Lectures

Part I: Basics of game theory

1. Introduction and some basic definitions (13.08)  [video]
   normal form games, payoff matrix, dominant strategy, dominant strategy equilibrium, pure strategy Nash equilibrium

2. Equilibria; Existence of Nash Equilibrium (21.08) [video]
   dominant strategy equilibrium, proof of Nash's theorem, fixed-point theorem

3. Finding Nash Equilibrium in special games: Two player zero sum game, Proof of Minimax Theorem (22.08)  [video]
   Nash equilibrium, zero sum game, minimax theorem, linear programming

4. Separable multi player zero sum game; Intractability of finding Nash Equilibrium in general: Introduction to PPAD-completeness, Approximate NE, Sperner's Lemma (29.08)  [video]
   zero sum game, Nash equilibrium, PPAD, Sperner's lemma, intractability

5. Road to PPAD-completeness (04.09) [slides] [video]
   Sperner's lemma, FNP, Nash, Brouwer, search problem, PPAD

6. PPAD-completeness of finding a Nash equilibrium (11.09) [slides] [video]
   Arithmetic circuit SAT, graphical games, poly-matrix games, Nash equilibrium

7. An introduction to fair cake-cutting (12.09) [video]
   cake-cutting, proportionality, envy, moving-knife

8. Existence of an envy-free division of a cake (14.09) [slides] [video]
   envy, fair division, Sperner's Lemma, chains, coloring

9. Existence of an envy-free division of a cake (Part 2); Introduction to auctions (18.09) [video]
   cake, envy, auction, price, utility, DSIC

Part II: Non-cooperative Game Theory

1. Myerson's Lemma (19.09) [video]
   DSIC, IR, single-parameter environment, mechanism, allocation, payment

2. VCG Mechanism (25.09)
   externality, social surplus, payment, DSIC

3. Bayesian Mechanism Design (26.09) [video]
   payment, DSIC, reserve price, revenue maximization

4. Introduction to Selfish Routing and Congestion Games  (23.10) [video]
   selfish routing, non-atomic selfish routing, price of anarchy, Pigou's network, Braess's paradox

5. Non-atomic Selfish Routing 1 (24.10) [video]
   price of anarchy, Pigou-like network, equilibrium flows

6. Non-atomic Selfish Routing 2 (30.10) [video]
   equilibrium and optimal flows, price of anarchy, capacity augmentation

7. Atomic Selfish Routing (31.10) [video]
   existence of equilibrium flows, potential arguments, affine cost function

8. Network Cost-Sharing Games 1 (06.11) [video]
   price of anarchy, price of stability, potential argument

9. Network Cost-Sharing Games 2 (07.11) [video]
   beneficial deviation, strong Nash equilibrium, price of anarchy

10. Game Dynamics 1 (20.11) [video]
    best-response dynamics, pure Nash equilibrium, potential games, convergence

11. Game Dynamics 2 (21.11) [video]
    fast convergence, epsilon-best-response dynamics, max gain, alpha-bounded jump condition, convergence

Part III: Cooperative Game Theory

Part IV: Evolutionary Game Theory

Part V: Learning in Game Theory