Tentative summary of topics:

• I. Static games of complete information
  • Dominant strategies, iterated elimination of dominated strategies, mixed strategies, Nash equilibrium, saddle-point theory,
  • Conditions for existence, and conditions for uniqueness, of Nash equilibrium
  • Correlated equilibria
  • Fictitious play and convergence results
  • Evolutionarily stable strategies (ESS) and evolutionarily stable states of replicator dynamics
  • Trembling hand equilibrium
  • Blackwell's approachability theorem and learning
• II. Dynamic games of complete information
  • Extensive form games with imperfect information: normal form, subgame perfect equilibrium, sequential equilibria
  • Multistage games with observed actions: one step deviation principle
  • Repeated games: trigger strategies, feasibility theorems (aka folk theorems)
• III. Static games of incomplete information
  • Bayes-Nash equilibrium
• IV. Mechanism design and the theory of auctions
  • Vikrey second price auction and its generalization (VCG mechanism)
  • Revenue optimal auctions (direct revelation principle, revenue equivalence, virtual valuations (Myerson theory)
  • Equilbrium bidding strategies and revenue ordering for second price and ascending auctions with correlated private information (Milgrom and Weber theory)
• V. Coalitions in cooperative games
  • Core, exchange economies with transferrable payments, Shapley value