Find the Nash Equilibrium/ Equilibria of the game below (the first payoff is for player 1): Player 2 Player 1 Left RightUp (30, 40) (25, 30)Down (60, 10) (35, 45) Group of answer choices(Up, Right)(Up, Left)(Down, Right)(Down, Left)None of the other answers are correct
Question
Find the Nash Equilibrium/ Equilibria of the game below (the first payoff is for player 1): Player 2 Player 1 Left RightUp (30, 40) (25, 30)Down (60, 10) (35, 45) Group of answer choices(Up, Right)(Up, Left)(Down, Right)(Down, Left)None of the other answers are correct
Solution
The Nash Equilibrium of a game is a set of strategies, one for each player, such that no player has incentive to unilaterally change her action given the other players' actions.
Let's find the Nash Equilibria for this game:
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Look at Player 1's payoffs to see if they have a dominant strategy. If Player 2 chooses Left, Player 1 gets 30 if they choose Up and 60 if they choose Down. If Player 2 chooses Right, Player 1 gets 25 if they choose Up and 35 if they choose Down. So, Player 1 would prefer to play Down regardless of what Player 2 does.
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Now look at Player 2's payoffs to see if they have a dominant strategy. If Player 1 chooses Up, Player 2 gets 40 if they choose Left and 30 if they choose Right. If Player 1 chooses Down, Player 2 gets 10 if they choose Left and 45 if they choose Right. So, Player 2 would prefer to play Left if Player 1 chooses Up and Right if Player 1 chooses Down.
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Now we look for Nash Equilibria. These are strategy profiles where no player wants to deviate given what the other player is doing. We have two potential Nash Equilibria: (Down, Left) and (Down, Right).
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Check if these are indeed Nash Equilibria. If Player 1 is playing Down and Player 2 is playing Left, Player 1 does not want to deviate (they get 60 instead of 30) but Player 2 would want to deviate (they get 10 instead of 45). So, (Down, Left) is not a Nash Equilibrium. If Player 1 is playing Down and Player 2 is playing Right, neither player wants to deviate (Player 1 gets 35 instead of 25 and Player 2 gets 45 instead of 10). So, (Down, Right) is a Nash Equilibrium.
So, the Nash Equilibrium of this game is (Down, Right).
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