Computing Equilibria of Dynamic Games

We develop a numerical method for computing all pure strategy subgame-perfect equilibrium values of dynamic strategic games with discrete states and actions. We define a monotone mapping that eliminates dominated strategies, and when applied iteratively, delivers an accurate approximation to the tru...

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Bibliographic Details
Published in:Operations research 2017-03, Vol.65 (2), p.337-356
Main Authors: Yeltekin, Şevin, Cai, Yongyang, Judd, Kenneth L.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Approximation
Cloud computing
Competition (Economics)
Computation
CROSSCUTTING AREAS
dynamic games
dynamic oligopoly
Equilibrium
Game theory
Games
Mathematical analysis
multiple equilibria
Numerical methods
Operations research
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Summary:We develop a numerical method for computing all pure strategy subgame-perfect equilibrium values of dynamic strategic games with discrete states and actions. We define a monotone mapping that eliminates dominated strategies, and when applied iteratively, delivers an accurate approximation to the true equilibrium payoffs of the underlying game. Our algorithm has three parts. The first provides an outer approximation to equilibrium values, constructed so that any value outside of this approximation is not an equilibrium value. The second provides an inner approximation; any value contained within this approximation is an equilibrium value. Together, the two approximations deliver a practical check of approximation accuracy. The third part of our algorithm delivers sample equilibrium paths. To illustrate our method, we apply it to a dynamic oligopoly competition with endogenous production capacity.
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.2016.1572