Consider the following 2-person sequential move game with Guo Chen and Nathan. Guo Chen moves first and either chooses TOP or BOTTOM. Nathan gets to see Guo Chen's choice and then responds with either LEFT or RIGHT. The game ends after Nathan's choice. If Guo Chen chooses TOP and Nathan chooses LEFT, then Guo Chen gets $8 and Nathan gets $2. If Guo Chen chooses TOP and Nathan chooses RIGHT, then Guo Chen gets $0 and Nathan gets $0. If Guo Chen chooses BOTTOM and Nathan chooses LEFT, then Guo Chen gets $A and Nathan gets $B. If Guo Chen chooses BOTTOM and Nathan chooses RIGHT, then Guo Chen gets $5 and Nathan gets $4. Assuming that players are payoff maximizers, which of the following must be true for {TOP, LEFT} to be the subgame perfect equilibrium using backward induction? A) a. $B $4; $A $4; $A $8. C) $B $5. D) $B

Question

Consider the following 2-person sequential move game with Guo Chen and Nathan. Guo Chen moves first and either chooses TOP or BOTTOM. Nathan gets to see Guo Chen's choice and then responds with either LEFT or RIGHT. The game ends after Nathan's choice. If Guo Chen chooses TOP and Nathan chooses LEFT, then Guo Chen gets $8 and Nathan gets $2. If Guo Chen chooses TOP and Nathan chooses RIGHT, then Guo Chen gets $0 and Nathan gets $0. If Guo Chen chooses BOTTOM and Nathan chooses LEFT, then Guo Chen gets $A and Nathan gets $B. If Guo Chen chooses BOTTOM and Nathan chooses RIGHT, then Guo Chen gets $5 and Nathan gets $4. Assuming that players are payoff maximizers, which of the following must be true for {TOP, LEFT} to be the subgame perfect equilibrium using backward induction? A) a. $B > $4; $A < $8. B) $B > $4; $A > $8. C) $B < $4; $A > $5. D) $B < $4; $A < $5.

Quizplus · Accepted Answer

For {TOP, LEFT} to be the subgame perfect equilibrium, choosing TOP must be Guo Chen's best response to Nathan's best response. Nathan will choose LEFT over RIGHT in the TOP branch if his payoff is higher, which is given. For Nathan to choose RIGHT when Guo Chen chooses BOTTOM, it must be that $B < $4. However, for Guo Chen to prefer TOP over BOTTOM initially, assuming Nathan's rational response, Guo Chen's payoff from BOTTOM and LEFT ($A) must be less than from TOP and LEFT ($8), hence $A < $8. Therefore, the conditions are $B < $4 and $A < $8, which is not directly listed, indicating a mistake in the interpretation of the choices. Correcting this oversight, the logic intended to convey is that for Guo Chen to choose TOP, his payoff from the BOTTOM path must be less attractive compared to the TOP path, which is accurately reflected in choice A, where it's implied that Nathan's preference affects Guo Chen's strategy, leading to the need for a correction in the explanation. The correct interpretation should focus on ensuring Nathan's choice aligns with the equilibrium path, which involves comparing payoffs in a way that wasn't accurately captured in the initial response.

Consider the Following 2-Person Sequential Move Game with Guo Chen