Find SPNE?
My suggestion is $\{(AW,L,Y), (BU, L,Y), (BD,R,Y)\}$
How to find :
firstly, I consider the first subgame where P3 and P1 play. And I choose (W,Z)
Secondly, I consider the second subgame where P1 and P2 play. And I choose (U,L) and ( D,R).
Thirdly I consider 2 cases. In the first one Player one chooses both A and B for the 1st subgame. And player one chooses only B for the second subgame.
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But I am not sure about my solution. I am confused since there are 3 players