Module #1 Introduction to Game Theory Overview of game theory, its importance, and applications in economics, politics, and biology.
Module #2 Basic Concepts:Games, Strategies, and Payoffs Definition of games, strategies, and payoffs. Types of games:cooperative and non-cooperative, simultaneous and sequential.
Module #3 Mathematical Preliminaries:Set Theory and Algebra Review of set theory, algebra, and basic mathematical concepts necessary for game theory.
Module #4 Graph Theory and Network Games Introduction to graph theory and its applications in game theory, including network games and graphical games.
Module #5 Utilities and Preference Relations Definition of utility functions, preference relations, and indifference curves. Axiomatic foundations of utility theory.
Module #6 Decision Theory:Decision Making Under Uncertainty Introduction to decision theory, including decision making under uncertainty, risk, and ambiguity.
Module #7 Game Representations:Normal and Extensive Forms Introduction to normal form games and extensive form games, including the conversion between the two forms.
Module #8 Nash Equilibrium:Definition and Existence Definition of Nash equilibrium, existence theorems, and examples of Nash equilibrium in different games.
Module #9 Nash Equilibrium:Computation and Refinements Computation of Nash equilibrium, refinements of Nash equilibrium, and limitations of the concept.
Module #10 Mixed Strategies and Randomization Introduction to mixed strategies, randomization, and its applications in game theory.
Module #11 Evolutionary Game Theory Introduction to evolutionary game theory, including the evolution of strategies and the replicator dynamics.
Module #12 Auction Theory Introduction to auction theory, including independent private values, common values, and auctions with interdependence.
Module #13 Mechanism Design Introduction to mechanism design, including the revelation principle, dominant strategies, and incentive compatibility.
Module #14 Cooperative Game Theory:Core and Shapley Value Introduction to cooperative game theory, including the core, Shapley value, and other cooperative solution concepts.
Module #15 Bargaining Theory Introduction to bargaining theory, including Nash bargaining solution, Kalai-Smorodinsky solution, and axiomatic bargaining theory.
Module #16 Signaling and Screening Introduction to signaling and screening, including separation, pooling, and the Spence-Mirrlees single-crossing condition.
Module #17 Repeated Games and Reputation Introduction to repeated games, including Nash equilibrium in repeated games and reputation effects.
Module #18 Stochastic Games Introduction to stochastic games, including Markov decision processes and stochastic stability.
Module #19 Algorithmic Game Theory Introduction to algorithmic game theory, including approximation algorithms and hardness results.
Module #20 Computational Complexity of Game-Theoretic Problems Analysis of the computational complexity of game-theoretic problems, including equilibrium computation and mechanism design.
Module #21 Experimental Game Theory Introduction to experimental game theory, including laboratory experiments and behavioral economics.
Module #22 Game Theory and Social Choice Introduction to social choice theory, including Arrows theorem, Condorcets paradox, and other impossibility results.
Module #23 Game Theory and Networks Introduction to network games, including network structure, diffusion, and centrality measures.
Module #24 Game Theory and Machine Learning Introduction to the intersection of game theory and machine learning, including learning in games and mechanism design.
Module #25 Course Wrap-Up & Conclusion Planning next steps in Mathematical Foundations of Game Theory career
