Modern Algoritmic Game Theory - NOPT021

• Title: Algoritmy moderní teorie her
• Guaranteed by: Department of Applied Mathematics (32-KAM)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2022
• Semester: winter
• E-Credits: 5
• Hours per week, examination: winter s.:2/2, C+Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• Virtual mobility / capacity: no
• State of the course: taught
• Language: Czech, English
• Teaching methods: full-time
• Additional information: http://Ústní zkouška. Požadavky k ústní zkoušce odvovídají sylabu.
• Guarantor: prof. RNDr. Martin Loebl, CSc.
• Class: Informatika Mgr. - Diskrétní modely a algoritmy
• Classification: Informatics > Optimalization

Annotation

English

Last update: doc. Mgr. Jan Hubička, Ph.D. (14.02.2022)

In this course, the students will learn the core concepts, models, theory and algorithms of modern and practical algorithmic game theory. During the practical part, they will gradually build the tools and codebase for implementing them in real games. At the end of the course, the students will have a working agent that converges to an optimal policy in Leduc poker and many other small games.

Czech

Last update: ()

Výklad základních matematických modelů a pojmů souvisejících s racionalním řešením konfliktních situací.

Course completion requirements

English

Last update: doc. Mgr. Jan Kynčl, Ph.D. (31.05.2019)

Oral exam.

Czech

Last update: doc. Mgr. Jan Kynčl, Ph.D. (31.05.2019)

Ústní zkouška.

Literature

Last update: T_KAM (20.04.2007)

G. Owen: Game Theory, London 1971 nebo kterékoliv pozdější vydání (or any later edition).

E. Mendelson: Introducing Game Theory and Its Applications,CRC Press LLC,ISBN 1-58488-300-6, 2004

M. Chobot, F. Turnovec, V. Ulašin: Teória hier a rozhodovania, Alfa Bratislava, 1991.

M. Maňas: Teorie her a její ekonomické aplikace, SPN Praha 1983 nebo pozdější vydání.

Requirements to the exam

Last update: doc. Mgr. Jan Kynčl, Ph.D. (31.05.2019)

Oral exam, requirements according to the sylabus of the lecture.

Syllabus

Last update: doc. Mgr. Jan Hubička, Ph.D. (14.02.2022)

Week 1

Course

• Matrix games formalism

• Best response

• Minimax policy, Nash equilibrium

• Zero sum games

Practice

• OpenSpiel

• Exploitability computation (i.e policy evaluation)

Week 2

Course

• Minimax theorem

• Minimax policy = Nash equilibrium

• Linear/convex optimization problem

Practice

• Linear programming for solving matrix games

Week 3 - Regret

Course

• Regret

• Folk’s theorem - connecting regret to exploitability

Practice

• Regret minimization in matrix games

• Average/current policy convergence

Week 4 - Sequential Decision Making

Course

• Extensive form games

• Factored observation games

Practice

• Small poker game

• Exploitability computation in extensive form games

Week 5 - Sequence Form

Course

• Sequence -> matrix = exponential explosion

• Sequence form

• Sequence LP

Practice

• Sequence LP

Week 6 - Counterfactual Regret Minimization

Course

• Counterfactual regret minimization

• CFR-BR

Practice

• CFR

Week 7 - Monte Carlo Methods

Course

• MCCFR

• Control variates

Practice

• MCCFR

• VR-MCCFR