An impossibility result concerningn-person bargaining games
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.