Consider the following game in which Sally can play T or B and John chooses between L or R. Each player makes their choice simultaneously. If Sally chooses T and John chooses L, Sally gets a payoff of 3 and John has a payoff of 7. If Sally plays T and John R, Sally’s payoff is 5 and John gets 1. If Sally Chooses B and John L, the payoffs are 1 to Sally and 2 to John. Finally, if Sally chooses B and John R, the payoffs are 4 to Sally and 3 to John. What are the Nash equilibria of the game?Group of answer choices(T,L) and (B,R)(T,L)(B,R)None of the other answers are correct.(T, R)
Question
Consider the following game in which Sally can play T or B and John chooses between L or R. Each player makes their choice simultaneously. If Sally chooses T and John chooses L, Sally gets a payoff of 3 and John has a payoff of 7. If Sally plays T and John R, Sally’s payoff is 5 and John gets 1. If Sally Chooses B and John L, the payoffs are 1 to Sally and 2 to John. Finally, if Sally chooses B and John R, the payoffs are 4 to Sally and 3 to John. What are the Nash equilibria of the game?Group of answer choices(T,L) and (B,R)(T,L)(B,R)None of the other answers are correct.(T, R)
Solution
The Nash equilibria of the game are (T,L) and (B,R).
Here's why:
A Nash equilibrium occurs when no player can improve their payoff by unilaterally changing their strategy, given the other player's strategy.
If Sally chooses T and John chooses L, neither player can improve their payoff by changing their strategy. So, (T,L) is a Nash equilibrium.
Similarly, if Sally chooses B and John chooses R, neither player can improve their payoff by changing their strategy. So, (B,R) is also a Nash equilibrium.
Therefore, the game has two Nash equilibria: (T,L) and (B,R).
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