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An exact non-cooperative support for the sequential Raiffa solution

Author

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  • Trockel, Walter

    (Center for 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.

Suggested Citation

  • Trockel, Walter, 2011. "An exact non-cooperative support for the sequential Raiffa solution," Center for Mathematical Economics Working Papers 426, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:426
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    File URL: https://pub.uni-bielefeld.de/download/2316443/2319868
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    References listed on IDEAS

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    1. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, vol. 55(2), pages 203-208, August.
    2. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    3. Trockel, Walter, 2011. "An axiomatization of the sequential Raiffa solution," Center for Mathematical Economics Working Papers 425, Center for Mathematical Economics, Bielefeld University.
    4. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    5. Salonen, Hannu, 1988. "Decomposable solutions for N -- person bargaining games," European Journal of Political Economy, Elsevier, vol. 4(3), pages 333-347.
    6. Claus-Jochen Haake & Walter Trockel, 2010. "On Maskin monotonicity of solution based social choice rules," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 17-25, March.
    7. Emily Tanimura & Sylvie Thoron, 2008. "A mechanism for solving bargaining problems between risk averse players," Working Papers halshs-00325695, HAL.
    8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    9. 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.
    10. Walter Trockel, 2002. "Integrating the Nash program into mechanism theory," Review of Economic Design, Springer;Society for Economic Design, vol. 7(1), pages 27-43.
    11. Walter Trockel, 2000. "Implementations of the Nash solution based on its Walrasian characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(2), pages 277-294.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Emily Tanimura & Sylvie Thoron, 2016. "How Best to Disagree in Order to Agree?," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-17, September.
    2. Diskin, A. & Koppel, M. & Samet, D., 2011. "Generalized Raiffa solutions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 452-458.
    3. repec:jmi:articl:jmi-v1i1a3 is not listed on IDEAS
    4. repec:kap:compec:v:52:y:2018:i:1:d:10.1007_s10614-017-9673-9 is not listed on IDEAS
    5. repec:spr:etbull:v:3:y:2015:i:1:d:10.1007_s40505-014-0046-4 is not listed on IDEAS
    6. Duman, Papatya & Trockel, Walter, 2016. "On non-cooperative foundation and implementation of the Nash Solution in subgame perfect equilibrium via Rubinstein’s game," Center for Mathematical Economics Working Papers 550, Center for Mathematical Economics, Bielefeld University.
    7. repec:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-017-0567-9 is not listed on IDEAS
    8. Haruo Imai & Hannu Salonen, 2012. "A characterization of a limit solution for finite horizon bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 603-622, August.

    More about this item

    Keywords

    Raiffa solution; Solution based social choice rule; Implementation; Nash program; Non-cooperative foundation;

    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
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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