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Game Theory in Wireless and Communication Networks by Walid Saad, Dusit Niyato, Zhu Han

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5    Differential games

The differential games framework extends static non-cooperative continuous-kernel game theory into dynamic environments by adopting the tools, methods, and models of optimal-control theory. Optimal-control theory [58] has been developed to obtain the optimal solutions to planning problems that involve dynamic systems, where the state evolves over time under the influence of a control input (which is the instrument variable that is designed). Differential games can be viewed as extensions of optimal-control problems in two directions: (i) the evolution of the state is controlled not by one input but by multiple inputs, with ...

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