题目
COMP90054_2025_SM1 Practice Quiz: Extensive-form games (not assessed)
多重下拉选择题
Consider the following abstract game consisting of three players. The numbers in the nodes refer to the player number: Select the right answers for the following: What is the sub-game perfect equilibrium for sub-game 3: [ Select ] (3, 4, 3) (2, 1, 0) What is the sub-game perfect equilibrium for sub-game 2: [ Select ] (2, 1, 0) (3, 4, 3) (6, 2, 1) What is the sub-game perfect equilibrium for the entire game: [ Select ] (3, 4, 3) (5, 2, 3) (6, 3, 3) (2, 1, 0) (6, 2, 1)
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标准答案
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思路分析
We start by identifying the options available at each subgame and then apply backward induction to determine the sub-game perfect equilibrium (SPE).
Sub-game 3:
- At this subgame, player 3 selects between P and Q. The terminal payoffs are: P leads to (2, 1, 0) and Q leads to (3, 4, 3).
- Player 3 cares about the third component of the payoff, i.e., their own payoff. Here, P gives 0 to player 3, while Q gives 3 to player 3. Therefore, player 3 will choose Q, since 3 > 0.
- Consequently, the SPE outcome for sub-game 3 is the terminal corresponding to Q, namely (3, 4, 3).
Option analysis for sub-game 3:
- If you considered (3, 4, 3) as the result of sub-game 3, that aligns with the logic above and is the correct SPE for this subgame.
- If you considered......Login to view full explanation登录即可查看完整答案
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类似问题
Consider an extensive form game between two players, A and B, where Player A plays first and Player B plays last. Player A can choose between Up and Down, and Player B can choose between Left and Right. If the payoffs are represented using this tree, what is the subgame perfect Nash equilibrium?
Consider the following abstract extensive-form game of two players, 1 and 2, each with two available moves. Select the right answers for the following: What move will player 1 make: [ Select ] A B What move will player 2 make: [ Select ] D C What is the equilibrium of the sub-game starting at node 2(a): 10, 0 What is the equilibrium of the sub-game starting at node 2(b): [ Select ] 4, 9 8, 6 What is the equilibrium of the game starting at node 1: [ Select ] -1, -2 10, 0 8, 6 4, 9
Consider the following abstract game consisting of three players. The numbers in the nodes refer to the player number: Select the right answers for the following: What is the sub-game perfect equilibrium for sub-game 3: [ Select ] What is the sub-game perfect equilibrium for sub-game 2: [ Select ] What is the sub-game perfect equilibrium for the entire game: [ Select ]
Consider the following abstract extensive-form game of two players, 1 and 2, each with two available moves. Select the right answers for the following: What move will player 1 make: [ Select ] A B What move will player 2 make: [ Select ] D C What is the equilibrium of the sub-game starting at node 2(a): 10, 0 What is the equilibrium of the sub-game starting at node 2(b): [ Select ] 4, 9 8, 6 What is the equilibrium of the game starting at node 1: [ Select ] -1, -2 10, 0 8, 6 4, 9
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