Mathematical Foundations of Game Theory
( 25 Modules )

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

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Mathematical Foundations of Game Theory ( 25 Modules )

Mathematical Foundations of Game Theory
( 25 Modules )