Operations Research for Economic Applications

Course Overview

This course is the second part of a two-part series on Operations Research. While the first part covers Linear Programming, this part focuses on Decision Analysis, Game Theory, and Markov Processes with applications in economic decision-making, strategic interactions, and stochastic systems.

The key objectives are:

• Understanding decision-making under uncertainty using expected monetary payoffs and utility theory.

• Applying game theory to model economic and strategic interactions.

• Analyzing Markov processes and their economic applications in dynamic decision-making, pricing strategies, and inventory models.

Course Outline

Part 1: Decision Analysis

📌 Understanding decision-making under uncertainty, comparing monetary payoffs and utility-based approaches.

1. Expected Monetary Payoffs
   
   

   • Decision Trees and Probabilistic Outcomes

   • Risk-Neutral Decision Making

   • Economic Applications: Investment Choices, Firm Strategy

2. Expected Utility Theory
   
   

   • Von Neumann–Morgenstern Utility Function

   • Risk Aversion and Certainty Equivalents

   • Applications: Insurance Markets, Portfolio Choice

🛠 Computational Tools: Python (NumPy for simulations, Matplotlib for decision trees)

Part 2: Game Theory

📌 Introduction to strategic interactions and equilibrium concepts, focusing on zero-sum games.

3. Zero-Sum Games
   
   

   • Minimax Theorem and Optimal Strategies

   • Solving Zero-Sum Games via Linear Programming

   • Applications: Trade Wars, Auction Design, Labor Bargaining

4. Mixed Strategy Nash Equilibrium
   
   

   • Concept of Mixed Strategies and Expected Payoffs

   • Applications: Pricing Competition, Market Entry Models

   • Computational Methods: Simplex for Mixed-Strategy Computation

🛠 Computational Tools: Python (Game Theory Toolkit, Linear Programming solvers)

Part 3: Markov Processes and Their Applications

📌 Understanding stochastic processes and their role in dynamic economic decision-making.

5. Introduction to Markov Chains
   
   

   • Transition Matrices and Steady-State Probabilities

   • Economic Applications: Customer Retention, Brand Loyalty Models

6. Markov Decision Processes (MDPs)
   
   

   • Bellman Equations and Dynamic Programming

   • Economic Applications: Pricing Strategies, Optimal Stopping Problems

7. Applications in Economics and Finance
   
   

   • Stochastic Inventory Models

   • Credit Rating Transitions and Default Probabilities

🛠 Computational Tools: Python (Markov Chain Simulation, Dynamic Programming Algorithms)

Reading Materials

Prescribed Textbooks:

• Frederick Hillier & Gerald Lieberman (2020) – Introduction to Operations Research (Core concepts in OR, decision analysis, and Markov processes)

• Wayne L. Winston (2003) – Operations Research: Applications and Algorithms (Algorithmic approaches to game theory and stochastic processes)

Recommended Readings:

• Robert Gibbons (1992) – Game Theory for Applied Economists (Economic applications of game theory)

• Sheldon Ross (2014) – Introduction to Stochastic Processes (Comprehensive treatment of Markov processes)