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Stability and the Nash solution. (English) Zbl 0657.90106
The author deals with the usual Nash bargaining n-person scheme and proves that the Nash solution can be characterized by the set of axioms differing from Nash’s axioms only by replacing the Axiom of Independence of Irrelevant Alternatives by Harsanyi’s Axiom of Multilateral Stability (the remaining axioms are: Pareto Optimality, Anonymity and Scale Invariance). The paper also deals with variants of the main result.
Reviewer: A.Wieczorek

MSC:
91A12 Cooperative games
91B10 Group preferences
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[1] Aumann, R.J; Maschler, M, Game theoretic analysis of a bankruptcy problem from the talmud, J. econ. theory, 36, 195-213, (1985) · Zbl 0578.90100
[2] Balinksy, M; Young, H.P, ()
[3] Harsanyi, J.C, A bargaining model for the cooperative n-person game, () · Zbl 0319.90078
[4] Harsanyi, J.C, A simplified bargaining model for the n-person cooperative game, Int. econ. rev., 4, 194-220, (1963) · Zbl 0118.15103
[5] Harsanyi, J.C, Rational behavior and bargaining equilibrium in games and social situations, (1977), Cambridge Univ. Press Cambridge · Zbl 0395.90087
[6] Hart, S; Mas-Colell, A, Potential, value and consistency, (1985), Harvard University Cambridge, MA, mimeo
[7] Hildenbrand, W, Core and equilibria of a large economy, (1974), Princeton Univ. Press Princeton, NJ · Zbl 0351.90012
[8] Kalai, E; Smorodinsky, M, Other solutions to Nash’s bargaining problem, Econometrica, 43, 513-518, (1975) · Zbl 0308.90053
[9] Lensberg, T, Stability and collective rationality, Econometrica, 55, 935-961, (1987) · Zbl 0622.90007
[10] Moulin, H, The separability axiom and equal-sharing methods, J. econ. theory, 36, 120-148, (1985) · Zbl 0603.90013
[11] Moulin, H, Equal or proportional division of a surplus, and other methods, (1985), Virginia Polytechnic Institute and State University Blacksburg, VA, mimeo · Zbl 0631.90093
[12] Nash, J.F, The bargaining problem, Econometrica, 18, 155-162, (1950) · Zbl 1202.91122
[13] Peleg, B, An axiomatization of the core of cooperative games without side payments, J. math. econ., 14, 203-214, (1985) · Zbl 0581.90102
[14] \scB. Peleg, On the reduced game property and its converse, Int. J. Game Theory, in press. · Zbl 0629.90099
[15] Roth, A.E, Independence of irrelevant alternatives and solutions to Nash’s bargaining problem, J. econ. theory, 16, 247-251, (1977) · Zbl 0399.90103
[16] Sobolev, A.I, The characterization of optimality principles in cooperative games by functional equations (in Russian), (), 94-151
[17] Thomson, W, A class of solutions to bargaining problems, J. econ. theory, 25, 431-441, (1981) · Zbl 0473.90092
[18] Thomson, W, The fair division of a fixed supply among a growing population, Math. oper. res., 8, 319-326, (1983) · Zbl 0524.90102
[19] Young, H.P, Consistency and optimality in taxation, (1984), University of Maryland, mimeo
[20] Young, H.P, Taxation and bankruptcy, (1984), University of Maryland, mimeo
[21] Young, H.P, On dividing an amount according to individual claims or liabilities, Math. oper. res., 12, 398-414, (1987) · Zbl 0629.90003
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