Computing Supergame Equilibria

Judd, Kenneth L.; Yeltekin, Şevin; Conklin, James

doi:10.1111/1468-0262.t01-1-00445

Cited by 82 publications

(17 citation statements)

References 11 publications

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“…As noted, these functions are fully determined on S × C (or a subset thereof). Moreover, their sub-linearity implies that, for all y ∈ C, Judd, Yeltekin, and Conklin (2003) used this approach to approximate the support function of a payoff set in a repeated game; we use it to approximate the recursive dual value function. In other aspects, our (recursive dual) formulation is different from that of Judd, Yeltekin, and Conklin (2003).…”

mentioning

confidence: 99%

“…Moreover, their sub-linearity implies that, for all y ∈ C, Judd, Yeltekin, and Conklin (2003) used this approach to approximate the support function of a payoff set in a repeated game; we use it to approximate the recursive dual value function. In other aspects, our (recursive dual) formulation is different from that of Judd, Yeltekin, and Conklin (2003). Alternative approaches to approximation on spherical domains are described in Sloan and Womersley (2000).…”

mentioning

confidence: 99%

“…Our implementation exploits the sub-linearity of dual value functions and uses a piecewise linear approximation (on the spherical domain C). Piecewise linear approximations to value functions defined on spheres were first applied in economics by Judd, Yeltekin, and Conklin (2003). We apply their approximation procedure to our setting.…”

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confidence: 99%

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The Dual Approach to Recursive Optimization: Theory and Examples

Pavoni¹,

Sleet²,

Messner³

2018

Econometrica

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APPENDIX A: NUMERICAL IMPLEMENTATION THIS SECTION DESCRIBES how to implement the recursive dual approach numerically. Under the conditions of Theorem 2, the dual Bellman operator is a contraction and, consequently, it is natural to calculate D * via value iteration. Numerical approximation of candidate dual value functions is facilitated by their sub-linearity and the simplicity of their domain. The dual Bellman involves an (outer) minimization over a set of multipliers; these multipliers are passed to (and "coordinate") a family of simple (inner) maximizations over current actions and states. Additive separability in the objective may be exploited to decompose the inner maximizations into a family of simpler maximizations that in parametric settings often have analytical solutions.Dual Value Function Approximation. Numerical implementation of a value function iteration algorithm requires approximations to candidate value functions. Our implementation exploits the sub-linearity of dual value functions and uses a piecewise linear approximation (on the spherical domain C). Piecewise linear approximations to value functions defined on spheres were first applied in economics by Judd, Yeltekin, and Conklin (2003). We apply their approximation procedure to our setting. 31 Recall that under the conditions of Theorem 2, the domain for the dual Bellman operator may be identified with an interval of functions D : S × Y → R, each of which is sub-linear in its second argument. As noted, these functions are fully determined on S × C (or a subset thereof). Moreover, their sub-linearity implies that, for all y ∈ C, Judd, Yeltekin, and Conklin (2003) used this approach to approximate the support function of a payoff set in a repeated game; we use it to approximate the recursive dual value function. In other aspects, our (recursive dual) formulation is different from that of Judd, Yeltekin, and Conklin (2003). Alternative approaches to approximation on spherical domains are described in Sloan and Womersley (2000). 32 For this and other properties of sub-linear functions used below, see Florenzano and Van (2001).

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The Dual Approach to Recursive Optimization: Theory and Examples

Pavoni¹,

Sleet²,

Messner³

2018

Econometrica

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“…We then turn to a comparison of our algorithm with that of Judd et al (2003) (JYC). To perform a practical comparison of running times, we use a Cournot duopoly example from JYC and calculate the equilibrium payoff set with the two algorithms.…”

Section: Lemma 2 the Function R(· U) Is Increasing In Its First Argumentioning

confidence: 99%

“…A classic paper by Judd et al (2003) (to which we refer frequently below as JYC) provides a numerical implementation of the APS algorithm based on linear programming problems. Each set W n is approximated by its supporting hyperplanes.…”

Section: Introductionmentioning

confidence: 99%