Game Theory Denotation Easy to Understand

 

 

Some of my challenge learning game theory is the symbols or denotation of. It is hard to change certain situation from sentence to the "mathys" language. Here I sum up some of the important Denotation.

 

INGREDIENTS OF THE GAME	Denotations
Player -	i ,j (little) 1,2,3
Set Of Players	N
Actions	a
Action Profile (set of action of each player)	a = (ai…an)
Action of other player other than ' i ' (notice there is a minus sign)	a-1 = (a1, a2,…a_i,a +i, …an).
Action of all player ; i and everyone else	a = ( ai , a_i )
Utility or Pay-offs;   *Utility must be attached with action. So the symbol must come together	Ui ( ai , a_i) *I understand it just like function f(x)
SET of Strategy Strategies = A plan of action for a game/strategy profile (little s)	S s s = (s1,…,sn)
particular strategy of player i	si
Strategy of i and other than i	s = ( s , s_i) which is s_i = (s1, s2 ,..,s_i,s+i,…sn)

 

Important Note!

All problem have particular Timing and Information of the game. It is important on the strategy to answer the question.

Timing of the game can be;

Static: simultaneous actions in a single period

Dynamic: non-simultaneous action over different periods

Repeated: Simultaneous action over multiple.

 

Information of the game can be;

Incomplete information: Payoffs of other may be unknown

Imperfect Information: Actions (or history of) is unobserved