Postgraduate course 2020/2021

Game Theory and Political Decision-making

Type: Elective course

Area of studies: Political Science and Area Studies

Delivered by: Department of Mathematics

When: 2 year, 1 semester

Mode of studies: offline

Open to: students of one campus

Instructors: Lyudmila Egorova

Language: English

ECTS credits: 4

Contact hours: 36

Course Syllabus

Abstract

The course aims to study methods of modern political decision-making and receive political analysis skills. The main topics covered include: (1) Game theory, (2) Voting Procedures and Social Choice, (3) other special methods of decision-making like fair division, matching, etc. Many real world examples are presented like power distribution analysis in Russian Parliament and International Monetary Fund, analysis of structural balance in parliaments, etc. This course will help students internalize practical and effective mathematical methods and tools of political decision-making, and apply them to solve many real world problems. Additional materials for the course are available at https://economics.hse.ru/demat/content/gtpdm Дистанционное обучение производится на платформах MS Teams, Webinar и Zoom. Ссылка на конкретные занятия заранее высылается преподавателем по почте.

Learning Objectives

• be able to model and analyze real-life problems from the politics, social issues and everyday life
• be able to apply methods and algorithms for practical purposes, i.e. to find collective decisions by different rules, Nash equilibria, stable matchings, fair divisions, etc.
• know and understand basics of game theory, voting theory, social choice theory, theory of power distribution and structural balance, matching theory, fair division theory, and basics of mathematical modeling

Expected Learning Outcomes

• be able for critical analysis and evaluation of current scientific achievements including interdisciplinary fields
• be able to plan and solve problems of their own professional and personal development
• be able to carry out theoretical and experimental research in the field of political science and regional studies, using modern research methods including information and communication technologies
• be able to adapt the results of current research in the field of political science and regional studies to solve the problems arising from the activities of organizations and public policy

Course Contents

• Introduction
  Introduction lecture: how do we make decisions? Individual preferences and social decisions. Voting models.
• Power indices
  Power distribution in elected bodies. Shapley-Shubik and Banzhaf indices. Power indices taking into account voters’ preferences to coalesce. Power distribution in Russian Duma and other parliaments.
• Polarization
  Main notions. Polarization in one-dimensional case. Polarization in multi-dimensional case. Polarization in Russian Parliament and US Congress. Ethnolinguistic polarization.
• Balance
  Structural balance. Signed graphs. Structural balance in Russian Duma and other parliaments.
• Voting procedures, manipulation, paradoxes of voting
  Some rules: position rules, rules based on majority relation, rules based on auxiliary number scale, rules based on tournament matrix, etc. Other aggregation models. Classification of procedures. Main notions about manipulation. Gibbard-Satherswaite Theorem. A degree of manipulability of aggregation procedures. Gerrymandering. Paradoxes in social choice.
• Political maps, spatial model of voting
  One-dimensional voting model. Median voter.
• Results of elections and how to evaluate them
  Distortion of the preferences of voters. Representativity of parliament. Main indices for the analysis of the results of election.
• Network models
  Main notions. Game-theoretic approach to network analysis. Centrality indices. Application to religion, migration, international trade, foreign claims, export of food and technologies.
• Static games with complete information: pure strategy.
  Definition of game. Examples of playing and non-playing problems. Examples of simple games: the prisoner’s dilemma, coordination game, the inspectorate. Concept of the strategy. Domination. Elimination of dominated strategy. The equilibrium dominance. Nash Equilibrium. The connection between equilibrium dominance and Nash equilibrium.
• Static games with complete information: mixed strategy.
  Concept of mixed strategy. Games of 2x2 and 2xN.
• Dynamic Games of Complete Information.
  Examples of dynamic games. The game in extensive form. Backward induction. Behavioral strategy. The equivalence of mixed and behavioral strategies. Threats and promises. Subgame perfect equilibrium. Alternative logic: equilibrium in secure strategies and Nash-2 equilibrium.

Assessment Elements

• homework
  The homework consisting of several tasks. Students are encouraged to work together to help each other in understanding the course material and completing the homework problems. However, everybody has to write up his/her own solutions. Late homework will not be accepted. The common mistakes made in the homework will be discussed during the seminars.
• exam
  The examination shall be held in writing (test) with the use of asynchronous proctoring on the StartExam platform. StartExam is an online platform for conducting test tasks of various levels of complexity. Asynchronous proctoring means that all the student's actions during the exam will be “watched” by the computer. The exam process is recorded and analyzed by artificial intelligence and a human (proctor). Please be careful and follow the instructions (https://elearning.hse.ru/en/student_steps/) clearly!

Interim Assessment

• Interim assessment (1 semester)
  0.7 * exam + 0.3 * homework

Bibliography

Recommended Core Bibliography

• Aleskerov F., Bouyssou D., Monjardet B. ‘Utility Maximization, Choice and Preference’, Springer Verlag, Berlin, 2007
• 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

• An introduction to game theory, Osborne, M. J., 2009