| By: |
John Duggan (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158);
Tasos Kalandrakis (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158) |
| 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. |
| Date: |
2009–08 |
| URL: |
https://d.repec.org/n?u=RePEc:roc:wallis:wp60 |