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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.

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

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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)

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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.

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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.

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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:

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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 CLCC URUC LRLL LC CR

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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

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It would look like this: O XOX O X OX A tie!

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The End. By Ben and Antony.

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