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A Newton collocation method for solving dynamic bargaining games

  • John Duggan

    ()

  • Tasos Kalandrakis

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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Article provided by Springer & The Society for Social Choice and Welfare 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
DOI: 10.1007/s00355-010-0513-2
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  1. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
  2. Stephen Coate & Marco Battaglini, 2005. "Inefficiency in Legislative Policy-Making: A Dynamic Analysis," 2005 Meeting Papers 209, Society for Economic Dynamics.
  3. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
  4. Pohan Fong, 2008. "Endogenous Limits on Proposal Power," Discussion Papers 1465, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Kalandrakis, Anastassios, 2004. "A three-player dynamic majoritarian bargaining game," Journal of Economic Theory, Elsevier, vol. 116(2), pages 294-322, June.
  6. 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.
  7. 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.
  8. Konstantin Sonin & Georgy Egorov & Daron Acemoglu, 2008. "Dynamics and Stability of Constitutions, Coalitions and Clubs," 2008 Meeting Papers 314, Society for Economic Dynamics.
  9. Tasos Kalandrakis, 2007. "Majority Rule Dynamics with Endogenous Status Quo," Wallis Working Papers WP46, University of Rochester - Wallis Institute of Political Economy.
  10. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, Junio.
  11. 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.
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