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Learning from a Piece of Pie: The Empirical Content of Nash Bargaining

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Author Info
Pierre-André Chiappori () (Columbia University)
Olivier Donni () (THEMA, University of Cergy-Pontoise and IZA Bonn)

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Abstract

Consider a model of bargaining, in which two players, 1 and 2, share a pie of size y. The bargaining environment is described by a set of parameters ? that may affect agents’ preferences over the agreement sharing, the status quo outcome, or both. The outcomes (i.e., whether an agreement is reached, and if so the individual shares) and the environment (including the size of the pie) are known, but neither the agents’ utilities nor their threat points. Assuming that the agents adopt a Nash bargaining solution, we investigate the empirical content of this assumption. We first show that in the most general framework, any outcome can be rationalized as a Nash solution. However, if (i) the size of the pie y does not influence the players’ threat points and (ii) there exist (at least) two parameters ?1 and ?2 that are player-specific, in the sense that ?i does not influence the utility or the threat point of player j ? i, then Nash bargaining generates strong testable restrictions. Moreover, the underlying structure of the bargaining, i.e., the players’ utility and threat point functions, can be recovered under slightly more demanding conditions.

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Publisher Info
Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 2128.

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Length: 35 pages
Date of creation: May 2006
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Handle: RePEc:iza:izadps:dp2128

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Related research
Keywords: bargaining game; Nash solution; testability; identifiability; cardinal utility;

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Find related papers by JEL classification:
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

References listed on IDEAS
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.:

  1. Chiappori, Pierre-Andre, 1992. "Collective Labor Supply and Welfare," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 437-67, June. [Downloadable!] (restricted)
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  2. Bossert, W. & Sprumont, Y., 2000. "Core Retionalizability in Two-Agent Exchange Economies," Cahiers de recherche 2000-09, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    Other versions:
  3. Daniel S. Hamermesh, 1973. "Who "wins" in wage bargaining?," Industrial and Labor Relations Review, ILR Review, ILR School, Cornell University, vol. 26(4), pages 1146-1149, July.
    Other versions:
  4. Carvajal, Andres & Ray, Indrajit & Snyder, Susan, 2004. "Equilibrium behavior in markets and games: testable restrictions and identification," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 1-40, February. [Downloadable!] (restricted)
  5. Lundberg, Shelly & Pollak, Robert A, 1993. "Separate Spheres Bargaining and the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 988-1010, December. [Downloadable!] (restricted)
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  6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  7. McElroy, Marjorie B & Horney, Mary Jean, 1990. "Nash-Bargained Household Decisions: Reply," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(1), pages 237-42, February. [Downloadable!] (restricted)
  8. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer. [Downloadable!] (restricted)
  9. Jan Svejnar, 1980. "On the empirical testing of the Nash-Zeuthen bargaining solution," Industrial and Labor Relations Review, ILR Review, ILR School, Cornell University, vol. 33(4), pages 536-542, July.
  10. Ray, Indrajit & Zhou, Lin, 2001. "Game Theory via Revealed Preferences," Games and Economic Behavior, Elsevier, vol. 37(2), pages 415-424, November. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  12. Bossert, Walter & Sprumont, Yves, 2003. "Efficient and non-deteriorating choice," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 131-142, April. [Downloadable!] (restricted)
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  13. 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. [Downloadable!] (restricted)
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  14. Coles, Melvyn G & Hildreth, Andrew K G, 2000. "Wage Bargaining, Inventories, and Union Legislation," Review of Economic Studies, Blackwell Publishing, vol. 67(2), pages 273-93, April.
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  15. Susan Snyder & Indrajit Ray, 2004. "Observable implications of Nash and subgame-perfect behavior in extensive games," Econometric Society 2004 North American Summer Meetings 407, Econometric Society. [Downloadable!]
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  16. McElroy, Marjorie B & Horney, Mary Jean, 1981. "Nash-Bargained Household Decisions: Toward a Generalization of the Theory of Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 333-49, June. [Downloadable!] (restricted)
  17. Chiappori, P.A. & Ekeland, I., 2006. "The micro economics of group behavior: General characterization," Journal of Economic Theory, Elsevier, vol. 130(1), pages 1-26, September. [Downloadable!] (restricted)
  18. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August. [Downloadable!] (restricted)
  19. Chiappori, Pierre-Andre, 1991. "Nash-Bargained Household Decisions: A Rejoinder," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 761-62, August. [Downloadable!] (restricted)
  20. Svejnar, Jan, 1986. "Bargaining Power, Fear of Disagreement, and Wage Settlements: Theory and Evidence from U.S. Industry," Econometrica, Econometric Society, vol. 54(5), pages 1055-78, September. [Downloadable!] (restricted)
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  21. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Arianna Degan & Antonio Merlo, 2007. "Do Voters Vote Sincerely?," NBER Working Papers 12922, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Blundell, Richard William & Chiappori, Pierre-André & Magnac, Thierry & Meghir, Costas, 2005. "Collective Labour Supply: Heterogeneity and Non-Participation," CEPR Discussion Papers 5287, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  3. Arianna Degan & Antonio Merlo, 2006. "Do Voters Vote Sincerely? Second Version," PIER Working Paper Archive 07-006, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 03 Jan 2007. [Downloadable!]
  4. Arianna Degan & Antonio Merlo, 2007. "Do Voters Vote Ideologically?, Third Version," PIER Working Paper Archive 08-034, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Aug 2008. [Downloadable!]
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