1 / 26

Game Theory - Or How To Make an Offer Your Opponent Can't Refuse

This article provides a brief introduction to game theory, including a history of important theorists and the two main types of games. It also explains Nash equilibrium and provides examples of different types of games. The article concludes with a discussion of game theory's applications in various fields and raises questions about its applicability to human interaction.

loaiza
Download Presentation

Game Theory - Or How To Make an Offer Your Opponent Can't Refuse

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 17.02.2009 Jouni Laitinen Game Theory - Or How To Make an Offer Your Opponent Can't Refuse

  2. Content A really brief Introduction Brief history & important theorists Two main types of games Examples References

  3. 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.

  4. 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

  5. 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

  6. 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

  7. Different Types of Games

  8. 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]

  9. 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

  10. Non-cooperative games Binding agreements are not possible      -Cooperation must enforce itself.    ->"How will rational players behave?"       Example: Ice cream game[6]

  11. 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

  12. Examples

  13. Coordination Game (cooperative)                                    Player 2 P l a y e r 1

  14. Prisoner's Dilemma [1] P1/P2                        Quiet            Frink  Quiet Frink

  15. Tit for Tat[1] =Repeated Prisoner's   Dilemma -Simple  strategy:  cooperate/retaliate/ forgive Used in Bittorrent to optimize download speeds.

  16. Rock Paper Scissors  P1/P2                Rock        Paper             Scissors Rock Paper Scissors

  17. Ice Cream Game (noncooperative)[6]

  18. Game Theory & IT Mainly used in AI Algorithmic  game theory     - e.g. Routing algorithms Simple Channel-Change Games for Spectrum-Agile Wireless Networks[5]

  19. 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

  20. 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)  

  21. 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

  22. 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)

  23. 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

More Related