A Newton Collocation Method for Solving Dynamic Bargaining Games
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.
|Date of creation:||Aug 2009|
|Date of revision:|
|Contact details of provider:|| Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.|
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- Daniel Diermeier & Pohan Fong, 2009.
"Endogenous Limits on Proposal Power,"
1464, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kalandrakis, Anastassios, 2004. "A three-player dynamic majoritarian bargaining game," Journal of Economic Theory, Elsevier, vol. 116(2), pages 294-322, June.
- 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.
- Marco Battaglini & Stephen Coate, 2005. "Inefficiency in Legislative Policy-Making: A Dynamic Analysis," NBER Working Papers 11495, National Bureau of Economic Research, Inc.
- Stephen Coate & Marco Battaglini, 2005. "Inefficiency in Legislative Policy-Making: A Dynamic Analysis," 2005 Meeting Papers 209, Society for Economic Dynamics.
- Battaglini, Marco & Coate, Stephen, 2005. "Inefficiency in Legislative Policy-Making: A Dynamic Analysis," Papers 08-09-2005, Princeton University, Research Program in Political Economy.
- Rubinstein, Ariel, 1982.
"Perfect Equilibrium in a Bargaining Model,"
Econometric Society, vol. 50(1), pages 97-109, January.
- Mas-Colell,Andreu, 1985.
"The Theory of General Economic Equilibrium,"
Cambridge University Press, number 9780521265140.
- 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.
- 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.
- Daron Acemoglu & Georgy Egorov & Konstantin Sonin, 2012.
"Dynamics and Stability of Constitutions, Coalitions, and Clubs,"
American Economic Review,
American Economic Association, vol. 102(4), pages 1446-76, June.
- Konstantin Sonin & Georgy Egorov & Daron Acemoglu, 2008. "Dynamics and Stability of Constitutions, Coalitions and Clubs," 2008 Meeting Papers 314, Society for Economic Dynamics.
- 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.
- John Duggan & Tasos Kalandrakis, 2007.
"Dynamic Legislative Policy Making,"
Wallis Working Papers
WP45, University of Rochester - Wallis Institute of Political Economy.
- Tasos Kalandrakis, 2007. "Majority Rule Dynamics with Endogenous Status Quo," Wallis Working Papers WP46, University of Rochester - Wallis Institute of Political Economy.
- 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.
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