what is game theory game theory attempts to mathematically capture behaviour in strategic...
TRANSCRIPT
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.