The graph shows the payoff matrix for two competing firms in an oligopolistic market. The columns represent the potential strategies of Producer A and the rows represent the potential strategies of Producer B. The upper-right payoffs in each box represent the payoffs for Producer A and the lower-left payoffs represent the payoffs for Producer B. Producer ALowPriceHigh PriceProducer B LowPrice4 14 12High Price12 101 10 a. Does Producer A have a dominant strategy? b. Does Producer B have a dominant strategy? c. The Nash equilibrium ismultiple choice 3Producer A: High price; Producer B: Low price.Producer A: High price; Producer B: High price.Producer A: Low price; Producer B: High price.Producer A: Low price; Producer B: Low price.
Question
The graph shows the payoff matrix for two competing firms in an oligopolistic market. The columns represent the potential strategies of Producer A and the rows represent the potential strategies of Producer B. The upper-right payoffs in each box represent the payoffs for Producer A and the lower-left payoffs represent the payoffs for Producer B. Producer ALowPriceHigh PriceProducer B LowPrice4 14 12High Price12 101 10 a. Does Producer A have a dominant strategy? b. Does Producer B have a dominant strategy? c. The Nash equilibrium ismultiple choice 3Producer A: High price; Producer B: Low price.Producer A: High price; Producer B: High price.Producer A: Low price; Producer B: High price.Producer A: Low price; Producer B: Low price.
Solution
a. Producer A does not have a dominant strategy. This is because the payoff for Producer A depends on the strategy of Producer B. If Producer B chooses a low price, Producer A is better off choosing a high price (12 > 4). However, if Producer B chooses a high price, Producer A is better off choosing a low price (14 > 1).
b. Producer B does not have a dominant strategy either. If Producer A chooses a low price, Producer B is better off choosing a high price (12 > 4). However, if Producer A chooses a high price, Producer B is better off choosing a low price (10 > 1).
c. The Nash equilibrium is the situation where neither producer has an incentive to change their strategy, given the strategy of the other producer. In this case, the Nash equilibrium is "Producer A: High price; Producer B: Low price." In this situation, given that Producer B is choosing a low price, Producer A has no incentive to change from a high price (12 > 4). Similarly, given that Producer A is choosing a high price, Producer B has no incentive to change from a low price (10 > 1).
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