Бакалавриат
2026/2027
Справедливое и эффективное принятие решений в задачах об обобщённых паросочетаниях и назначениях
Статус:
Курс по выбору (Прикладная математика и информатика)
Кто читает:
Департамент математики
Где читается:
Факультет экономических наук
Когда читается:
4-й курс, 1 модуль
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
5
Контактные часы:
32
Course Syllabus
Abstract
Title of a Course: « Fair and Efficient Decision Making in Matching and
Assignment»
Many real-life resource allocation problems can be analyzed through
matching and assignment models, including the assignment of workers to firms,
doctors to hospitals, students to schools and universities, donated organs to patients,
donated goods to those in need, indigent defendants to public lawyers, and so on. The
success of both positive and normative approaches to decision making is judged by the
extent to which they satisfy relevant fairness and efficiency criteria, as well as by their
practical implementability. This course discusses fairness and efficiency notions in
various matching and assignment models and provides a theoretical analysis of
solutions proposed in the literature for different real-life applications of these
problems.
Pre-requisites: Basic courses in Calculus, Discrete Mathematics, Linear Algebra,
Theory of Probability and Mathematical Statistics, Theory of Individual and Social Choice
Learning Objectives
- The objective of this course is to familiarize students with the theoretical literature on matching and assignment problems and with its use in designing solutions to important large-scale real-life resource allocation problems
Expected Learning Outcomes
- Students should easily read and understand basics of the modeling part in the academic papers. Students should know the axioms and their implications in various models including choice, social choice, assignment, matching, school choice, cooperative games, and fair allocation. Students should be able to understand formal statements and prove formal statements. Then should understand strategic issues associated with the rule/mechanism design
- Students should be able to contemplate about the efficiency and fairness criteria in any real life resource allocation procedure
- Students should be able to contemplate on the congestion effects in any real life assignment problem
- Student should be able to design and contemplate on probabilistic assignment procedures
- Students should be able to apply stable matching mechanisms in any real world matching procedure
- Students should be able to contemplate on the pros and cons of different school choice mechanisms and decide which one would give better outcomes depending on the specific environment, its legal procedures and social norms.
Course Contents
- Introduction to efficiency and fairness notions
- Object assignment problem with or without ownership
- Random assignment
- Matching
- School choice
- Congested assignment
Bibliography
Recommended Core Bibliography
- Abdulkadiroglu, A., & Sonmez, T. (1999). House Allocation with Existing Tenants. Journal of Economic Theory, (2), 233. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.a.eee.jetheo.v88y1999i2p233.260
- Abdulkadiroglu, A., Angrist, J. D., Dynarski, S. M., Kane, T. J., & Pathak, P. A. (2011). Accountability and Flexibility in Public Schools: Evidence from Boston’s Charters And Pilots. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.8BDDA230
- Fehr, E., & Schmidt, K. M. (1999). A Theory of Fairness, Competition, and Cooperation. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.8A52174F
- Fuad Aleskerov, & Andrey Subochev. (2013). Modeling optimal social choice: matrix-vector representation of various solution concepts based on majority rule. Journal of Global Optimization, (2), 737. https://doi.org/10.1007/s10898-012-9907-2
- Handbook of Computational Social Choice. (2016). Cambridge University Press. https://doi.org/10.1017/cbo9781107446984
- Market design : auctions and matching, Haeringer, G., 2017
- Roth, A. E., & Sotomayor, M. A. O. (1992). Two-Sided Matching. Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.cup.cbooks.9780521437882
- Two-sided matching: a study in game-theoretic modeling and analysis, Roth, A. E., 1992
Recommended Additional Bibliography
- Arrow, K. J. (2012). Social Choice and Individual Values (Vol. 3rd ed). New Haven, Conn: Yale University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=470436