Here’s a list of 100 chapter titles on Game Theory with a focus on mathematical aspects, progressing from beginner to advanced levels:
- Introduction to Game Theory: Foundations and Key Concepts
- Players, Strategies, and Payoffs: The Building Blocks of Game Theory
- Zero-Sum Games: A Mathematical Overview
- Introduction to Normal Form Games and Matrix Representation
- The Concept of Dominated Strategies: Elimination and Simplification
- Pure Strategy Nash Equilibrium: The Core Idea
- Mixed Strategy Nash Equilibrium: An Introduction
- The Prisoner’s Dilemma: Understanding Cooperation and Defection
- Sequential Games: The Role of Time and Decision Order
- The Extensive Form Representation of Games
- Backward Induction: Solving Sequential Games
- Subgame Perfect Nash Equilibrium: Formalizing Rationality
- Dominance Solvability in Games
- Mixed Strategies and Probability in Game Theory
- The Battle of the Sexes: A Classic Coordination Game
- Coordination Games and Pareto Efficiency
- The Stag Hunt: A Case of Risk Dominance and Coordination
- Game Theory and Social Dilemmas: Insights and Applications
- Repeated Games: Strategies Over Time
- The Concept of Nash Equilibrium in Simple Two-Player Games
- Introduction to Cooperative Game Theory: Core and Shapley Value
- The Core of a Cooperative Game: Mathematical Formulation
- The Shapley Value: Fair Division and Allocation of Payoffs
- Bargaining Games: Nash’s Solution and Its Implications
- Coalitions and Grand Coalitions: Structure and Stability
- Games with Asymmetric Information: Basic Concepts and Examples
- Bayesian Games: Introduction to Incomplete Information
- Bayesian Nash Equilibrium: Solving Games with Incomplete Information
- Auctions and Game Theory: Bidding Strategies and Equilibria
- Voting Games: Preferences, Majority, and Strategic Voting
- Mechanism Design: Designing Rules for Optimal Outcomes
- The Winner’s Curse: Strategic Bidding in Auctions
- Evolutionary Game Theory: Applications to Biology and Economics
- The Hawk-Dove Game: A Biological and Evolutionary Perspective
- Evolutionarily Stable Strategies (ESS): Stability in Populations
- The Replicator Dynamics: Modeling Strategy Changes Over Time
- The Public Goods Game: Contributions and Free-Rider Problems
- Prisoner’s Dilemma in Repeated Games: Tit-for-Tat and Other Strategies
- Sequential Bargaining: Strategic Negotiation and Agreements
- The Nash Program: From Equilibrium to Solution Concepts
- Advanced Topics in Nash Equilibrium: Existence and Uniqueness
- The Generalized Nash Equilibrium: New Models and Concepts
- Refinements of Nash Equilibrium: Subgame Perfection and Perfect Equilibrium
- Mixed Strategy Nash Equilibrium: Solving for Probabilistic Strategies
- Correlated Equilibrium: A Generalization of Nash Equilibrium
- The Folk Theorem in Repeated Games: Characterizing Outcomes
- Differential Game Theory: Continuous Strategies and Dynamic Systems
- Markov Strategies and Markov Perfect Equilibrium
- The Shapley-Shubik Power Index: Power Distribution in Voting Games
- Evolutionary Dynamics and Adaptive Strategies in Game Theory
- Learning in Games: Replicator and Belief Dynamics
- Quantal Response Equilibrium: Behavior under Uncertainty
- Computational Game Theory: Algorithms and Complexity
- Games on Graphs: Strategy and Network Games
- Bounded Rationality in Game Theory: Models of Limited Decision-Making
- Differential and Stochastic Games: Continuous-Time and Randomness
- Dynamic Games with Information Structure: Signaling and Screening
- Game Theory in Economics: Strategic Market Behavior
- Games with Incomplete Information: Modeling and Equilibria
- Adverse Selection and Moral Hazard in Agency Games
- Aumann’s Agreement Theorem: Rational Consensus and Information Sharing
- The Voting Paradox: When Majority Preferences are Inconsistent
- The Arrow Impossibility Theorem: Social Choice and Fairness
- Advanced Auction Theory: Combinatorial Auctions and Bidding Strategies
- Game Theory and Mechanism Design: Optimal Auction Design
- The Ramsey Problem: Optimal Resource Allocation in Economics
- Auction Theory with Multi-Dimensional Preferences
- Repeated Game Theory: The Role of Reputation and Trust
- Perfect Bayesian Equilibrium: Solving for Incomplete Information Games
- Dynamic Programming and Game Theory: Optimal Decision-Making
- Auctions with Externalities: Effects Beyond the Auction
- Stochastic Games: Markov Decision Processes and Game Theory
- Hierarchical Games: Multi-Level Decision Making
- Team Games: Cooperative Solutions in Competitive Environments
- The Theory of Envy-Free Allocations in Cooperative Games
- Non-Cooperative Bargaining: Game-Theoretic Approaches
- Game Theory in Cooperative Systems: Collaborations and Conflicts
- Robust Optimization and Game Theory: Dealing with Uncertainty
- Fairness and Efficiency in Cooperative Game Theory
- The Price of Anarchy: How Inefficient Equilibria Can Be
- The Applications of Game Theory to Network Economics and Design
- Game Theory in International Trade: Negotiation and Competition
- Quantum Game Theory: New Perspectives and Applications
- Multi-Agent Systems and Game Theory in Artificial Intelligence
- The Evolution of Cooperation: Game Theory in Evolutionary Biology
- Algorithmic Game Theory: Computation in Strategic Settings
- Approximation Algorithms for Game Theory: Computational Approaches
- Game Theory in Machine Learning: Algorithms and Applications
- Stackelberg Games: Leader-Follower Models and Strategies
- Continuous Games and Differential Games in Continuous-Time
- Algorithmic Mechanism Design: Designing Auctions and Market Systems
- The War of Attrition: Mathematical Models and Strategies
- Network Game Theory: Connectivity, Routing, and Flow Games
- Cooperative Game Theory and the Shapley Value in Network Design
- The Modeling of Social Networks Using Game Theory
- Game Theory and Cryptography: Security and Strategic Computation
- Stochastic Games and Markov Decision Processes in AI
- The Nash Equilibrium in High-Dimensional Spaces: Mathematical Insights
- The Use of Game Theory in Predictive Models for Market Behavior
- Future Challenges in Game Theory: Quantum Computing, Cryptography, and Beyond
These chapters span from fundamental principles of game theory to complex applications and advanced topics in mathematics, ensuring a deep understanding of both theoretical and practical aspects of the subject.