Consider the extensive form game of complete and imperfect i

Consider the extensive form game of complete and imperfect information above. The following strategy profiles are Subgame Perfect Nash Equilibrium (Select all that apply)

(ZX, AD)

(ZY, BC)

(ZX, BC)

(ZY, BD)

(WY, AC)

please explain

(WY, AD)

Solution

Strategy set

Player 1

S1 =(W, Z) *(X, Y) = [ WX, WY, ZX, ZY]

S2 =(A, B)*(C, D) = (AC, AD, BC, BD)

Using backward induction

Suppose the player 1 has chosen W and Player 2 has chosen A. The player 1 will choose Y given player 2 chooses A and player will choose X given player 2 has chosen B. Looking at his player 2 will always choose B .

Given player 1 chooses Z at stage 1 player 2 will always choose C the one with higher payoff.

Looking at this the player 1 will choose Z.

So the SPNE is (ZX, BC)

So the correct answer is C.