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Abstract

Bargaining problems are considered where the preferences of the bargainers deviate from expected utility but can be modelled according to rank dependent utility theory. Under rank dependent utility two factors influence the risk attitude of a decision maker: the utility function and the probability weighting function. Arising from the same definition of risk aversion, two forms of risk aversion can be distinguished: utility risk aversion and probabilistic risk aversion.The main finding is that these two forms of risk aversion can have surprisingly opposite consequences for bargaining solutions that exhibit a weak monotonicity property. In particular, in a large class of bargaining problems both increased utility risk aversion and decreased probabilistic risk aversion of the opponent are advantagous for a player. This is demonstrated for the Kalai-Smorodinsky bargaining solution. The Nash bargaining solution does not behave regularly in this respect.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 110 (2003)
Issue (Month): 1 (May)
Pages: 154-175

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Handle: RePEc:eee:jetheo:v:110:y:2003:i:1:p:154-175

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Web page: http://www.elsevier.com/locate/inca/622869

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1. Volij, Oscar & Winter, Eyal, 2002. "On risk aversion and bargaining outcomes," Games and Economic Behavior, Elsevier, vol. 41(1), pages 120-140, October.
   
   • Volij, Oscar & Winter, Eyal, 2002. "On Risk Aversion and Bargaining Outcomes," Staff General Research Papers 10130, Iowa State University, Department of Economics.
2. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
3. 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.
4. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
5. 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.
6. Chateauneuf, Alain & Cohen, Michele, 1994. "Risk Seeking with Diminishing Marginal Utility in a Non-expected Utility Model," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 77-91, July.
7. SHALEV, Jonathan, 1997. "Loss aversion and bargaining," CORE Discussion Papers 1997006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
   
   • Jonathan Shalev, 2002. "Loss Aversion and Bargaining," Theory and Decision, Springer, vol. 52(3), pages 201-232, May.
   • Jonathan Shalev, 1996. "Loss Aversion and Bargaining," Game Theory and Information 9606001, EconWPA, revised 18 Mar 1997.
8. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
9. 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.
10. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
11. Zilcha & I. & Safra, Z., 1990. "Bargaining Solutions Without The Expected Utility Hypothesis," Papers 33-90, Tel Aviv.
    
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12. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
13. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
14. Oscar Volij, 1999. "On Risk Aversion and Bargaining Outcomes," Economic theory and game theory 010, Oscar Volij.
15. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
16. Peters, Hans, 1992. "A criterion for comparing strength of preference, with an application to bargaining," Open Access publications from Maastricht University urn:nbn:nl:ui:27-12279, Maastricht University.
17. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
18. Crawford, Vincent P. & Varian, Hal R., 1979. "Distortion of preferences and the Nash theory of bargaining," Economics Letters, Elsevier, vol. 3(3), pages 203-206.
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20. Burgos, Albert & Grant, Simon & Kajii, Atsushi, 2002. "Bargaining and Boldness," Games and Economic Behavior, Elsevier, vol. 38(1), pages 28-51, January.

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Cited by:

1. Caroline Berden & Hans Peters, 2006. "On the Effect of Risk Aversion in Bimatrix Games," Theory and Decision, Springer, vol. 60(4), pages 359-370, 06.
   
   • Berden,Caroline & Peters,Hans, 2005. "On the effect of risk aversion in bimatrix games," Research Memoranda 029, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
2. Ross Cressman, Maria Gallego, 2005. "On the Ranking of Bilateral Bargaining Opponents," Working Papers eg0043, Wilfrid Laurier University, Department of Economics, revised 2005.
   
   • Cressman, Ross & Gallego, Maria, 2009. "On the ranking of bilateral bargaining opponents," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 64-83, July.
3. Predtetchinski, Arkadi, 2006. "A General Structure Theorem for the Nash Equilibrium Correspondence," Research Memoranda 010, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
4. Driesen, Bram & Perea, Andrés & Peters, Hans, 2012. "Alternating offers bargaining with loss aversion," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 103-118.
   
   • Driesen Bram & Perea Andrés & Peters Hans, 2009. "Alternating offers bargaining with loss aversion," Research Memoranda 001, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
5. Driesen, Bram & Perea, Andrés & Peters, Hans, 2011. "The Kalai-Smorodinsky bargaining solution with loss aversion," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 58-64, January.
   
   • Driesen Bram & Perea Andrés & Peters Hans, 2009. "The Kalai-Smorodinsky Solution with Loss Aversion," Research Memoranda 030, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.

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