Mathematical Economics

  1. Advanced Topics in Mathematical Economics
    1. Game Theory
      1. Introduction to Game Theory
        1. Strategic Interactions
          1. Players, Strategies, and Payoffs
          2. Strategic Form Games
            1. Normal Form Representation
              1. Payoff Matrices
                1. Dominant Strategies
                2. Nash Equilibrium
                  1. Definition and Existence
                    1. Uniqueness Properties
                      1. Pure Strategy Nash Equilibrium
                      2. Mixed Strategies
                        1. Definition and Motivation
                          1. Calculation of Mixed Strategy Equilibria
                            1. Expected Payoffs
                            2. Sequential Games
                              1. Extensive Form Representation
                                1. Game Trees
                                  1. Backward Induction
                                    1. Subgame Perfect Equilibrium
                                    2. Applications in Economics
                                      1. Oligopoly Models
                                        1. Auction Theory
                                          1. Bargaining Theory
                                        2. Calculus of Variations
                                          1. Introduction to Calculus of Variations
                                            1. Functionals
                                              1. Variational Problems
                                              2. The Euler Equation
                                                1. Derivation and Interpretation
                                                  1. Necessary Conditions for Extrema
                                                  2. Boundary Conditions
                                                    1. Fixed Endpoint Problems
                                                      1. Free Endpoint Problems
                                                      2. Applications in Economics
                                                        1. Optimal Consumption Paths
                                                          1. Investment Theory
                                                            1. Resource Extraction
                                                          2. Optimal Control Theory
                                                            1. Introduction to Optimal Control
                                                              1. Control Variables and State Variables
                                                                1. Objective Functionals
                                                                2. The Pontryagin Maximum Principle
                                                                  1. Statement and Economic Interpretation
                                                                    1. Necessary Conditions
                                                                    2. The Hamiltonian Function
                                                                      1. Construction and Properties
                                                                        1. Costate Variables
                                                                        2. Transversality Conditions
                                                                          1. Terminal Conditions
                                                                            1. Infinite Horizon Problems
                                                                            2. Applications in Economics
                                                                              1. Optimal Growth Models
                                                                                1. Resource Extraction Problems
                                                                                  1. Macroeconomic Policy
                                                                                    1. Environmental Economics
                                                                                  2. Mathematical Programming
                                                                                    1. Linear Programming
                                                                                      1. Standard Form
                                                                                        1. Graphical Method
                                                                                          1. Simplex Method
                                                                                            1. Duality Theory
                                                                                            2. Nonlinear Programming
                                                                                              1. Convex Programming
                                                                                                1. Quadratic Programming
                                                                                                  1. Integer Programming
                                                                                                  2. Dynamic Programming
                                                                                                    1. Principle of Optimality
                                                                                                      1. Bellman Equation
                                                                                                        1. Value Functions
                                                                                                          1. Policy Functions
                                                                                                          2. Economic Applications
                                                                                                            1. Production Planning
                                                                                                              1. Portfolio Optimization
                                                                                                                1. Inventory Models

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                                                                                                            6. Dynamic Analysis

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                                                                                                            1. Introduction to Mathematical Economics