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On the ranking of bilateral bargaining opponents

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  • 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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  • Cressman, Ross & Gallego, Maria, 2009. "On the ranking of bilateral bargaining opponents," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 64-83, July.
    • Handle: RePEc:eee:matsoc:v:58:y:2009:i:1:p:64-83
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    as
    1. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    2. Volij, Oscar & Winter, Eyal, 2002. "On risk aversion and bargaining outcomes," Games and Economic Behavior, Elsevier, vol. 41(1), pages 120-140, October.
    3. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
    4. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    5. Cressman, Ross & Gallego, Maria, 2009. "On the ranking of bilateral bargaining opponents," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 64-83, July.
    6. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    8. 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.
    9. 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.
    10. Hans Peters, 1992. "A Criterion for Comparing Strength of Preference with an Application to Bargaining," Operations Research, INFORMS, vol. 40(5), pages 1018-1022, October.
    11. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    12. Jansen, M.J.M. & Tijs, S.H., 1983. "Continuity of bargaining solutions," Other publications TiSEM 6c8fa22d-61f9-43b6-9224-a, Tilburg University, School of Economics and Management.
    13. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    14. Austen-Smith, David & Banks, Jeffrey, 1988. "Elections, Coalitions, and Legislative Outcomes," American Political Science Review, Cambridge University Press, vol. 82(2), pages 405-422, June.
    15. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(1), pages 187-223.
    16. 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.
    17. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
    18. 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.
    19. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    20. Maria Gallego, David Scoones, 2005. "The Art of Compromise," Working Papers eg0042, Wilfrid Laurier University, Department of Economics, revised 2005.
    21. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    22. Alesina, Alberto & Rosenthal, Howard, 1996. "A Theory of Divided Government," Econometrica, Econometric Society, vol. 64(6), pages 1311-1341, November.
    23. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, Decembrie.
    24. Zinde-Walsh, Victoria, 1995. "ESTIMATION AND INFERENCE IN ECONOMETRICSRussell Davidson and James G. MacKinnon Oxford University Press, 1993," Econometric Theory, Cambridge University Press, vol. 11(3), pages 631-635, June.
    25. 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.
    26. Scott Ashworth & Ethan Bueno de Mesquita, 2006. "Monotone Comparative Statics for Models of Politics," American Journal of Political Science, John Wiley & Sons, vol. 50(1), pages 214-231, January.
    27. 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.
    28. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    29. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    30. Alvin E Roth, 2008. "Axiomatic Models of Bargaining," Levine's Working Paper Archive 122247000000002376, David K. Levine.
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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.
    3. Cressman, Ross & Gallego, Maria, 2009. "On the ranking of bilateral bargaining opponents," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 64-83, July.

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    More about this item

    Keywords

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

    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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