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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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State-Feedback Zero-Sum Dynamic Games

State-Feedback Zero-Sum Dynamic Games

(p.201) Lecture 17 State-Feedback Zero-Sum Dynamic Games
Noncooperative Game Theory

João P. Hespanha

Princeton University Press

This chapter focuses on the computation of the saddle-point equilibrium of a zero-sum discrete time dynamic game in a state-feedback policy. It begins by considering solution methods for two-player zero sum dynamic games in discrete time, assuming a finite horizon stage-additive cost that Player 1 wants to minimize and Player 2 wants to maximize, and taking into account a state feedback information structure. The discussion then turns to discrete time dynamic programming, the use of MATLAB to solve zero-sum games with finite state spaces and finite action spaces, and discrete time linear quadratic dynamic games. The chapter concludes with a practice exercise that requires computing the cost-to-go for each state of the tic-tac-toe game, and the corresponding solution.

Keywords:   saddle-point equilibrium, discrete time dynamic, state-feedback policy, zero sum dynamic, tic-tac-toe, state feedback information structure, discrete time dynamic programming, MATLAB, zero-sum, discrete time linear quadratic dynamic

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