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

  • Chiappori, Pierre-André

    ()

    (Columbia University)

  • Donni, Olivier

    ()

    (University of Cergy-Pontoise)

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 λ 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 λ1 and λ2 that are player-specific, in the sense that λi 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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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
Date of revision:
Publication status: published as 'Learning from a Piece of Pie in: Review of Economic Studies, 2012, 79 (1), 162 - 196 (with Ivana Komunjer)
Handle: RePEc:iza:izadps:dp2128
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  1. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
  2. Ray, Indrajit & Snyder, Susan, 2013. "Observable implications of Nash and subgame-perfect behavior in extensive games," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 471-477.
  3. 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.
  4. Chiappori, P.A., 1989. "Collective Labour Supply and Welfare," DELTA Working Papers 89-07, DELTA (Ecole normale supérieure).
  5. Coles, Melvyn G & Hildreth, Andrew, 1996. "Wage Bargaining, Inventories, and Union Legislation," CEPR Discussion Papers 1361, C.E.P.R. Discussion Papers.
  6. 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.
  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.
  8. Lundberg, S. & Pollak, R.A., 1991. "Separate Spheres Bargaining and the Marriage Market," Working Papers 91-08, University of Washington, Department of Economics.
  9. SVEJNAR, Jan, . "Bargaining power, fear of disagreement, and wage settlements: theory and evidence from U.S. industry," CORE Discussion Papers RP -720, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Indrajit Ray & Lin Zhou, . "Game Theory Via Revealed Preferences," Discussion Papers 00/15, Department of Economics, University of York.
  11. Chiappori, Pierre-Andre, 1988. "Nash-Bargained Households Decisions: A Comment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 791-96, November.
  12. Walter Bossert & Yves Sprumont, 2002. "Core rationalizability in two-agent exchange economies," Economic Theory, Springer, vol. 20(4), pages 777-791.
  13. BOSSERT, Walter & SPRUMONT, Yves, 2002. "Efficient and Non-Deteriorating Choice," Cahiers de recherche 2002-10, Universite de Montreal, Departement de sciences economiques.
  14. 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.
  15. 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.
  16. Daniel Hamermesh, 1971. "Who `Wins' in Wage Bargaining," Working Papers 398, Princeton University, Department of Economics, Industrial Relations Section..
  17. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
  18. 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.
  19. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  20. 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.
  21. 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.
  22. Jan Svejnar, 1980. "On the empirical testing of the Nash-Zeuthen bargaining solution," Industrial and Labor Relations Review, ILR Review, Cornell University, ILR School, vol. 33(4), pages 536-542, July.
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