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On the ranking of bilateral bargaining opponents

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Listed author(s):
  • Cressman, Ross
  • Gallego, Maria

Abstract

We fix the status quo (Q) and one of the bilateral bargaining agents to examine how facing opponents with different single-peaked utility functions over a unidimensional space affects the Nash, Kalai-Smorodinsky and Perles-Maschler bargaining solutions. We find that when one opponent's utility is a concave transformation of the other's, the agent doing the ranking prefers the more risk averse, easier to satisfy, opponent. When opponents' utilities are translations of each other, we find that the bargainer whose ideal point is farthest from Q prefers an opponent whose ideal is closest to his own. For the agent closest to Q, the ranking of opponents depends on the absolute risk aversion (ARA) of the opponents' utility functions. Another intuitive result emerges when opponents' preferences exhibit increasing ARA: the ranking of solutions and opponents' ideal points coincide. However, under decreasing ARA, the agent closest to Q prefers the opponent whose ideal is farthest from her own. We also study rankings when one opponents' utility is a combination of a concave transformation and a right translation of the other's. For the concave/DARA and convex/IARA combinations, the effects on the solutions reinforce one another. In the concave/IARA and convex/DARA cases, the effect is ambiguous.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 58 (2009)
Issue (Month): 1 (July)
Pages: 64-83

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Handle: RePEc:eee:matsoc:v:58:y:2009:i:1:p:64-83
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

Keywords: Game theory Nash bargaining problems Bargaining solutions Rankings Monotone comparative statics;

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Find related papers by JEL classification:
  • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
  • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
  • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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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.
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  6. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
  7. Maria Gallego, David Scoones, 2005. "The Art of Compromise," Working Papers eg0042, Wilfrid Laurier University, Department of Economics, revised 2005.
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  10. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284 Elsevier.
  11. Hans Peters & Walter Bossert, 2002. "Efficient solutions to bargaining problems with uncertain disagreement points," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 489-502.
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  13. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
  14. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
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  16. de Koster, R. & Peters, H. J. M. & Tijs, S. H. & Wakker, P., 1983. "Risk sensitivity, independence of irrelevant alternatives and continuity of bargaining solutions," Mathematical Social Sciences, Elsevier, vol. 4(3), pages 295-300, July.
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Cited by:

  1. Maria Gallego & David Scoones, 2011. "Intergovernmental negotiation, willingness to compromise, and voter preference reversals," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(3), pages 591-610, April.
  2. Maria Gallego, David Scoones, 2005. "The Art of Compromise," Working Papers eg0042, Wilfrid Laurier University, Department of Economics, revised 2005.

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