Finding Nash Equilibria directly from the extensive form/game tree How can you find the Nash equilibrium of a game directly from the extensive form game/game tree of a game. You can find Nash equilibria from the strategic form (normal form table), but finding it directly from the extensive form seems very interesting as well. A position/strategy profile is a Nash equilibrium if it is a best response to other strategies of the other players. (The photo is in the link). Thank you.
How can we do this for the 3 player game tree below:enter image description here
 A: It's a bit tedious to describe, but with enough practice, you should be able to follow the steps below to quickly identify NEs (not only the subgame perfect ones) from a game tree. 
The idea is that you first suppose player 1 plays a certain strategy. Then you find out the best responses of the other players. Lastly you check whether the initially supposed strategy for player 1 is a best response to the other players' best responses (to it). If it is, you have a profile of mutually best responding strategies, hence a NE; if it isn't, then you don't have any NE with the initially supposed strategy of player 1. 


*

*Suppose player 1 plays $A$


*

*Player 2's best response to $A$ is $w$ and player 3's best response to $A$ is both $S$ and $T$  


*

*Suppose player 3 plays $S$  


*

*Player 1's best response to $(w,S)$ is $A$, same as the initial supposition. NE: $(A,w,S)$


*Suppose instead player 3 plays $T$ 


*

*Player 1's best response to $(w,T)$ is $C$, not $A$. No NE.




*Suppose player 1 plays $B$


*

*Player 2's best response to $B$ is $\{u,v,w\}$ and player 3's best response to $B$ is $\{S,T\}$

*Check whether $B$ is a best response to each of $\{(u,S),(u,T),(v,S),(v,T),(w,S),(w,T)\}$. If it is, we have a NE; if not, we don't.

*We can verify that only $(B,v,S)$ is a NE 


*Suppose player 1 plays $C$ 


*

*Player 2's best response to $C$ is $\{u,v,w\}$ and player 3's best response to $C$ is $S$

*Check whether $C$ is a best response to each of $\{(u,S),(v,S),(w,S)\}$. If it is, we have a NE; if not, we don't.

*Only NE is $(C,v,S)$. 



Overall, there are three NEs: $(A,w,S)$, $(B,v,S)$, $(C,v,S)$, with the first being the only SPE. 
