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?Correct! 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 the outcome of the game is (High, Low); this game is a prisoners’ dilemma the outcome of the game is (Low, Low); this game is not a prisoners’ dilemma the outcome of the game is (High, High); this game is 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?Correct! 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 the outcome of the game is (High, Low); this game is a prisoners’ dilemma the outcome of the game is (Low, Low); this game is not a prisoners’ dilemma the outcome of the game is (High, High); this game is a prisoners’ dilemma
Solution
In game theory, a prisoner's dilemma is a situation where individual decision makers always have an incentive to choose in a way that creates a less than optimal outcome for the individuals as a group.
Let's analyze the options for Coles and Woolworths:
- 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.
- If Coles plays High and Woolworths Low, Coles gets 7 and Woolworths receives a payoff of 6.
From Coles' perspective, if Woolworths chooses High, Coles should choose Low to get a payoff of 5 instead of 3. If Woolworths chooses Low, Coles should still choose Low to get a payoff of 8 instead of 7. So, Coles' dominant strategy is to choose Low.
From Woolworths' perspective, if Coles chooses High, Woolworths should choose Low to get a payoff of 6 instead of 4. If Coles chooses Low, Woolworths should choose High to get a payoff of 7 instead of 2. So, Woolworths does not have a dominant strategy.
The outcome of the game is (Low, High), where Coles is playing the first strategy Low and Woolworths High. However, this game is not a prisoner's dilemma because Woolworths does not have a dominant strategy. In a prisoner's dilemma, both players have a dominant strategy that leads to an outcome that is worse for both compared to if they had cooperated.
So, the correct answer is "the outcome of the game is (Low, High), where Coles is playing the first strategy Low and Woolworths High; this game is not a prisoners’ dilemma".
Similar Questions
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