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A folk theorem for the one-dimensional spatial bargaining model

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  • Seok-ju Cho
  • John Duggan

Abstract

We show that in the one-dimensional bargaining model based on the protocol of Baron and Ferejohn (Am Polit Sci Rev 83:1181–1206, 1989 ), if voting is simultaneous, publicly observed, and no agent has the power to unilaterally impose a choice, then arbitrary policies can be supported by subgame perfect equilibria in stage-undominated voting strategies when agents are patient. Moreover, in the model with a bad status quo, arbitrary outcomes can be supported for arbitrary positive discount factors. We formulate sufficient conditions for supporting arbitrary alternatives in terms of a system of equations. The system has a straightforward solution in the model with no discounting, and after verifying non-singularity of this system, we use the implicit function theorem to derive the folk theorem when agents are sufficiently patient. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Seok-ju Cho & John Duggan, 2015. "A folk theorem for the one-dimensional spatial bargaining model," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 933-948, November.
  • Handle: RePEc:spr:jogath:v:44:y:2015:i:4:p:933-948
    DOI: 10.1007/s00182-014-0460-8
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "The folk theorem for irreducible stochastic games with imperfect public monitoring," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1664-1683, July.
    3. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    4. Banks, Jeffrey S. & Duggan, John, 2006. "A General Bargaining Model of Legislative Policy-making," Quarterly Journal of Political Science, now publishers, vol. 1(1), pages 49-85, January.
    5. John Duggan & Mark Fey, 2006. "Repeated Downsian electoral competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(1), pages 39-69, December.
    6. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    7. Cho, Seok-ju & Duggan, John, 2003. "Uniqueness of stationary equilibria in a one-dimensional model of bargaining," Journal of Economic Theory, Elsevier, vol. 113(1), pages 118-130, November.
    8. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    9. Cardona, Daniel & Ponsati, Clara, 2011. "Uniqueness of stationary equilibria in bargaining one-dimensional policies under (super) majority rules," Games and Economic Behavior, Elsevier, vol. 73(1), pages 65-75, September.
    10. Cho, Seok-ju & Duggan, John, 2009. "Bargaining foundations of the median voter theorem," Journal of Economic Theory, Elsevier, vol. 144(2), pages 851-868, March.
    11. Quan Wen, 2002. "A Folk Theorem for Repeated Sequential Games," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 493-512.
    12. Duggan, John, 2014. "A Folk Theorem for Repeated Elections with Adverse Selection," Political Science Research and Methods, Cambridge University Press, vol. 2(2), pages 213-242, October.
    13. Norman, Peter, 2002. "Legislative Bargaining and Coalition Formation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 322-353, February.
    14. Banks, Jeffrey s. & Duggan, John, 2000. "A Bargaining Model of Collective Choice," American Political Science Review, Cambridge University Press, vol. 94(1), pages 73-88, March.
    15. 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.
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    1. Herings, P. Jean-Jacques & Meshalkin, Andrey & Predtetchinski, Arkadi, 2018. "Subgame perfect equilibria in majoritarian bargaining," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 101-112.

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