Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
An introduction to game theory, focusing on strategic and extensive games. It covers concepts such as domination, iteration, Nash equilibria, and repeated games. The document also mentions the Nim game and its modeling as a strategic game and on a graph.
Typology: Slides
1 / 214
This page cannot be seen from the preview
Don't miss anything!
Tutorial on Basic Game Theory
Patricia Bouyer
LSV, CNRS & ENS Paris-Saclay Universit´e Paris-Saclay, Cachan, France
Thanks to: my co-authors Nicolas Markey, Romain Brenguier, Michael Ummels, Nathan Thomasset St´ephane Le Roux for recent discussions on the subject Thomas Brihaye for some of the slides
Import game theory solutions to the verification field Lift reasoning based on two-player zero-sum games to multiplayer games
Import game theory solutions to the verification field Lift reasoning based on two-player zero-sum games to multiplayer games
two-player zero-sum games multiplayer non-zero-sum games winning objective payoff function winning strategy equilibria (various kinds) von Neumann Theorem Nash Theorem ... ...
Give basics of game theory Discuss aspects that will be helpful for analyzing models useful for verification
1 What is a game? Games we play for fun A broader sense to the notion of game
(^2) Strategic games – Playing only once simultaneously (Strict) Domination and Iteration Stability: Nash equilibria
(^3) Extensive games – Playing several times sequentially
(^4) Repeated games – Playing the same game again and again
(^5) Conclusion
Number of players: 1 or 2 or 3 or... 1 ; Pacman, Candy Crush, Freecel... 2 ; Chess, Tennis, Stratego, Four in a row, ... 3 (or more) ; Poker, Monopoly,...
Type of interactions: simultaneous or sequential
Maximal length of a play: finite ou infinite
Type of information: perfect or imperfect
Presence of randomness: deterministic or probabilistic
Type of payoff: boolean or quantitative
Number of players: 1 or 2 or 3 or...
Type of interactions: simultaneous or sequential
Maximal length of a play: finite ou infinite finite ; Four in a row, Battleship,... infinite ; Tennis, Monopoly,...
Type of information: perfect or imperfect
Presence of randomness: deterministic or probabilistic
Type of payoff: boolean or quantitative
Number of players: 1 or 2 or 3 or...
Type of interactions: simultaneous or sequential
Maximal length of a play: finite ou infinite
Type of information: perfect or imperfect perfect ; Four in a row, Chess,... imperfect ; Battleship, Poker, Stratego...
Presence of randomness: deterministic or probabilistic
Type of payoff: boolean or quantitative
Number of players: 1 or 2 or 3 or...
Type of interactions: simultaneous or sequential
Maximal length of a play: finite ou infinite
Type of information: perfect or imperfect
Presence of randomness: deterministic or probabilistic
Type of payoff: boolean or quantitative boolean ; Four in a row, Chess,... quantitative ; Poker,...
Number of players: 1 or 2 or 3 or...
Type of interactions: simultaneous or sequential
Maximal length of a play: finite ou infinite
Type of information: perfect or imperfect
Presence of randomness: deterministic or probabilistic
Type of payoff: boolean or quantitative
[MSZ13] Maschler, Solan, Zamir. Game theory (Cambridge University Press)
Goal: Model and analyze (using mathematical tools) situations of interactive decision making
[MSZ13] Maschler, Solan, Zamir. Game theory (Cambridge University Press)
Goal: Model and analyze (using mathematical tools) situations of interactive decision making
Several decision makers (called players) All with different goals The decision of each players impacts the outcome for all
[MSZ13] Maschler, Solan, Zamir. Game theory (Cambridge University Press)
Goal: Model and analyze (using mathematical tools) situations of interactive decision making
Several decision makers (called players) All with different goals The decision of each players impacts the outcome for all
[MSZ13] Maschler, Solan, Zamir. Game theory (Cambridge University Press)
Goal: Model and analyze (using mathematical tools) situations of interactive decision making
Several decision makers (called players) All with different goals The decision of each players impacts the outcome for all
