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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Daniel Diermeier & Pohan Fong, 2008.
"Endogenous Limits on Proposal Power,"
Discussion Papers
1464, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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