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​There are several techniques to study noncooperative dynamic games, such as dynamic programming and the maximum principle (also called the Lagrange method).
Discrete-Time Stochastic Control and Dynamic Potential Games
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Stochastic Control in Discrete and Continuous Time
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This book contains an introduction to three topics in stochastic control: discrete time stochastic control, i. e. , stochastic dynamic programming (Chapter 1),
Potential Game Theory
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Mathematical Optimization Theory and Operations Research
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This book constitutes the proceedings of the 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019, held in Ekat