Game Theory - Or How To Make an Offer Your Opponent Can't Refuse 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, ? 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 u i is a payoff function that represents player i's preferences ->What does that mean?

Examples

Coordination Game (cooperative) Player 2 Player1Player1

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 [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