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A Newton collocation method for solving dynamic bargaining games

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  • John Duggan

    ()

  • Tasos Kalandrakis

Abstract

We develop and implement a collocation method to solve for an equilibrium in the dynamic legislative bargaining game of Duggan and Kalandrakis (2008). We formulate the collocation equations in a quasi-discrete version of the model, and we show that the collocation equations are locally Lipchitz continuous and directionally differentiable. In numerical experiments, we successfully implement a globally convergent variant of Broyden's method on a preconditioned version of the collocation equations, and the method economizes on computation cost by more than 50% compared to the value iteration method. We rely on a continuity property of the equilibrium set to obtain increasingly precise approximations of solutions to the continuum model. We showcase these techniques with an illustration of the dynamic core convergence theorem of Duggan and Kalandrakis (2008) in a nine-player, two-dimensional model with negative quadratic preferences.

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File URL: http://hdl.handle.net/10.1007/s00355-010-0513-2
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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 36 (2011)
Issue (Month): 3 (April)
Pages: 611-650

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Handle: RePEc:spr:sochwe:v:36:y:2011:i:3:p:611-650

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References

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  1. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 661465000000000387, David K. Levine.
  2. John Duggan & Tasos Kalandrakis & Vikram Manjunath, 2008. "Dynamics of the Presidential Veto: A Computational," Wallis Working Papers WP56, University of Rochester - Wallis Institute of Political Economy.
  3. Konstantin Sonin & Georgy Egorov & Daron Acemoglu, 2008. "Dynamics and Stability of Constitutions, Coalitions and Clubs," 2008 Meeting Papers 314, Society for Economic Dynamics.
  4. Banks, Jeffrey S. & Duggan, John, 2006. "A General Bargaining Model of Legislative Policy-making," International Quarterly Journal of Political Science, now publishers, vol. 1(1), pages 49-85, January.
  5. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
  6. Tasos Kalandrakis, 2007. "Majority Rule Dynamics with Endogenous Status Quo," Wallis Working Papers WP46, University of Rochester - Wallis Institute of Political Economy.
  7. Kalandrakis, Anastassios, 2004. "A three-player dynamic majoritarian bargaining game," Journal of Economic Theory, Elsevier, vol. 116(2), pages 294-322, June.
  8. Stephen Coate & Marco Battaglini, 2005. "Inefficiency in Legislative Policy-Making: A Dynamic Analysis," 2005 Meeting Papers 209, Society for Economic Dynamics.
  9. Banks, Jeffrey S. & Duggan, John, 1999. "A Bargaining Model of Collective Choice," Working Papers 1053, California Institute of Technology, Division of the Humanities and Social Sciences.
  10. Daniel Diermeier & Pohan Fong, 2009. "Endogenous Limits on Proposal Power," Discussion Papers 1464, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. Anesi, Vincent, 2010. "Noncooperative foundations of stable sets in voting games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 488-493, November.
  2. Vincent Anesi & Daniel J. Seidmann, 2011. "Bargaining over an Endogenous Agenda," Discussion Papers 2011-10, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  3. Facundo Piguillem & Alessandro Riboni, 2013. "Spending Biased Legislators - Discipline Through Disagreement," EIEF Working Papers Series 1317, Einaudi Institute for Economics and Finance (EIEF), revised Jul 2013.
  4. Facundo Piguillem & Alessandro Riboni, 2012. "Dynamic Bargaining over Redistribution in Legislatures," EIEF Working Papers Series 1206, Einaudi Institute for Economics and Finance (EIEF), revised Dec 2012.
  5. John Duggan & Tasos Kalandrakis, 2007. "Dynamic Legislative Policy Making," Wallis Working Papers WP45, University of Rochester - Wallis Institute of Political Economy.

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