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Subgame-perfect implementation of bargaining solutions

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  • Eiichi Miyagawa

    ()
    (Columbia University - Department of Economics)

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

Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0102-16.

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Length: 27 pages
Date of creation: 2002
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Handle: RePEc:clu:wpaper:0102-16

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  1. 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.
  2. Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, vol. 6(3), pages 474-501, May.
  3. 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.
  4. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  5. 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.
  6. Amrita Dhillon & Jean-Francois Mertens, 1999. "Relative Utilitarianism," Econometrica, Econometric Society, vol. 67(3), pages 471-498, May.
  7. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  8. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
  9. Sjostrom Tomas, 1994. "Implementation in Undominated Nash Equilibria without Integer Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 502-511, May.
  10. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
  11. 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.
  12. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  13. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  14. 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.
  15. 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.
  16. 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.
  17. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January.
  18. 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.
  19. 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.
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Cited by:
  1. l’Haridon, Olivier & Malherbet, Franck & Pérez-Duarte, Sébastien, 2011. "Does bargaining matter in the small firm's matching model?," Working Paper Series 1359, European Central Bank.
  2. Thorsten Upmann & Julia M�ller, 2013. "The Structure of Firm-Specific Labour Unions," Tinbergen Institute Discussion Papers 13-080/I, Tinbergen Institute.
  3. 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.
  4. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
  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. 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.
  7. 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.
  8. Esat Cetemen & Emin Karagözoğlu, 2014. "Implementing equal division with an ultimatum threat," Theory and Decision, Springer, vol. 77(2), pages 223-236, August.
  9. 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.

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