Delivered at:: Department of Mathematics

Course type:: Elective course

When:: 3 year, 3, 4 module

Instructor

Sandomirskaia, Marina

Full 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

To familiarize students with the basic concepts, models and statements of the operations research theory
To familiarize students with the basic concepts, models and statements of the modern game theory

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.

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
Operations research. Mathematical models of operations research. Solution of the operations research models.
Linear Programming
Transportation models
Classic and modern network models
Integer linear programming.
Deterministic model of the dynamic programming.
Deterministic models of inventory.
Queueing theory.
Simulation modeling Monte-Carlo method.

Assessment Elements

Homework 1 OR
Homework 2 OR
Midterm OR
Homework 3 GT
Homework 4 GT
Exam
Game theoretical part only

Interim Assessment

2023/2024 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 OR

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

Bachelor’s Programme 'Data Science and Business Analytics'

Operations Research and Game Theory