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
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