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A non-cooperative foundation for the continuous Raiffa solution

Author

Listed:
  • Bram Driesen

    () (University of Glasgow)

  • Peter Eccles

    () (British Airways Plc)

  • Nora Wegner

    () (Bank of England)

Abstract

This paper provides a non-cooperative foundation for (asymmetric generalizations of) the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Ståhl–Rubinstein bargaining model, in which there is a finite deadline that ends the negotiations, and in which each player’s opportunity to make proposals is governed by a player-specific Poisson process, in that the rejecter of a proposal becomes proposer at the first next arrival of her process. Under the assumption that future payoffs are not discounted, it is shown that the expected payoffs players realize in subgame perfect equilibrium converge to the continuous Raiffa solution outcome as the deadline tends to infinity. The weights reflecting the asymmetries among the players correspond to the Poisson arrival rates of their respective proposal processes.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-017-0567-9
    DOI: 10.1007/s00182-017-0567-9
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    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Imai, Haruo & Salonen, Hannu, 2000. "The representative Nash solution for two-sided bargaining problems," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 349-365, May.
    3. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    4. Hans Peters & Eric Van Damme, 1991. "Characterizing the Nash and Raiffa Bargaining Solutions by Disagreement Point Axioms," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 447-461, August.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    6. Zvi A. Livne, 1989. "Axiomatic Characterizations of the Raiffa and the Kalai-Smorodinsky Solutions to the Bargaining Problem," Operations Research, INFORMS, vol. 37(6), pages 972-980, December.
    7. Kalyan Chatterjee & Bhaskar Dutia & Debraj Ray & Kunal Sengupta, 2013. "A Noncooperative Theory of Coalitional Bargaining," World Scientific Book Chapters, in: Bargaining in the Shadow of the Market Selected Papers on Bilateral and Multilateral Bargaining, chapter 5, pages 97-111, World Scientific Publishing Co. Pte. Ltd..
    8. Chen-Ying Huang, 2002. "Multilateral bargaining: conditional and unconditional offers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 401-412.
    9. Francis Bloch & Effrosyni Diamantoudi, 2011. "Noncooperative formation of coalitions in hedonic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 263-280, May.
    10. John Conley & Simon Wilkie, 1994. "Implementing the nash extension bargaining solution for non-convex problems," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 205-216, December.
    11. Ray, Debraj & Vohra, Rajiv, 1999. "A Theory of Endogenous Coalition Structures," Games and Economic Behavior, Elsevier, vol. 26(2), pages 286-336, January.
    12. Klaus Kultti & Hannu Vartiainen, 2010. "Multilateral non-cooperative bargaining in a general utility space," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 677-689, October.
    13. 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.
    14. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May.
    15. Tomohiko Kawamori, 2008. "A note on selection of proposers in coalitional bargaining," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 525-532, December.
    16. Herrero, Maria Jose, 1989. "The nash program: Non-convex bargaining problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 266-277, December.
    17. Attila Ambrus & Shih En Lu, 2015. "A Continuous-Time Model of Multilateral Bargaining," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 208-249, February.
    18. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
    19. Emily Tanimura & Sylvie Thoron, 2008. "A mechanism for solving bargaining problems between risk averse players," Working Papers halshs-00325695, HAL.
    20. Ma, Ching-To Albert & Manove, Michael, 1993. "Bargaining with Deadlines and Imperfect Player Control," Econometrica, Econometric Society, vol. 61(6), pages 1313-1339, November.
    21. Diskin, A. & Koppel, M. & Samet, D., 2011. "Generalized Raiffa solutions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 452-458.
    22. 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.
    23. John C. Harsanyi & Reinhard Selten, 1972. "A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information," Management Science, INFORMS, vol. 18(5-Part-2), pages 80-106, January.
    24. 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.
    25. Suh, Sang-Chul & Wen, Quan, 2006. "Multi-agent bilateral bargaining and the Nash bargaining solution," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 61-73, February.
    26. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 61-80.
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    More about this item

    Keywords

    Continuous Raiffa solutions; Non-cooperative foundation;

    JEL classification:

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

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