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Regular version of the site
Bachelor 2024/2025

Operations Research and Game Theory

Area of studies: Applied Mathematics and Information Science
When: 3 year, 3, 4 module
Mode of studies: offline
Open to: students of one campus
Language: English
ECTS credits: 6

Course Syllabus

Abstract

This course has two parts. The first part introduces main concepts and models of classic and modern operations research. The operations research combines methods from different fields of mathematics in order to aid decision makers in making optimal decisions. In order to apply operations research methods, one needs to transform an actual problem into an appropriate mathematical model. In order to develop intuition for developing mathematical models all the operations research techniques are widely illustrated by examples from different industries, including agriculture, oil and gas, manufacturing, urban development, and retail. The second part of the course is devoted to game theory is a mathematical language of modern social science including economic theory, political science, evolutionary biology, computer science, etc. This course covers the non-cooperative game theory, bargaining theory, foundations of mechanism design, as well as giving insights into some of its present-day applications. The course presents main ideas and techniques of game-theoretic analysis. The aim is to teach students to use game theoretic approach in modeling of real-life problem and to think strategically. Success with this course gives edge both in deeper understanding of human behavior and in tackling business problems.
Learning Objectives

Learning Objectives

  • To familiarize students with the basic concepts and mathematical models of operations research.
  • To familiarize students with the basic concepts, models and statements of the modern game theory
Expected Learning Outcomes

Expected Learning Outcomes

  • calculate Nash equilibria in pure strategies in simultaneous-move games
  • Understanding Nash Equilibrium in pure strategies.
  • A student should find Nash equilibrium in mixed strategies in games 2x2 and 2xN
  • A student should solve dynamic games with complete information and find Nash equilibria and SPNE
  • A student should apply the Folk theorem to solving repeated games
  • A student should solve sealed-bid first-price and second-price auctions
  • A student should learn the notion of types and calculate the equilibrium profile in Bayesian games
  • A student should analyze dynamic games, know the notion of information set, beliefs, can find WSE and check if it is SSE
  • A student should model the dynamic game as signaling and find and interpret its equilibria
  • A student should solve different types of two-person bargaining problems
  • Apply Lagrange multipliers methods for solving extremum problems
  • Formulate linear programs and solve them
  • Learn properties of transportation models.
  • Realize network optimization algorithms.
  • Formulate integer linear programs and solve them.
  • Learn dynamic programming method and its classical applications.
  • Learn queuieng theory models and applications.
  • Estimate performance measures of queueing models with simulation modeling.
  • A student should learn what kind of problems are covered by operations research.
  • A student should formulate a linear programming problem.
  • A student should use optimization software (AMPL) to solve linear programming problem.
  • A student should formulate optimization problems as network models.
  • A student should critical path method and create a schedule for a project.
  • A student should formulate and solve mixed integer linear programming problems.
  • A student should linearize disjunctive and if-then constraints.
  • A student should formulate and solve traveling salesperson problem.
  • A student should apply economic order qunatity model.
  • A student should solve deterministic dynamic inventory problems.
  • A student should determine safety stocks for stochastic stationary demand given target cycle service level or fill rate.
  • A student should make simulations for testing inventory policies for stochastic demand.
Course Contents

Course Contents

  • Static games with complete information: pure strategy
  • Static games with complete information: mixed strategy
  • Dynamic Games of Complete Information
  • Repeated games
  • Bayesian games: Games with incomplete information
  • Dynamic games with incomplete information
  • Signaling games
  • Bargaining Problem
  • Introduction in Operation Research
  • Inventory modeling
  • Integer linear programming
  • Network models
  • Linear programming
Assessment Elements

Assessment Elements

  • non-blocking Homework 1 - OR
  • non-blocking Homework 2 - OR
  • non-blocking Midterm
    Operation research part.
  • non-blocking Homework 3 - GT
  • non-blocking Homework 4 - GT
  • non-blocking Exam
    Game theory part only.
Interim Assessment

Interim Assessment

  • 2024/2025 4th module
    0.3 * Exam + 0.1 * Homework 1 - OR + 0.1 * Homework 2 - OR + 0.1 * Homework 3 - GT + 0.1 * Homework 4 - GT + 0.3 * Midterm
Bibliography

Bibliography

Recommended Core Bibliography

  • A course in game theory, Osborne, M. J., 1994
  • A first course in optimization theory, Sundaram, R. K., 2011
  • An introduction to game theory, Osborne, M. J., 2009
  • Game theory : a multy-leveled approach, Peters, H., 2008
  • Game theory : analysis of conflict, Myerson, R. B., 2004
  • Game theory, Maschler, M., 2013
  • Maschler,Michael, Solan,Eilon, & Zamir,Shmuel. (2013). Game Theory. Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.cup.cbooks.9781107005488

Recommended Additional Bibliography

  • Michael Spence. (1973). Job Market Signaling. The Quarterly Journal of Economics, (3), 355. https://doi.org/10.2307/1882010

Authors

  • Sandomirskaia MARINA SERGEEVNA
  • Абдулхакимов Мухиддин Мураджанович