# Learning From a Piece of Pie: The Empirical Content of Nash Bargaining

## Author Info

• Pierre-André Chiappori

(Department of Economics, University of Chicago)

• Olivier Donni

(THEMA, Université de Cergy-Pontoise)

Registered author(s):

## 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 $\lambda$ 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 $\lambda_1$ and $\lambda_2$ that are player-specific, in the sense that $\lambda_i$ does not influence the utility or the threat point of player $j \neq i$, 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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## Bibliographic Info

Paper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2006-07.

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Handle: RePEc:ema:worpap:2006-07

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## Related research

Keywords: 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
• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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## References

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1. 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.
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## Citations

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Cited by:
1. 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.
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.
3. Chiappori, Pierre-André & Donni, Olivier, 2006. "Les modèles non unitaires de comportement du ménage : un survol de la littérature," L'Actualité Economique, Société Canadienne de Science Economique, vol. 82(1), pages 9-52, mars-juin.
4. Chiappori, Pierre-André & Donni, Olivier, 2009. "Non-unitary Models of Household Behavior: A Survey of the Literature," IZA Discussion Papers 4603, Institute for the Study of Labor (IZA).
5. Antonio Merlo & Arianna Degan, 2007. "Do Voters Vote Sincerely?," 2007 Meeting Papers 307, Society for Economic Dynamics.
6. de Clippel, Geoffroy & Eliaz, Kfir, 2012. "Reason-based choice: a bargaining rationale for the attraction and compromise effects," Theoretical Economics, Econometric Society, vol. 7(1), January.
7. Majlesi, Kaveh, 2014. "Labor Market Opportunities and Women's Decision Making Power within Households," Working Papers 2014:4, Lund University, Department of Economics.
8. Carvajal, Andrés & González, Natalia, 2014. "On refutability of the Nash bargaining solution," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 177-186.
9. Antonio Merlo & Xun Tang, 2011. "Identification and Estimation of Stochastic Bargaining Models, Fourth Version," PIER Working Paper Archive 11-035, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 19 Oct 2011.
10. Antonio Merlo & Xun Tang, 2010. "Identification and Estimation of Stochastic Bargaining Models, Third Version," PIER Working Paper Archive 11-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 11 Mar 2011.
11. 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.

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