An impossibility result concerningn-person bargaining games

International Journal of Game Theory - Tập 8 - Trang 129-132 - 1979
A. E. Roth1
1Department of Business Administration, University of Illinois, Urbana, USA

Tóm tắt

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.

Tài liệu tham khảo

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.