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Consider a pricing game between Coles and Woolworths. Each firm simultaneously chooses whether to price High or Low. If both firms price Low, the payoffs are 8 to Coles and 2 to Woolworths. If both firms choose High, the payoffs are 3 to Coles and 7 to Woolworths. If Coles opts for Low and Woolworths High, Coles gets 5 and Woolworths 4. Finally, if Coles plays High and Woolworths Low, Coles gets 7 and Woolworths receives a payoff of 6. Which statement is true?Group of answer choicesthe outcome of the game is (Low, High), where Coles if playing the first strategy Low and Woolworths High; this game is a prisoners’ dilemmathe outcome of the game is (High, Low); this game is a prisoners’ dilemmathe outcome of the game is (Low, Low); this game is not a prisoners’ dilemmathe outcome of the game is (High, High); this game is a prisoners’ dilemmathe outcome of the game is (High, High); this game is not a prisoners’ dilemma

Question

Consider a pricing game between Coles and Woolworths. Each firm simultaneously chooses whether to price High or Low. If both firms price Low, the payoffs are 8 to Coles and 2 to Woolworths. If both firms choose High, the payoffs are 3 to Coles and 7 to Woolworths. If Coles opts for Low and Woolworths High, Coles gets 5 and Woolworths 4. Finally, if Coles plays High and Woolworths Low, Coles gets 7 and Woolworths receives a payoff of 6. Which statement is true?Group of answer choicesthe outcome of the game is (Low, High), where Coles if playing the first strategy Low and Woolworths High; this game is a prisoners’ dilemmathe outcome of the game is (High, Low); this game is a prisoners’ dilemmathe outcome of the game is (Low, Low); this game is not a prisoners’ dilemmathe outcome of the game is (High, High); this game is a prisoners’ dilemmathe outcome of the game is (High, High); this game is not a prisoners’ dilemma

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Solution 1

In this game, let's analyze the payoffs for Coles:

  1. If Woolworths chooses High, Coles gets 5 by choosing Low and 3 by choosing High. So, in this case, Low is the best choice for Coles.

  2. If Woolworths chooses Low, Coles gets 8 by choosing Low and 7 by choosing High. So, in this case, Low is also the best choice for Coles.

In both scenarios, Coles gets a higher payoff by choosing Low, regardless of what Woolworths does.

Now, let's analyze the payoffs for Woolworths:

  1. If Coles chooses High, Woolworths gets 6 by choosing Low and 7 by choosing High. So, in this case, High is the best choice for Woolworths.

  2. If Coles chooses Low, Woolworths gets 2 by choosing Low and 4 by choosing High. So, in this case, High is also the best choice for Woolworths.

In both scenarios, Woolworths gets a higher payoff by choosing High, regardless of what Coles does.

So, the outcome of the game is (Low, High), with Coles choosing Low and Woolworths choosing High.

However, this game is not a prisoners' dilemma because the outcome that results from each player choosing their dominant strategy (Low for Coles, High for Woolworths) does not result in a lower total payoff than if they could cooperate (for example, both choosing High or both choosing Low).

Therefore, the correct answer is "the outcome of the game is (Low, High), where Coles if playing the first strategy Low and Woolworths High; this game is not a prisoners’ dilemma".

This problem has been solved

Solution 2

The correct answer is:

The outcome of the game is (High, High); this game is not a prisoners’ dilemma

Here's why:

  1. The outcome of the game is (Low, High), where Coles if playing the first strategy Low and Woolworths High; this game is a prisoners’ dilemma: This is incorrect. If Coles chooses Low and Woolworths chooses High, Coles gets 5 and Woolworths gets 4. However, if Coles chooses High and Woolworths chooses Low, Coles gets 7 and Woolworths gets 6, which is a better outcome for both.

  2. The outcome of the game is (High, Low); this game is a prisoners’ dilemma: This is also incorrect. If Coles chooses High and Woolworths chooses Low, Coles gets 7 and Woolworths gets 6. However, if both firms choose High, Coles gets 3 and Woolworths gets 7, which is a better outcome for Woolworths.

  3. The outcome of the game is (Low, Low); this game is not a prisoners’ dilemma: This is incorrect. If both firms choose Low, Coles gets 8 and Woolworths gets 2. However, if Coles chooses High and Woolworths chooses Low, Coles gets 7 and Woolworths gets 6, which is a better outcome for Woolworths.

  4. The outcome of the game is (High, High); this game is a prisoners’ dilemma: This is incorrect. In a prisoners' dilemma, each player's dominant strategy leads to a less optimal outcome for both. However, in this game, the (High, High) outcome is not less optimal for both firms.

  5. The outcome of the game is (High, High); this game is not a prisoners’ dilemma: This is correct. If both firms choose High, Coles gets 3 and Woolworths gets 7. This is not a prisoners' dilemma because the (High, High) outcome is not less optimal for both firms.

This problem has been solved

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