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Course, academic year 2022/2023
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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 -
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.
Course completion requirements -
Last update: Mgr. Jan Kynčl, Ph.D. (31.05.2019)

Oral exam.

Literature - Czech
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: 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

 
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