Kalai E, Rosenthal RW (1978) Arbitration of two-party disputes under ignorance. Int J Game Theory 7:65–72CrossRefGoogle Scholar
  7. Kıbrıs Ö (2002) Nash bargaining in ordinal environments. Sabancı University Economics Discussion Paper, suecdp-02-02, at http://www.sabanciuniv.edu/ssbf/economics/eng/research/index. html.Google Scholar
  8. Kıbrıs Ö (2004) Egalitarianism in ordinal bargaining: the Shapley–Shubik rule. Games Econ Behav 49(1):157–170CrossRefGoogle Scholar
  9. Mariotti M(1998) Nash bargaining theory when the number of alternatives can be finite. Soc Choice Welfare 15:413–421CrossRefGoogle Scholar
  10. Maskin E (1986) The theory of implementation in Nash Equilibria: a survey. In: Hurwicz L, Schmeidler D, Sonnenschein M (eds) Social goods and social organization: volume in memory of Elisha Pazner. Cambridge University Press, CambridgeGoogle Scholar
  11. Nagahisa R, Tanaka M (2002) An axiomatization of the Kalai–Smorodinsky solution when the feasible sets can be finite. Soc Choice Welfare 19:751–761CrossRefGoogle Scholar
  12. Nash JF (1950) The bargaining problem. Econometrica 18:155–162CrossRefGoogle Scholar
  13. Roemer J(1996) Theories of distributive justice. Harvard University Press, CambridgeGoogle Scholar
  14. Roth AE (1979) Axiomatic models of bargaining. Springer, Berlin Heidelberg New yorkGoogle Scholar
  15. Rubinstein A, Safra Z, Thomson W (1992) On the interpretation of the Nash bargaining solution and its extension to non-expected utility preferences. Econometrica 60:1171–1186CrossRefGoogle Scholar
  16. Sertel MR (1985) Lecture notes in microeconomic theory. Boğaziçi University (unpublished manuscript)Google Scholar
  17. Sertel MR, Yılmaz B (1999) The Majoritarian Compromise is majoritarian-optimal and subgame-perfect implementable. Soc Choice Welfare 16:615–627CrossRefGoogle Scholar
  18. Sertel MR, Yıldız M (2003) The impossibility of a Walrasian bargaining solution. In: Koray S, Sertel MR (eds) Advances in economic design. Springer, Berlin Heidelberg New YorkGoogle Scholar
  19. Shapley L (1969) Utility comparison and the theory of games. In: La Décision: Agrégation et Dynamique des Ordres de Préférence. Editions du CNRS, Paris, pp 251–263Google Scholar
  20. Shubik M (1982) Game theory in the social sciences. MIT Press, CambridgeGoogle Scholar
  21. Thomson W (1994) Cooperative models of bargaining. In: Aumann RJ, Hart S (eds) Handbook of game theory, Vol II. North-HollandGoogle Scholar
  22. Thomson W (1996) Bargaining theory: the axiomatic approach, book manuscriptGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Faculty of Arts and Social SciencesSabancı UniversityIstanbulTurkey
  2. 2.Department of EconomicsKoç ÜniversityIstanbulTurkey

Personalised recommendations