Consider the following game. Player 1 has 3 actions (Top, middle,Bottom) and player 2 has three actions (Left, Middle, Right). Each player chooses their action simultaneously. The game is played only once. The first element of the payoff vector is player 1’s payoff. Note that one of the payoffs to player 2 has been omitted (denoted by x). Determine the range of values for x such that Player 2 has a strictly dominant strategy. Player 2 Left Middle Right Top (2.-1) (-2.3) (3.2) Middle (3.0) (3.3) (-1.2) Bottom (1.2) (-2.x) (2.3)
Consider the following game. Player 1 has 3 actions (Top, middle,Bottom) and player 2 has three actions (Left, Middle, Right). Each player chooses their action simultaneously. The game is played only once. The first element of the payoff vector is player 1’s payoff. Note that one of the payoffs to player 2 has been omitted (denoted by x). Determine the range of values for x such that Player 2 has a strictly dominant strategy. Player 2 Left Middle Right Top (2.-1) (-2.3) (3.2) Middle (3.0) (3.3) (-1.2) Bottom (1.2) (-2.x) (2.3)
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.1P
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Question 1
Consider the following game. Player 1 has 3 actions (Top, middle,Bottom) and player 2 has three actions (Left, Middle, Right). Each player chooses their action simultaneously. The game is played only once. The first element of the payoff vector is player 1’s payoff. Note that one of the payoffs to player 2 has been omitted (denoted by x).
- Determine the range of values for x such that Player 2 has a strictly dominant strategy.
Player 2 | ||||
Left | Middle | Right | ||
Top | (2.-1) | (-2.3) | (3.2) | |
Middle | (3.0) | (3.3) | (-1.2) | |
Bottom | (1.2) | (-2.x) | (2.3) |
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