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Subgame-perfect implementation of bargaining solutions

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  • Miyagawa, Eiichi

Abstract

This paper provides simple four-stage game forms that fully implement a large class of two-person bargaining solutions in subgame-perfect equilibrium. The solutions that can be implemented by our game forms are those that maximize a monotonic and quasi-concave function of utilities after normalizing each agent's utility function so that the maximum utility is 1 and the utility of the disagreement outcome is 0. This class of solutions includes the Nash, Kalai{Smorodinsky, and Relative Utilitarian solutions. The game forms have a structure of alternating offers and contain no integer device.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 41 (2002)
Issue (Month): 2 (November)
Pages: 292-308

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Handle: RePEc:eee:gamebe:v:41:y:2002:i:2:p:292-308

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Amrita Dhillon & Jean-Francois Mertens, 1999. "Relative Utilitarianism," Econometrica, Econometric Society, vol. 67(3), pages 471-498, May.
  2. Matthew O. Jackson, 1990. "Undominated Nash Implementation in Bounded Mechanisms," Discussion Papers 966, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Howard, J. V., 1992. "A social choice rule and its implementation in perfect equilibrium," Journal of Economic Theory, Elsevier, vol. 56(1), pages 142-159, February.
  4. 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.
  5. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  6. Sjostrom Tomas, 1994. "Implementation in Undominated Nash Equilibria without Integer Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 502-511, May.
  7. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January.
  8. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 59(4), pages 757-75, October.
  9. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
  10. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  11. Abreu, Dilip & Sen, Arunava, 1990. "Subgame perfect implementation: A necessary and almost sufficient condition," Journal of Economic Theory, Elsevier, vol. 50(2), pages 285-299, April.
  12. Uzi Segal, 2000. "Let's Agree That All Dictatorships Are Equally Bad," Journal of Political Economy, University of Chicago Press, vol. 108(3), pages 569-589, June.
  13. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  14. Hurwicz, L, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 217-25, April.
  15. John Moore, 1991. "Implementation in Environments with Complete Information (Now published as 'Implementation, Contracts and Renegotiation in Environments with Complete Information' in J-J Laffont (ed.), Advances in Eco," STICERD - Theoretical Economics Paper Series /1991/235, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  16. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  17. Saijo, Tatsuyoshi & Tatamitani, Yoshikatsu & Yamato, Takehiko, 1996. "Toward Natural Implementation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 949-80, November.
  18. Conley, John P. & Wilkie, Simon, 1996. "An Extension of the Nash Bargaining Solution to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 13(1), pages 26-38, March.
  19. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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Citations

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Cited by:
  1. Argenton, Cédric, 2005. "Producers bargaining over a quality standard," Working Paper Series in Economics and Finance 618, Stockholm School of Economics, revised 18 Jan 2006.
  2. L'Haridon, Olivier & Malherbet, Franck & Pérez-Duarte, Sébastien, 2010. "Does Bargaining Matter in the Small Firm Matching Model?," IZA Discussion Papers 5181, Institute for the Study of Labor (IZA).
  3. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
  4. Haake, Claus-Jochen, 2009. "Two support results for the Kalai-Smorodinsky solution in small object division markets," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 177-187, March.
  5. Nejat Anbarci & John H. Boyd III, 2008. "Nash Demand Game and the Kalai-Smorodinsky Solution," Economics Series 2008_11, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  6. Thorsten Upmann & Julia M�ller, 2013. "The Structure of Firm-Specific Labour Unions," Tinbergen Institute Discussion Papers 13-080/I, Tinbergen Institute.
  7. Claus-Jochen Haake, 2005. "Two support results for the Kalai-Smorodinsky solution in small object division markets," Working Papers 366, Bielefeld University, Center for Mathematical Economics.
  8. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "Non-cooperative support for the asymmetric Nash bargaining solution," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1951-1967, September.

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