This course presents a mathematical treatment of classical and evolutionary game theory.
Topics covered in classical game theory: matrix games, continuous games, Nash equilibrium (NE) solution, existence and uniqueness, best-response correspondence. Topics covered in evolutionary games: evolutionary stable strategy concept, population games, replicator dynamics, relation to dynamic asymptotic stability.
Learning in games: imitation dynamics, fictitious play and their relation to replicator dynamics. Applications to engineering: communication networks, multi-agent learning.
There is no required textbook. PDF course notes are available; the notes are self-contained and serve as a textbook. Weekly formal lectures based on the course notes.