Non-cooperative Game Theory

1. What is game theory? Its origins. Different types of games; classifications
2. Non-cooperative games; zero-sum and non-zero-sum games; saddle-point and Nash equilibria
3. Finite games; pure and mixed strategies; existence of equilibria; off-line and on-line computation of

   equilibria; fictitious play algorithm and its variants

4. Refinements on Nash equilibrium, such as trembling hand perfect equilibrium, proper equilibrium
5. Correlated equilibria
6. Repeated games; trigger strategies; threat strategies
7. Infinite / continuous-kernel games; existence and uniqueness of equilibria; computation of equilibria; on-line

   update algorithms and their convergence; learning

8. Evolutionary games and evolutionary stable strategies
9. Games with an infinite number of players; with a continuum of players
10. Hierarchical games; Stackelberg games and equilibria; incentive strategies; mechanism design; complete

    information versus incomplete information games

11. Stochastic static games; private and common information
12. Dynamic games; informationally non-unique equilibria; weak and strong time consistency; subgame-perfectness;

    open-loop, feedback, and memory strategies; existence, uniqueness, and derivation of Nash equilibria

13. Stochastic Markov games
14. Selected applications:
    1. Communication networks (CDMA power control; congestion control; routing; flow control; cognitive radio; pricing

       of services)

    2. Network security; jamming of communication signals
    3. Auctioning divisible resources
    4. Network economics; social networks; biological networks
    5. Worst-case designs
15. A brief introduction to cooperative game theory