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An exact non-cooperative support for the sequential Raiffa solution

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  • Trockel, Walter

Abstract

This article provides an exact non-cooperative foundation of the sequential Raiffa solution for two-person bargaining games. Based on an approximate foundation due to Myerson (1991) for any two-person bargaining game (S, d) an extensive form game GS,d is defined that has an infinity of weakly subgame perfect equilibria whose payoff vectors coincide with that of the sequential Raiffa solution of (S, d). Moreover all those equilibria share the same equilibrium path consisting of proposing the Raiffa solution and accepting it in the first stage of the game. By a modification of GS,d the analogous result is provided for subgame perfect equilibria. These results immediately extend to implementation of a sequential Raiffa (solution based) social choice rule in subgame perfect equilibrium.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 1 (January)
Pages: 77-83

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Handle: RePEc:eee:mateco:v:47:y:2011:i:1:p:77-83

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Raiffa solution Non-cooperative foundation Nash program Subgame perfect equilibrium Implementation Solution based social choice rule;

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  1. Walter Trockel, 2009. "An axiomatization of the Sequential Raiffa solution," Working Papers, Bielefeld University, Center for Mathematical Economics 425, Bielefeld University, Center for Mathematical Economics.
  2. Trockel,W., 1999. "Integrating the Nash program into mechanism theory," Working Papers, Bielefeld University, Center for Mathematical Economics 305, Bielefeld University, Center for Mathematical Economics.
  3. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, Econometric Society, vol. 21(1), pages 128-140, April.
  4. Bergin, James & Duggan, John, 1999. "An Implementation-Theoretic Approach to Non-cooperative Foundations," Journal of Economic Theory, Elsevier, Elsevier, vol. 86(1), pages 50-76, May.
  5. Claus-Jochen Haake & Walter Trockel, 2010. "On Maskin monotonicity of solution based social choice rules," Review of Economic Design, Springer, Springer, vol. 14(1), pages 17-25, March.
  6. Nejat Anbarci & Ching-jen Sun, 2009. "Robustness of Intermediate Agreements and Bargaining Solutions," Economics Series 2009_14, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  7. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, Elsevier, vol. 55(2), pages 203-208, August.
  8. Walter Trockel, 2000. "Implementations of the Nash solution based on its Walrasian characterization," Economic Theory, Springer, Springer, vol. 16(2), pages 277-294.
  9. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers, Brown University, Department of Economics 2004-20, Brown University, Department of Economics.
  10. Emily Tanimura & Sylvie Thoron, 2008. "A mechanism for solving bargaining problems between risk averse players," Working Papers, HAL halshs-00325695, HAL.
  11. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, Econometric Society, vol. 18(2), pages 155-162, April.
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Cited by:
  1. Haruo Imai & Hannu Salonen, 2012. "A characterization of a limit solution for finite horizon bargaining problems," International Journal of Game Theory, Springer, Springer, vol. 41(3), pages 603-622, August.

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