Game Theory Don’t hate the game...hate the player.

1. Game TheoryDon’t hate the game...hate the player.

3. What is game theory Game theory attempts to mathematically capture behaviour in strategic situations, in which an individual's success in making choices depends on the choices of others.

4. Where’s it used? • Applied mathematics • Social sciences such as: • Economics • Political Psychology • Computer Science (to understand A.I.) • Philosophy

5. Basic Concepts • Game: a particular sort of conflict in which n players participate. • Move: when the game progresses (e.g. the roll of a dice) • Payoff/outcome: what happens at the end (e.g. the winnings at the end of a round of poker)

6. A strategy is the set of best choices for a player for an entire game. It is an overlying plan that cannot be upset by occurrences in the game itself.

7. Extensive and Normal • Extensive: a set of rules and the player’s strategy determines what they do at each stage. Examples are noughts and crosses or chess. • Normal: a way of representing a game so calculations can be done on it.

8. Types of Game • One-person: games such as solitaire, the only interest is that of the player. • 2-person: games like chess of backgammon • Zero-sum games: where the payoff is exactly the same as the sum of all loses. Any n-person non-zero-sum game can be reduced to an n + 1 zero-sum game • The Game:

9. An example Game theory can be applied to many games. A simple game is Noughts and Crosses. If we start by labelling every box as follows. UL: upper-left CC: centre LR: lower right etc.. UL UC UR CL CC CR LC LL LR

10. We can use the notation to use XUL to signify a game position where X has been placed in the upper-left box. A game might progress as follows: XUL-OUR-XCC-OCR-XLC-OLL-XCL-OUC

11. It would look like this: A tie! X O O X X O O X

12. The End. By Ben and Antony.