What is game theoryGame theory attempts to mathematically

capture behaviour in strategic situations, in which an individual's success in making choices depends on the choices of others.

Where’s it used?Applied mathematicsSocial sciences such as:

EconomicsPolitical PsychologyComputer Science (to understand A.I.)Philosophy

Basic ConceptsGame: 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)

• 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.

Extensive and NormalExtensive: 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.

Types of GameOne-person: games such as solitaire, the only

interest is that of the player.2-person: games like chess of backgammonZero-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:

An exampleGame 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-leftCC: centreLR: lower right etc..

UL

CL CC

URUC

LRLL LC

CR

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

It would look like this:

O

X OX

O X

O X

A tie!

The End.

By Ben and Antony.