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An exact non-cooperative support for the sequential Raiffa solution

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  • Walter Trockel

    ()
    (Institute of Mathematical Economics, Bielefeld University)

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 (1997) for any two-person bargaining game (S, d) an extensive form game G^{S,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 G^{S,d} the analogous result is provided for subgame perfect equilibria. Finally, it is indicated how these results can be extended to implementation of a sequential Raiffa (solution based) social choice rule in subgame perfect equilibrium.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-426.pdf
File Function: First version, 2009
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 426.

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Length: 12 pages
Date of creation: Dec 2009
Date of revision:
Handle: RePEc:bie:wpaper:426

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Keywords: Raiffa solution; non-cooperative foundation Nash program; implementation; solution based social choice rule;

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References

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  1. Nejat Anbarci & Ching-jen Sun, 2012. "Robustness of Intermediate Agreements and Bargaining Solutions," Economics Series 2012_7, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  2. Claus-Jochen Haake & Walter Trockel, 2010. "On Maskin monotonicity of solution based social choice rules," Review of Economic Design, Springer, vol. 14(1), pages 17-25, March.
  3. Walter Trockel, 2009. "An axiomatization of the Sequential Raiffa solution," Working Papers 425, Bielefeld University, Center for Mathematical Economics.
  4. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, vol. 55(2), pages 203-208, August.
  5. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  6. Walter Trockel, 2000. "Implementations of the Nash solution based on its Walrasian characterization," Economic Theory, Springer, vol. 16(2), pages 277-294.
  7. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  8. Bergin, James & Duggan, John, 1999. "An Implementation-Theoretic Approach to Non-cooperative Foundations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 50-76, May.
  9. Emily Tanimura & Sylvie Thoron, 2008. "A mechanism for solving bargaining problems between risk averse players," Working Papers halshs-00325695, HAL.
  10. Walter Trockel, 1999. "Integrating the Nash Program into Mechanism Theory," UCLA Economics Working Papers 787, UCLA Department of Economics.
  11. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
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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, vol. 41(3), pages 603-622, August.

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