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A Newton Collocation Method for Solving Dynamic Bargaining Games

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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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Paper provided by University of Rochester - Wallis Institute of Political Economy in its series Wallis Working Papers with number WP60.

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Length: 40 pages
Date of creation: Aug 2009
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Handle: RePEc:roc:wallis:wp60

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Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

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  1. Daron Acemoglu & Georgy Egorov & Konstantin Sonin, 2008. "Dynamics and Stability of Constitutions, Coalitions, and Clubs," NBER Working Papers 14239, National Bureau of Economic Research, Inc.
  2. John Duggan & Tasos Kalandrakis, 2007. "Dynamic Legislative Policy Making," Wallis Working Papers WP45, University of Rochester - Wallis Institute of Political Economy.
  3. 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.
  4. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  5. Marco Battaglini & Stephen Coate, 2007. "Inefficiency in Legislative Policymaking: A Dynamic Analysis," American Economic Review, American Economic Association, vol. 97(1), pages 118-149, March.
  6. Daniel Diermeier & Pohan Fong, 2009. "Endogenous Limits on Proposal Power," Discussion Papers 1464, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Kalandrakis, Anastassios, 2004. "A three-player dynamic majoritarian bargaining game," Journal of Economic Theory, Elsevier, vol. 116(2), pages 294-322, June.
  8. 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.
  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. Tasos Kalandrakis, 2007. "Majority Rule Dynamics with Endogenous Status Quo," Wallis Working Papers WP46, University of Rochester - Wallis Institute of Political Economy.
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Cited by:
  1. 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.
  2. Vincent Anesi, 2007. "Noncooperative Foundations of Stable Sets in Voting Games," Discussion Papers 2007-09, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  3. Vincent Anesi & Daniel J Seidmann, 2012. "Bargaining over an Endogenous Agenda," Discussion Papers 2012-03, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  4. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
  5. 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.

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