The course is a graduate-level introduction to game theory, and to its applications to system design, verification, analysis, and optimal control.
The course contains a brief introduction to 1-player games (both deterministic and probabilistic), and then considers 2-player zero-sum games. Zero-sum games model the competition between a player and an opponent, where the gain of the player is the loss of the opponent. Such games are used in several applications:
Control: One player models the controller, the other player models the system. The moves of the controller correspond to the different control actions, the moves of the systems correspond to variability (due to uncertainty, inputs from the environment, etc) about the system behavior. Typical control goals are safety (can we ensure the system stays in a set of safe states) and reachability (can we ensure that a goal is reached?).
Scheduling: One player models the scheduler, and one player models the set of activities to be scheduled. The moves of the scheduler are scheduling actions; the moves of the system correspond to the possible interactions and outcomes of the activities. A strategy for the scheduler encodes a schedule.
System design and verification: many questions in the design and verification of digital and software systems can be phrased as games. For example, one may wish to design a routing strategy such that, regardless of network link disruptions, no circular routing occurs. Such a routing strategy can be cast as a strategy in a game, routing vs. link disruption.
The course also provides an introduction to recent developments in game theory, such as game simulation (when is a game more general, or harder to win, than another?), and real-time games (games in which players must choose the precise instant in time in which the moves are played).