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A Continuous-Time Model of Multilateral Bargaining

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  • Attila Ambrus
  • Shih En Lu

Abstract

We propose a finite-horizon continuous-time framework for coalitional bargaining, in which players can make offers at random discrete times. In our model: (i) expected payoffs in Markov perfect equilibrium (MPE) are unique, generating sharp predictions and facilitating comparative statics; and (ii) MPE are the only subgame perfect Nash equilibria (SPNE) that can be approximated by SPNE of nearby discrete-time bargaining models. We investigate the limit MPE payoffs as the time horizon goes to infinity and players get infinitely patient. In convex games, we establish that the set of these limit payoffs achievable by varying recognition rates is exactly the core of the characteristic function. (JEL C78)

Suggested Citation

  • 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.
  • Handle: RePEc:aea:aejmic:v:7:y:2015:i:1:p:208-49
    Note: DOI: 10.1257/mic.20100029
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    References listed on IDEAS

    as
    1. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
    2. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    3. Ma, Ching-To Albert & Manove, Michael, 1993. "Bargaining with Deadlines and Imperfect Player Control," Econometrica, Econometric Society, vol. 61(6), pages 1313-1339, November.
    4. Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 52(6), pages 1351-1364, November.
    5. Ali, S. Nageeb M., 2006. "Waiting to settle: Multilateral bargaining with subjective biases," Journal of Economic Theory, Elsevier, vol. 130(1), pages 109-137, September.
    6. Yildirim, Huseyin, 2007. "Proposal power and majority rule in multilateral bargaining with costly recognition," Journal of Economic Theory, Elsevier, vol. 136(1), pages 167-196, September.
    7. Muhamet Yildiz, 2003. "Bargaining without a Common Prior-An Immediate Agreement Theorem," Econometrica, Econometric Society, vol. 71(3), pages 793-811, May.
    8. Eraslan, Hulya, 2002. "Uniqueness of Stationary Equilibrium Payoffs in the Baron-Ferejohn Model," Journal of Economic Theory, Elsevier, vol. 103(1), pages 11-30, March.
    9. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954.
    10. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    11. Evans, Robert, 1997. "Coalitional Bargaining with Competition to Make Offers," Games and Economic Behavior, Elsevier, vol. 19(2), pages 211-220, May.
    12. repec:cup:apsrev:v:85:y:1991:i:01:p:137-164_17 is not listed on IDEAS
    13. Fershtman Chaim & Seidmann Daniel J., 1993. "Deadline Effects and Inefficient Delay in Bargaining with Endogenous Commitment," Journal of Economic Theory, Elsevier, vol. 60(2), pages 306-321, August.
    14. Huibin Yan, 2003. "Noncooperative selection of the core," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(4), pages 527-540, September.
    15. Perry Motty & Reny Philip J., 1993. "A Non-cooperative Bargaining Model with Strategically Timed Offers," Journal of Economic Theory, Elsevier, vol. 59(1), pages 50-77, February.
    16. Baron David & Kalai Ehud, 1993. "The Simplest Equilibrium of a Majority-Rule Division Game," Journal of Economic Theory, Elsevier, vol. 61(2), pages 290-301, December.
    17. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2008. "Trees and extensive forms," Journal of Economic Theory, Elsevier, vol. 143(1), pages 216-250, November.
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    Citations

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    Cited by:

    1. Sofia Moroni, 2015. "Existence of trembling hand equilibrium in revision games with imperfect information," Working Paper 5874, Department of Economics, University of Pittsburgh.
    2. Ambrus, Attila & Greiner, Ben & Pathak, Parag A., 2015. "How individual preferences are aggregated in groups: An experimental study," Journal of Public Economics, Elsevier, vol. 129(C), pages 1-13.
    3. repec:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-017-0567-9 is not listed on IDEAS
    4. Alp Simsek & Muhamet Yildiz, 2016. "Durability, Deadline, and Election Effects in Bargaining," NBER Working Papers 22284, National Bureau of Economic Research, Inc.
    5. Calcagno, Riccardo & Kamada, Yuichiro & Lovo, Stefano & Sugaya, Takuo, 2014. "Asynchronicity and coordination in common and opposing interest games," Theoretical Economics, Econometric Society, vol. 9(2), May.
    6. Lu, Shih En, 2016. "Self-control and bargaining," Journal of Economic Theory, Elsevier, vol. 165(C), pages 390-413.

    More about this item

    JEL classification:

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

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