Useful Links
Mathematics
Game Theory
Mathematical Tools in Game Theory
Linear Programming
Formulation of Game Theory Problems as Linear Programs
Objective Functions
Constraints
Duality in Linear Programming
Primal-Dual Relationships
Applications in Game Theory
Applications in Game Strategy Optimization
Simplex Method
Interior Point Methods
Fixed Point Theorems
Brouwer's Fixed Point Theorem
Background and Statement of the Theorem
Applications in Proving Equilibrium Existence
Kakutani’s Fixed Point Theorem
Generalization for Set-Valued Functions
Use in Proving Nash Equilibria in Games
Utility Theory
Representation of Preferences
Utility Functions
Ordinal vs. Cardinal Utility
Expected Utility Theory
Risk and Uncertainty
Von Neumann-Morgenstern Utility Theorem
Utility in Cooperative and Non-Cooperative Games
Transferable Utility
Non-transferable Utility
Game Trees and Graphs
Representation of Sequential Games
Nodes and Edges as Decision Points and Actions
Terminal Nodes and Payoffs
Solving Games with Backward Induction
Subgame Perfect Equilibrium Analysis
Graph Theoretical Approaches
Network Flows and Connectivity
Algorithmic Solutions for Game Graphs
Probability and Statistics in Game Theory
Role of Randomness in Mixed Strategies
Probability Distributions Over Strategies
Statistical Analysis of Game Outcomes
Experimental Games and Analysis
Data-Driven Strategy Refinement
Convex Analysis
Convex Sets and Functions
Properties and Representation
Applications in Strategy Space Analysis
Convex Hulls of Strategy Sets
Use in Optimization Problems within Games
Convex Optimization Methods
Differential Equations and Dynamics
Modeling Evolutionary Game Dynamics
Differential Equations for Population Games
Stability Analysis in Dynamic Games
Stability Theorems
Phase Space Analysis
Computational Methods
Algorithms for Equilibrium Computation
Polynomial Time Algorithms
Approximation Algorithms for Complex Games
Computational Complexity of Game-Theoretic Problems
Classifications (P, NP, etc.)
Hardness Results for Computing Solutions
6. Applications of Game Theory
First Page
8. Historical and Theoretical Development