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

Player1

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