Consider a simultaneous-move game with two players. The payoff table with order of payoffs (Player 1, Player 2) is provided above. Choose the statement that is consistent with it.

Question

BlackTom AI · Accepted Answer

Question restatement: In a simultaneous-move 2x2 game, identify which statements about Nash equilibria in pure strategies are consistent with the given payoff table. Options: a) Down and Left constitute Nash Equilibrium. b) Down and Right constitute Nash Equilibrium. c) Top and Right constitute Nash Equilibrium. d) There is no Nash Equilibrium in pure strategies.

Option a: Down and Left constitute Nash Equilibrium. To check if (Down, Left) is a Nash equilibrium, each player must be playing a best response to the other. If Player 2 plays Left, Player 1’s payoffs are Top=20 and Down=16, so the best response for Player 1 is Top, not Down. Therefore Down is not a best response to Left, so (Down, Left) is not a Nash equilibrium. This option is inconsistent with the payoff structure.

Option b: Down and Right constitute Nash Equilibrium. If Player 2 plays Right, Player 1’s payoffs are Top=18 and Down=19, so the best response for Player 1 is Down (not Top). So Down is a best response to Right. Now, if Player 1 plays Down, Player 2’s payoffs are Left=17 and Right=16, so the best response for Player 2 is Left (not Right). Therefore Right is not a best response to Down, and (Down, Right) is not a Nash equilibrium. This option is inconsistent with the best-response pattern.

Option c: Top and Right constitute Nash Equilibrium. If Player 2 plays Right, Player 1’s best response is Down (as just noted), not Top. Hence Top is not a best response to Right, so (Top, Right) cannot be a Nash equilibrium. This option is incorrect given the payoffs.

Option d: There is no Nash Equilibrium in pure strategies. Based on the best-response analyses above, no cell in the 2x2 payoff matrix satisfies both players playing a best response to the other at the same time. Player 1’s best responses depend on Player 2’s action, and Player 2’s best responses depend on Player 1’s action, and these do not align in any single outcome. Therefore, this option accurately reflects the absence of a pure-strategy Nash equilibrium in the given game.

SESS0007_24-25 LSA Test

Consider a simultaneous-move game with two players. The payoff table with order of payoffs (Player 1, Player 2) is provided above. Choose the statement that is consistent with it.

查看解析

登录即可查看完整答案

类似问题

The advertising agency raises its prices, causing a firm that chooses to run ads to earn $200 less in profits. Once the firms adjust to the higher advertising prices, what is the total combined profit of the two firms in the new Nash equilibrium?

Consider a matrix form game between two players, A and B. Player A can choose between Up and Down, and Player B can choose between Left and Right. If the payoffs are represented using this matrix, what is the pure Nash equilibrium?

In the following duopoly game, the two firms can either set the price of their product high or low. For each firm, the final profit depends on the price they set as well as the price the other firm sets. The game is represented in the table below. The Nash equilibrium for this game is for:

Consider a sequential-move game with two players. The game tree with order of payoffs (Player 1, Player 2) is provided above. Choose the answer that is consistent with it.

Consider the payoff matrix below. Which is correct for the following payoff matrix? Player 2 A B C Player 1 A (3,2) (3,1) (2,2) B (1,3) (2,2) (0,2) C (5,1) (8,1) (1,7)

Which pure strategy profiles are Nash equilibria? Select all that apply.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单