Conflict and Cooperation

2024/2025

Учебный год

ENG

Обучение ведется на английском языке

4

Кредиты

Кто читает:

Департамент математики

Статус:

Курс по выбору

Когда читается:

4-й курс, 3 модуль

Преподаватель

Сандомирская Марина Сергеевна

Course Syllabus

Abstract

This course presents a game-theoretic, strategic approach to modeling situations in which agents are involved in joint activities and collective decision-making. Although cooperation often provides more attractive outcomes overall, the participants in the interaction then face the problem of a fair division of the final utility. The course critically examines various concepts of divisions, with an emphasis on the logical foundations of each of them, understanding the class of real problems and their mathematical formalization, the advantages and disadvantages of each approach. The central idea of ​​the course is to learn to see and implement various opportunities for compromise within groups of agents who have individual preferences but are interested in implementing a collective outcome acceptable to all. The course also examines the main models of voting and social choice.

Learning Objectives

• To familiarize students with the concepts, models and statements of the cooperative games in application to the theory of conflict.
• To introduce the basic notions of social choice theory.

Expected Learning Outcomes

• A student should formalize cooperative games using coalitional function and should distinguish the well-known classes of cooperative games.
• A student should learn the foundations and main concepts in social choice theory and should apply them to conflict resolution
• A student should determine the relevant solution concept for a given cooperative game, calculate the solution and interpret the result.
• A student should incorporate the network structure among participants into the cooperative game, choose and realize the proper solution

Course Contents

• Cooperative games with transferable utility and their interpretation
• Main solution concepts for cooperative games, their properties and axiomatic characterization.
• Cooperative games with limited cooperation and their solutions
• Solution Concepts in Social choice models.

Assessment Elements

• Homework 1
• Homework 2
• Exam

Interim Assessment

• 2024/2025 3rd module
  0.5 * Exam + 0.25 * Homework 1 + 0.25 * Homework 2

Bibliography

Recommended Core Bibliography

• Aleskerov, F., & Subochev, A. (2016). Matrix-vector representation of various solution concepts.
• 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
• Game theory, Maschler, M., 2013
• Roger B. Myerson. (1977). Graphs and Cooperation in Games. Mathematics of Operations Research, (3), 225. https://doi.org/10.1287/moor.2.3.225
• Zamir, S., Solan, E., & Maschler, M. (2013). Game Theory. Cambridge: Cambridge eText. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=527892

Recommended Additional Bibliography

• Bezalel Peleg, & Peter Sudhölter. (2007). Introduction to the Theory of Cooperative Games. Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.spr.thdlic.978.3.540.72945.7

Authors

• Sandomirskaia MARINA SERGEEVNA