Part I: Normal-Form Games
Session 1: Introduction
Topics: Introduction to the course and logistics.
Session 2: Setting and Equilibria: The Nash Equilibrium
Topics: Definition of normal-form games. Solution concepts and Nash equilibrium. Nash equilibrium existence theorem.
Session 3: Setting and Equilibria: The Correlated Equilibrium
Topics: Topological and computational properties of the set of Nash equilibria in normal-form games. Connections with linear programming. Definition of correlated and coarse correlated equilibria; relationships with Nash equilibria.
Session 4: Learning in Games: Foundations
Key Date: Problem set 1 out.
Topics: Regret and hindsight rationality. Definition of regret minimization and relationships with equilibrium concepts.
Session 5: Learning in Games: Algorithms (part I)
Topics: General principles in the design of learning algorithms. Follow-the-leader, regret matching, multiplicative weights update, online mirror descent.
Session 6: Learning in Games: Algorithms (part II)
Topics: Optimistic mirror descent and optimistic follow-the-regularized-leader. Accelerated computation of approximate equilibria.
Session 7: Learning in Games: Bandit Feedback
Topics: From multiplicative weights to Exp3. General principles. Obtaining high-probability bounds.
Session 8: Learning in Games: Φ-Regret Minimization
Topics: Gordon, Greenwald, and Marks (2008); Blum and Mansour; Stolz-Lugosi.
Part II: Extensive-Form Games
Session 9: Foundations of Extensive-Form Games
Topics: Complete versus imperfect information. Kuhn’s theorem. Normal-form and sequence-form strategies. Similarities and differences with normal-form games.
Session 10: Learning in Extensive-Form Games
Key Date: Problem set 2 out.
Topics: No-regret algorithms for extensive-form games. Counterfactual utilities and counterfactual regret minimization (CFR).
Session 11: Equilibrium Refinements
Topics: Sequential irrationality. Extensive-form perfect equilibria and quasi-perfect equilibrium.
Session 12: No class (student holiday)
Session 13: Project ideas and brainstorming
Session 14: Project break
Coincides with INFORMS 2024 Annual Meeting.
Session 15: Project break
Coincides with INFORMS 2024 Annual Meeting.
Session 16: Deep Reinforcement Learning for Large-Scale Games (part I)
Topics: Rough taxonomy of deep RL methods for games. Decision-time planning in imperfect-information games, construction of superhuman agents for no-limit hold’em poker. Public belief states techniques (ReBeL).
Session 17: Deep Reinforcement Learning for Large-Scale Games (part II)
Topics: PPO and magnetic mirror descent.
Part III: Other Structured Games
Session 18: Combinatorial Games and Kernelized MWU (Part I)
Topics: Example of combinatorial games. Kernelized multiplicative weights update algorithm.
Session 19: Combinatorial Games and Kernelized MWU (Part II)
Topics: Example of combinatorial games. Kernelized multiplicative weights update algorithm.
Session 20: Computation of Exact Equilibria
Key Date: Problem set 3 out.
Topics: A second look at the minimax theorem. Hart and Schmeidler’s proof of existence of correlated equilibria. Ellipsoid against hope algorithm.
Session 21: Stochastic Games
Topics: Minimax theorem, and existence of equilibrium. Stationary Markov Nash equilibria. Coarse correlated and correlated equilibria in stochastic games.
Part IV: Complexity of Equilibrium Computation
Session 22: PPAD-Completeness of Nash Equilibria (part I)
Topics: Sperner’s lemma. The PPAD complexity class. Nash ∈ PPAD.
Session 23: PPAD-Completeness of Nash Equilibria (part II)
Topics: Arithmetic circuit SAT. PPAD-hardness of Nash equilibria. Project break and presentations.
