×

zbMATH — the first resource for mathematics

On risk aversion and bargaining outcomes. (English) Zbl 1046.91075
From the authors’ abstract: “We revisit the well-known result that asserts that an increase in the degree of one’s risk aversion improves the position of one’s opponents. To this end, we apply Yaari’s dual theory of choice under risk both to Nash’s bargaining problem and to Rubinstein’s game of alternating offers. Under this theory, unlike under expected utility, risk aversion influences the bargaining outcome only when this outcome is random, namely, when the players are risk lovers. In this case, an increase in one’s degree of risk aversion increases one’s share of the pie.”
The paper refers to M. E. Yaari [Econometrica 55, 95–115 (1987; Zbl 0616.90005)], J. F. Nash [Econometrica 28, 155–162 (1950)] and to A. Rubinstein [Econometrica 50, 97–110 (1982; Zbl 0474.90092)].

MSC:
91B30 Risk theory, insurance (MSC2010)
91A12 Cooperative games
91A05 2-person games
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Binmore, K.G., Nash bargaining theory II, (), 61-76
[2] Binmore, K.G.; Rubinstein, A.; Wolinsky, A., The Nash bargaining solution in economic modeling, RAND J. econ., 17, 176-188, (1986)
[3] Dagan, N., Volij, O., Winter, E., 2001. The time-preference Nash solution. Discussion paper 265, Center for Rationality and Interactive Decision Theory
[4] Demers, F.; Demers, M., Price uncertainty, the competitive firm and the dual theory of choice under risk, Europ. econ. rev., 34, 1181-1199, (1990)
[5] Hadar, J.; Seo, T.K., Asset diversification in Yaari’s dual theory, Europ. econ. rev., 39, 1171-1180, (1995)
[6] Kannai, Y., Concavifiability and constructions of concave utility functions, J. math. econ., 4, 1-56, (1977) · Zbl 0361.90008
[7] Khilstrom, R.E.; Roth, A.E.; Schmeidler, D., Risk aversion and solutions to Nash’s bargaining problem, (), 65-71
[8] Murnighan, J.K.; Roth, A.E.; Schoumaker, F., Risk aversion in bargaining: an experimental study, J. risk uncertainty, 1, 101-124, (1988)
[9] Nash, J.F., The bargaining problem, Econometrica, 28, 155-162, (1950) · Zbl 1202.91122
[10] Osborne, M.J., The role of risk aversion in a simple model of bargaining, ()
[11] Osborne, M.J.; Rubinstein, A., A course in game theory, (1994), MIT Press Cambridge · Zbl 1194.91003
[12] Roth, A.E., A note on risk aversion in a perfect equilibrium model of bargaining, Econometrica, 53, 207-211, (1985) · Zbl 0587.90106
[13] Roth, A.E., Risk aversion and the relation between Nash’ solution and subgame perfect equilibrium of sequential bargaining, J. risk uncertainty, 2, 353-365, (1989)
[14] Roth, A.E.; Rothblum, U., Risk aversion and Nash’s solution for bargaining games with risky outcomes, Econometrica, 50, 639-647, (1982) · Zbl 0478.90090
[15] Rubinstein, A., Perfect equilibrium in a bargaining model, Econometrica, 50, 97-110, (1982) · Zbl 0474.90092
[16] Rubinstein, A.; Safra, Z.; Thomson, W., On the interpretation of the Nash bargaining solution and its extension to non-expected utility preferences, Econometrica, 60, 1171-1186, (1992) · Zbl 0767.90094
[17] Safra, Z.; Zhou, L.; Zilcha, I., Risk aversion in Nash bargaining problems with risky outcomes and risky disagreement points, Econometrica, 58, 961-965, (1990) · Zbl 0747.90116
[18] Safra, Z.; Zilcha, I., Bargaining solutions without the expected utility hypothesis, Games econ. behav., 5, 288-306, (1993) · Zbl 0776.90094
[19] Sobel, J., Distortion of utilities and the bargaining problem, Econometrica, 49, 597-620, (1981) · Zbl 0456.90092
[20] Thomson, W., The manipulability of the Shapley value, Int. J. game theory, 46, 101-127, (1988) · Zbl 0646.90102
[21] Volij, O., 2002. Payoff equivalence in sealed bid auctions and the dual theory of choice under risk. Econ. Letters, in press · Zbl 1031.91040
[22] Yaari, M.E., Univariate and multivariate comparisons of risk aversion: A new approach, () · Zbl 0204.18803
[23] Yaari, M.E., The dual theory of choice under risk, Econometrica, 55, 95-115, (1987) · Zbl 0616.90005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.