International Journal of Game Theory

, Volume 15, Issue 1, pp 59–63 | Cite as

Replication invariance of bargaining solutions

  • William Thomson


This note is concerned with the behavior of bargaining solutions under replication of bargaining problems. A notion of replication, alternative to that studied by Kalai, is proposed, and it is shown that for both the Nash and Kalai-Smorodinsky solutions, the sum of what the agents of each type obtain in the replicated problem is equal to what the agent they are representing would obtain in the original problem under an application of the asymmetric generalization of the solution with weights proportional to the orders of replication of the different types. This similarity in behavior of the two solutions is in contrast with the conclusions reached by Kalai.


Economic Theory Game Theory Original Problem Bargaining Solution Bargaining Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Harsanyi J, Selten R (1972) A generalized Nash solution for two-person bargaining games with incomplete information. Management Science 18:80–106Google Scholar
  2. Kalai E (1977) Non-symmetric Nash solutions and replications of 2-person bargaining. International Journal of Game Theory 6:129–133Google Scholar
  3. Kalai E, Smorodinsky M (1975) Other solutions to Nash's bargaining problem. Econometrica 43: 513–518Google Scholar
  4. Kaneko M, Wooders M (1982) Cores of partitioning games. Mathematical Social Sciences 3:313–327Google Scholar
  5. Moulin H (1985) Egalitarianism and Utilitarianism in quasi-linear bargaining. Econometrica 53:49–67Google Scholar
  6. Nash JF (1950) The bargaining problem. Econometrica 18:155–162Google Scholar
  7. Peters HJM, Tijs SH (1982) Characterization of all individually monotonic bargaining solutions. Discussion paperGoogle Scholar
  8. Roth AE (1979) Axiomatic models of bargaining. Springer, No 170Google Scholar

Copyright information

© Physica-Verlag 1986

Authors and Affiliations

  • William Thomson
    • 1
  1. 1.Department of EconomicsUniversity of RochesterRochesterUSA

Personalised recommendations