On the ranking of bilateral bargaining opponents
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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
- Oscar Volij, 1999.
"On Risk Aversion and Bargaining Outcomes,"
Economic theory and game theory
010, Oscar Volij.
- Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
- Alejandro Saporiti & Fernando Tohmé, 2003.
"Single-Crossing, Strategic Voting and the Median Choice Rule,"
CEMA Working Papers: Serie Documentos de Trabajo.
237, Universidad del CEMA.
- Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 363-383, April.
- 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.
- de Koster, R. & Peters, H. & Tijs, S.H. & Wakker, P., 1983. "Risk sensitivity, independence of irrelevant alternatives and continuity of bargaining solutions," Other publications TiSEM ca1db065-9070-4741-9bbe-0, Tilburg University, School of Economics and Management.
- Maria Gallego, David Scoones, 2005. "The Art of Compromise," Working Papers eg0042, Wilfrid Laurier University, Department of Economics, revised 2005.
- Milgrom, P. & Shannon, C., 1991.
"Monotone Comparative Statics,"
11, Stanford - Institute for Thoretical Economics.
- Alvin E Roth, 2008. "Axiomatic Models of Bargaining," Levine's Working Paper Archive 122247000000002376, David K. Levine.
- Alesina, Alberto & Rosenthal, Howard, 1996. "A Theory of Divided Government," Econometrica, Econometric Society, vol. 64(6), pages 1311-41, November.
- 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.
- Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
- Thomson, W., 1989.
"Cooperative Models Of Bargaining,"
RCER Working Papers
177, University of Rochester - Center for Economic Research (RCER).
- 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.
- Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, June.
- Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
- Thomson, William, 1987. "Monotonicity of bargaining solutions with respect to the disagreement point," Journal of Economic Theory, Elsevier, vol. 42(1), pages 50-58, June.
- Peters Hans & Köbberling Vera, 2000.
"The Effect of Decision Weights in Bargaining Problems,"
037, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Kobberling, Veronika & Peters, Hans, 2003. "The effect of decision weights in bargaining problems," Journal of Economic Theory, Elsevier, vol. 110(1), pages 154-175, May.
When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:58:y:2009:i:1:p:64-83. See general information about how to correct material in RePEc.
If references are entirely missing, you can add them using this form.