-Suppose that the game depicted in Figure 11.7 is modeled as a sequential move game with Player B moving first and the payoffs are (Player A, Player B). The subgame perfect equilibrium for this game is:
A) {B3 6 A3}
B) {B2 6 A1}
C) {B1 6 A3}
D) {B3 6 A2}
E) None of the above.

Question

-Suppose that the game depicted in Figure 11.7 is modeled as a sequential move game with Player B moving first and the payoffs are (Player A, Player B). The subgame perfect equilibrium for this game is:
A) {B3 6 A3} 
B) {B2 6 A1} 
C) {B1 6 A3} 
D) {B3 6 A2} 
E) None of the above.

Quizplus · Accepted Answer

In a sequential move game, the subgame perfect equilibrium is found by backward induction. Player B, moving first, will anticipate Player A's responses to each of his possible moves. Player A, aiming to maximize their payoff, will choose A3 if Player B chooses B1, because it gives Player A the highest payoff in response to B1. Knowing this, Player B will choose B1 to maximize their own payoff, leading to the equilibrium {B1 6 A3}.

-Suppose That the Game Depicted in Figure 11