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Noncooperative Game TheoryAn Introduction for Engineers and Computer Scientists$
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João P. Hespanha

Print publication date: 2017

Print ISBN-13: 9780691175218

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691175218.001.0001

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One-Player Dynamic Games

One-Player Dynamic Games

(p.178) Lecture 15 One-Player Dynamic Games
Noncooperative Game Theory

João P. Hespanha

Princeton University Press

This chapter focuses on one-player discrete time dynamic games, that is, the optimal control of a discrete time dynamical system. It first considers solution methods for one-player dynamic games, which are simple optimizations, before discussing discrete time cost-to-go. It shows that, regardless of the information structure (open loop, state feedback or other), it is not possible to obtain a cost lower than the cost-to-go. A computationally efficient recursive technique that can be used to compute the cost-to-go is dynamic programming. After providing an overview of discrete time dynamic programming, the chapter explores the complexity of computing the cost-to-go at all stages, the use of MATLAB to solve finite one-player games, and linear quadratic dynamic games. It concludes with a practice exercise and the corresponding solution, along with an additional exercise.

Keywords:   discrete time dynamic, discrete time cost-to-go, discrete time dynamic programming, MATLAB, finite one-player, linear quadratic dynamic

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