Game Theory Or How To Make an Offer Your Opponent Can't Refuse
17.02.2009
Jouni Laitinen
Content
A really brief Introduction
Brief history & important theorists
Two main types of games
Examples
References
A Really Brief Introduction
Definition:
“The analysis of a situation involving conflicting interests (as in
business or military strategy) in terms of gains and losses among
opposing players."(Merriam-Webster)
"People will always do what is best for them"
Eight theorists have won Nobel Prizes in Economics.
What can you do with it:
You can show that players don't have dominant strategies in Rock
paper scissors.
History [4]
1713: James Waldegrave's minimax mixed strategy solution to
le Her
1838: Antoine Augustin Cournot's Recherches sur les principes
mathématiques de la théorie des richesses
John Von Neumann[3]
December 28, 1903 – February 8, 1957
Contributions to science
1928: Zur Theorie der Gesellschaftsspiele
1944: Theory of Games and Economic Behavior
John Forbes Nash Jr. [2]
June 13, 1928 - ?
Carnegie Institute of Technology -> Princeton
->Rand Corporation
1950: Non-cooperative Games
1950: Equilibrium Points in N-person Games
-> Nash Equilibrium
1994: Nobel Prize in Economics
Different Types of Games
Definitions
What is a Game [1]?
-A set of players
-For each player, a set of actions
-For each player, preferences over the set of action profiles
2 main types of games [6]
Cooperative games
-Binding agreements are possible
Players work together to maximize their profits
->"How to divide among individuals what they can earn by
cooperating together?"
Example: the Coordination game
Non-cooperative games
Binding agreements are not possible
-Cooperation must enforce itself.
->"How will rational players behave?"
Example: Ice cream game[6]
Nash Equilibrium
Developed in 1950 by John Nash
Definition[1]:
ui(a*) ≥ui(ai,a*-1) for every action ai of player i,
where ui is a payoff function that represents player i's preferences
->What does that mean?
http://www.youtube.com/watch?v=CWtM5pZzZIU#t=2m00s
Examples
Coordination Game
(cooperative)
Player 2
P
l
a
y
e
r
1
Prisoner's Dilemma [1]
P1/P2
Quiet
Frink
Quiet
Frink
Tit for Tat[1]
=Repeated Prisoner's
Dilemma
-Simple strategy:
cooperate/retaliate/
forgive
Used in Bittorrent to optimize download speeds.
Rock Paper Scissors
P1/P2
Rock
Paper
Scissors
Rock
Paper
Scissors
Ice Cream Game (noncooperative)[6]
Game Theory & IT
Mainly used in AI
Algorithmic game theory
- e.g. Routing algorithms
Simple Channel-Change Games for Spectrum-Agile Wireless Networks[5]
Simple Channel-Change Games...
"Simple Channel-Change Games for Spectrum Agile Wireless Networks"
Roli G. Wendorf and Howard Blum, Proceedings of Student/Faculty Research Day,
CSIS, Pace University, May 5th, 2006
Game Theory in University of Jyväskylä
Maria Dementieva: Regularization in Multistage
Cooperative Games. (2004)
Yulia Pavlova:Multistage Coalition Formation Game of a
Selfenforcing International Environment Agreement. (2008)
TIEJ599 Game Theory and Applications
TIEJ633 SC2: Game Theory (JSS18)
What have we learned from this presentation?
Game Theory :
Deals with strategic decisions made by rational players.
Can be used in various scenarios to analyze different
moves to determine the best possible outcome.
Might be hard to learn thanks to the difficult notation
Questions
Because game theory assumes that players act rationally, can
it be used to analyze human interaction?
Altruism in game theory?
(e.g.playing a non-NE move to influence your opponent’s
future games)
References
[1]"An Introduction to Game Theory" Orsborne, M, 2004, Oxford University Press
[2]John Nash http://www.princeton.edu/mudd/news/faq/topics/nash.shtml
[3]Wikipedia article on John Von Neumann
[4] Game Theory For Wireless Engineers, Allen Mackenzie et al,2006
[5]"Simple Channel-Change Games for Spectrum Agile Wireless
Networks",Wendorf, R.G.; Blum, H.
[6] “TIEJ633 SC2: Game Theory” course material, Rene van den Brink, 2008