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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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  • Trockel, Walter, 2011. "An exact non-cooperative support for the sequential Raiffa solution," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 77-83, January.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:1:p:77-83
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    1. Trockel, Walter, 2011. "An axiomatization of the sequential Raiffa solution," Center for Mathematical Economics Working Papers 425, Center for Mathematical Economics, Bielefeld University.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
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    5. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, vol. 55(2), pages 203-208, August.
    6. Walter Trockel, 1999. "Integrating the Nash Program into Mechanism Theory," UCLA Economics Working Papers 787, UCLA Department of Economics.
    7. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
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    13. 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.
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    Cited by:

    1. Diskin, A. & Koppel, M. & Samet, D., 2011. "Generalized Raiffa solutions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 452-458.
    2. 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.
    3. Roberto Serrano, 2020. "Sixty-Seven Years of the Nash Program: Time for Retirement?," Working Papers 2020-20, Brown University, Department of Economics.
    4. Ephraim Zehavi & Amir Leshem, 2018. "On the Allocation of Multiple Divisible Assets to Players with Different Utilities," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 253-274, June.
    5. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.
    6. Walter Trockel, 2015. "Axiomatization of the discrete Raiffa solution," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 9-17, April.
    7. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    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.
    9. Papatya Duman & Walter Trockel, 2016. "On non-cooperative foundation and implementation of the Nash solution in subgame perfect equilibrium via Rubinstein's game," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 83-107, December.
    10. Bram Driesen & Peter Eccles & Nora Wegner, 2017. "A non-cooperative foundation for the continuous Raiffa solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1115-1135, November.

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    More about this item

    Keywords

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

    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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