BHP and Rio simultaneously choose to set either a LOW or HIGH level of iron ore production. The payoffs are as follows. If both choose LOW, the payoffs are (30, 20) to BHP and Rio, respectively. If BHP chooses LOW and Rio HIGH, the payoffs are (35, 30). If BHP opts for HIGH and Rio LOW the payoffs are (40, 10). And, lastly, if BHP plays HIGH and Rio HIGH, the payoffs are (25, 20). Which statement is true?Group of answer choicesThe Nash equilibrium is (LOW, LOW), where the first strategy in the parentheses is BHP’s and the second Rio’s.The Nash equilibrium is (LOW, HIGH)The Nash equilibrium is (HIGH, LOW)The Nash equilibrium is (HIGH, HIGH)The Nash equilibria are (LOW, LOW) and (HIGH, HIGH)
Question
BHP and Rio simultaneously choose to set either a LOW or HIGH level of iron ore production. The payoffs are as follows. If both choose LOW, the payoffs are (30, 20) to BHP and Rio, respectively. If BHP chooses LOW and Rio HIGH, the payoffs are (35, 30). If BHP opts for HIGH and Rio LOW the payoffs are (40, 10). And, lastly, if BHP plays HIGH and Rio HIGH, the payoffs are (25, 20). Which statement is true?Group of answer choicesThe Nash equilibrium is (LOW, LOW), where the first strategy in the parentheses is BHP’s and the second Rio’s.The Nash equilibrium is (LOW, HIGH)The Nash equilibrium is (HIGH, LOW)The Nash equilibrium is (HIGH, HIGH)The Nash equilibria are (LOW, LOW) and (HIGH, HIGH)
Solution
To answer this question, we need to analyze the payoff matrix for both BHP and Rio.
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The Nash equilibrium is (LOW, LOW): A Nash equilibrium is a set of strategies where no player can improve their payoff by unilaterally changing their strategy. If BHP and Rio both choose LOW, the payoffs are (30, 20). However, if BHP unilaterally changes its strategy to HIGH, its payoff increases to 40. Similarly, if Rio unilaterally changes its strategy to HIGH, its payoff increases to 30. Therefore, (LOW, LOW) is not a Nash equilibrium.
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The Nash equilibrium is (LOW, HIGH): If BHP chooses LOW and Rio chooses HIGH, the payoffs are (35, 30). If BHP unilaterally changes its strategy to HIGH, its payoff decreases to 25. If Rio unilaterally changes its strategy to LOW, its payoff decreases to 10. Therefore, (LOW, HIGH) is a Nash equilibrium.
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The Nash equilibrium is (HIGH, LOW): If BHP chooses HIGH and Rio chooses LOW, the payoffs are (40, 10). If BHP unilaterally changes its strategy to LOW, its payoff decreases to 35. If Rio unilaterally changes its strategy to HIGH, its payoff increases to 20. Therefore, (HIGH, LOW) is not a Nash equilibrium.
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The Nash equilibrium is (HIGH, HIGH): If BHP and Rio both choose HIGH, the payoffs are (25, 20). However, if BHP unilaterally changes its strategy to LOW, its payoff increases to 35. Similarly, if Rio unilaterally changes its strategy to LOW, its payoff remains the same. Therefore, (HIGH, HIGH) is not a Nash equilibrium.
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The Nash equilibria are (LOW, LOW) and (HIGH, HIGH): As we've seen, neither (LOW, LOW) nor (HIGH, HIGH) are Nash equilibria.
So, the true statement is "The Nash equilibrium is (LOW, HIGH)".
Similar Questions
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