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# Game Theory and Its Applications

2019/2020
Учебный год
ENG
Обучение ведется на английском языке
6
Кредиты
Статус:
Курс обязательный
Когда читается:
3-й курс, 1, 2 модуль

#### Преподаватели

Гриних Александра Леонидовна

Косян Давид Агаикович

Панкратова Ярославна Борисовна

### Course Syllabus

#### Abstract

Game theory is a framework for hypothetical social situations among competing players. In some respects, game theory is the science of strategy, or at least the optimal decision-making of independent and competing actors in a strategic setting. The key pioneers of game theory were mathematicians John von Neumann and John Nash, as well as economist Oskar Morgenstern. This course is aimed at students, researchers, and practitioners who wish to understand more about strategic interactions. You must be comfortable with mathematical thinking and rigorous arguments. Relatively little specific math is required; but you should be familiar with basic probability theory (for example, you should know what a conditional probability is), and some very light calculus would be helpful. Topics: 1. Basic concepts of game theory. Classification and description of games 2. Static noncooperative games 3. Dynamic games with perfect and imperfect information 4. Repeated games 5. Cooperative games 6. Matching, Social rules, Voting rules 7. Bankruptcy problem, Auctions

#### Learning Objectives

• The goals of mastering the discipline "Game Theory" are to familiarize student managers with the basic concepts of the theory of non-cooperative games, with a focus on the Nash equilibrium apparatus, the formation of theoretical analysis skills by solving problems and analyzing real or stylized situations.

#### Expected Learning Outcomes

• Is able to classify different types of games, to find a solution of a game
• Can find Pareto optimum and Nash Equilibrium in pure and in mixed strategies
• Can sind a solution in dynamic games with perfect and imperfect information
• Is able to find a solution of finitely or infinitely repeated game
• Can define a coalition value function, Shapely value and find a core
• Can use Gale-Shapely algorithm, know Impossibility Theorem and Condorset paradox
• Knows the basics of mechanism design

#### Course Contents

• Basic concepts of game theory. Classification and description of games
Definition of a game Types of games Solution of a game
• Static noncooperative games
Finite games in normal form. Pareto optimality. Strategy. Best Response. Nash Equilibrium in pure strategies Zero-sum games. Saddle point. Value of a game. Infinite extension of finite game. Nash Equilibrium in mixed strategies.
• Dynamic games with perfect and imperfect information
Finite game in extensive form. Subgame. Subgame perfect Nash equilibrium. Information sets. Games with imperfect information.
• Repeated games
Games repeated finitely. Games repeated infinitely. Discounting. The Folk Theorem
• Cooperative games
Cooperative game. Coalition. Coalition value function Symmetric players. Dummy players. Summation and splitting of games. Shapely value. Core Majority games. Veto players. Null players. Shapely-Shubik index
• Matching, Social rules, Voting rules
Matching. Stable matching system. Gale-Shapely algorithm Social rules. Condorset paradox. Imposibility Theorem. Voting rules.
• Bankruptcy problem, Auctions
Auctions. Mechanism design. Bankruptcy problem.

• Test 1
• Quiz 1
• Quiz 2
• Test 2
• Activity
• Exam

#### Interim Assessment

• Interim assessment (2 module)
0.06 * Activity + 0.4 * Exam + 0.12 * Quiz 1 + 0.12 * Quiz 2 + 0.15 * Test 1 + 0.15 * Test 2