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On Risk Aversion and Bargaining Outcomes

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  • Volij, Oscar
  • Winter, Eyal

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.

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Bibliographic Info

Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 10130.

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Date of creation: 01 Jan 2002
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Publication status: Published in Games and Economic Behavior 2002, vol. 41 no. 1, pp. 120-140
Handle: RePEc:isu:genres:10130

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Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
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Web page: http://www.econ.iastate.edu
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References

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  1. Fanny Demers & Michel Demers, 1989. "Price Uncertainty, The Competitive Firm and the Dual Theory of Choice Under Risk," Carleton Industrial Organization Research Unit (CIORU) 89-09, Carleton University, Department of Economics.
  2. Oscar Volij, 1999. "Utility Equivalence in Sealed Bid Auctions and the Dual Theory of Choice Under Risk," Economic theory and game theory 009, Oscar Volij, revised 25 Mar 1999.
  3. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
  4. Nir Dagan & Oscar Volij & Eyal Winter, 2001. "The time-preference Nash solution," Economic theory and game theory 019, Nir Dagan.
  5. Roth, Alvin E, 1985. "A Note on Risk Aversion in a Perfect Equilibrium Model of Bargaining," Econometrica, Econometric Society, vol. 53(1), pages 207-11, January.
  6. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  7. Volij, Oscar, 2002. "Payoff Equivalence in Sealed Bid Auctions and the Dual Theory of Choice Under Risk," Staff General Research Papers 10129, Iowa State University, Department of Economics.
  8. Murnighan, J Keith & Roth, Alvin E & Schoumaker, Francoise, 1988. " Risk Aversion in Bargaining: An Experimental Study," Journal of Risk and Uncertainty, Springer, vol. 1(1), pages 101-24, March.
  9. Zilcha & I. & Safra, Z., 1990. "Bargaining Solutions Without The Expected Utility Hypothesis," Papers 33-90, Tel Aviv.
  10. Roth, Alvin E & Rothblum, Uriel G, 1982. "Risk Aversion and Nash's Solution for Bargaining Games with Risky Outcomes," Econometrica, Econometric Society, vol. 50(3), pages 639-47, May.
  11. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  12. Safra, Zvi & Zhou, Lin & Zilcha, Itzhak, 1990. "Risk Aversion in the Nash Bargaining Problem with Risky Outcomes and Risky Disagreement Points," Econometrica, Econometric Society, vol. 58(4), pages 961-65, July.
  13. Rubinstein, Ariel & Safra, Zvi & Thomson, William, 1992. "On the Interpretation of the Nash Bargaining Solution and Its Extension to Non-expected Utility Preferences," Econometrica, Econometric Society, vol. 60(5), pages 1171-86, September.
  14. Hadar, Josef & Seo, Tae Kun, 1995. "Asset diversification in Yaari's dual theory," European Economic Review, Elsevier, vol. 39(6), pages 1171-1180, June.
  15. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  16. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  17. Roth, Alvin E, 1989. " Risk Aversion and the Relationship between Nash's Solution and Subgame Perfect Equilibrium of Sequential Bargaining," Journal of Risk and Uncertainty, Springer, vol. 2(4), pages 353-65, December.
  18. Thomson, William, 1988. "The Manipulability of the Shapley-Value," International Journal of Game Theory, Springer, vol. 17(2), pages 101-27.
  19. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
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Citations

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Cited by:
  1. Kohlscheen, Emanuel & O’Connell, Stephen, 2008. "On Risk Aversion in the Rubinstein Bargaining Game," The Warwick Economics Research Paper Series (TWERPS) 878, University of Warwick, Department of Economics.
  2. Oscar Volij, 2002. "A Remark on Bargaining and Non-Expected Utility," Economic theory and game theory 016, Oscar Volij.
  3. Ross Cressman, Maria Gallego, 2005. "On the Ranking of Bilateral Bargaining Opponents," Working Papers eg0043, Wilfrid Laurier University, Department of Economics, revised 2005.
  4. Nir Dagan & Oscar Volij & Eyal Winter, 2001. "The Time-Preference Nash Solution," Discussion Paper Series dp265, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  5. Huang, Rachel J. & Huang, Yi-Chieh & Tzeng, Larry Y., 2013. "Insurance bargaining under ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 812-820.

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