Abstract
In this note we show that a solution proposed byRaiffa for two-person bargaining games, which has recently been axiomatized byKalai/Smorodinsky, does not generalize in a straightforward manner to generaln-person bargaining games. Specifically, the solution is not Pareto optimal on the class of alln-person bargaining games, and no solution which is can possess the other properties which characterizeRaiffa's solution in the two-person case.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Butrim, B.I.: A Modified Solution of the Bargaining Problem. (Russian), Zhurnal Vychislitel' noi Matematiki Matematicheskoi Fiziki16, 1976, 340–350.
Crott, H. W.: Experimentelle Untersuchung zum Verhandlungsverhalten in Kooperativen Spielen. Zeitschrift für Sozialpsychologie2, 1971, 61–74.
Harsanyi, J.C.: Rational Behavior and Bargaining Equilibrium in Games and Social Situations. Cambridge 1977.
Kalai, E.: Nonsymmetric Nash Solutions and Replications of 2-Person Bargaining. International Journal of Game Theory, 1977a, 129–133.
—: Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparison. Econometrica45, 1977b, 1623–1630.
Kalai, E., andM. Smorodinsky: Other Solutions to Nash's Bargaining Problem. Econometrica43, 1975, 513–518.
Luce, R.D., andH. Raiffa: Games and Decisions: Introduction and Critical Survey. New York 1957.
Myerson, R.B.: Two-Person Bargaining Problems and Comparable Utility. Econometrica45, 1977, 1631–1637.
Nash, J.F.: The Bargaining Problem. Econometrica28, 1950, 155–162.
Raiffa, H.: Arbitration Schemes for Generalized Two-Person Games. Contributions to the Theory of Games II. Ed. by H.W. Kuhn and A.W. Tucker. Annals of Mathematics Studies, No. 28, Princeton 1953, 361–387.
Roth, A.E.: Individual Rationality and Nash's Solution to the Bargaining Problem. Mathematics of Operations Research2, 1977a, 64–65.
—: Independence of Irrelevant Alternatives and Solutions to Nash's Bargaining Problem. Journal of Economic Theory16, 1977b, 247–251.
—: The Nash Solution and the Utility of Bargaining. Econometrica46, 1978, 587–594, 983.
—: Proportional Solutions to the Bargaining Problems. Econometrica47, 1979a, 775–778.
-: Axiomatic Models of Bargaining. Lecture Notes in Economics and Mathematical Systems,# 170, Berlin-Heidelberg-New York, forthcoming, 1979b.
Author information
Authors and Affiliations
Additional information
This work was supported by National Science Foundation Grant SOC 78-09928 to the University of Illinois. It has also benefitted from discussion and correspondence with H. Imai, E. Kalai, and M. Maschler.
Rights and permissions
About this article
Cite this article
Roth, A.E. An impossibility result concerningn-person bargaining games. Int J Game Theory 8, 129–132 (1979). https://doi.org/10.1007/BF01770063
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01770063