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The effect of decision weights in bargaining problems

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  • Kobberling, Veronika
  • Peters, Hans

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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Bibliographic Info

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. 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.
  2. 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.
  3. Zilcha & I. & Safra, Z., 1990. "Bargaining Solutions Without The Expected Utility Hypothesis," Papers 33-90, Tel Aviv.
  4. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  5. 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.
  6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  7. 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.
  8. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
  9. Burgos, Albert & Grant, Simon & Kajii, Atsushi, 2002. "Bargaining and Boldness," Games and Economic Behavior, Elsevier, vol. 38(1), pages 28-51, January.
  10. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
  11. 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.
  12. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
  13. 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.
  14. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
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Cited by:
  1. Predtetchinski, Arkadi, 2006. "A General Structure Theorem for the Nash Equilibrium Correspondence," Research Memorandum 010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Craig Webb, 2013. "Bargaining with subjective mixtures," Economic Theory, Springer, vol. 52(1), pages 15-39, January.
  3. Driesen, Bram & Perea, Andrés & Peters, Hans, 2012. "Alternating offers bargaining with loss aversion," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 103-118.
  4. Cressman, Ross & Gallego, Maria, 2009. "On the ranking of bilateral bargaining opponents," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 64-83, July.
  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.
  6. Berden,Caroline & Peters,Hans, 2005. "On the effect of risk aversion in bimatrix games," Research Memorandum 029, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  7. Driesen Bram & Perea Andrés & Peters Hans, 2009. "Alternating offers bargaining with loss aversion," Research Memorandum 001, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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