1. Introduction to Game Theory Kamal Aboul-Hosn Cornell University Computers Playing Games

2. A sequence of moves from a starting position made by player(s) until a win, loss, or draw Can represent every game as a tree Label each node with a player Arrows indicate possible moves Payoffs at the leaf nodes Game Trees

3. Choose “Heads” or “Tails” Flip a coin If you chose correctly, you win A Simple Game

4. Guarantee the “least-worst” payoff Start from the last nodes in the tree Your nodes: Choose the best Other players’ nodes: Chose the worst Continue back to the beginning of the tree Strategy from Game Trees

5. Finding a Strategy 0 0 0 11

6. How do people still win games that are fair? Game trees can be huge Impossible for a person to remember all possible moves People play on “intuition” Winning Fair Games?

7. Very simple game 31,896 possible games! Tic Tac Toe

8. Mega Tic Tac Toe: http://pnahay.home.sprynet.com/games/M egaTTT.htm Select “Tic-Tac-Toe (3x3, Win=3)” from “Preset Game” Uncheck “Force Computer...Randomly” Experiment with Search Depth A Game Experiment