In: Economics
onsider the following matrix
Firm A | Firm B | ||
Low Price | High Price | ||
Low Price | 6, 5 | 10, 3 | |
High Price | 4, 11 | 8, 9 |
Which of the following statements is true regarding the players' secure strategies?
Group of answer choices
Both firms have a secure strategy to play low price.
Neither firm has a secure strategy to play low price.
Only Firm A has a secure strategy to play low price.
Only Firm B has a secure strategy to play low price.
A secure strategy of a player is his maximin strategy, a strategy that maximizes the minimum payoff for one player.
If firm A chooses low price, firm B's payoff minimizing action against firm A will be to play low price, thus giving firm A a payoff of 6 (because 6 < 10).
If firm A chooses high price, B's payoff minimizing action against A is to choose low price, yielding firm A a payoff of 4.
Now firm A plays the strategy that yields the maximum of the two payoffs by choosing low price (because 6 > 4). Therefore, low price is firm A's secure strategy.
Now for firm B, when it chooses low price, firm A's payoff minimizing action against firm B is to choose low price, yielding B a payoff of 5.
When firm B chooses high price, firm A's payoff minimizing action against firm B is to choose low price, yielding firm B a payoff of 3.
Now firm B plays the strategy that yields the maximum of the two payoffs by choosing low price (because 5 > 3). Therefore, low price is firm B's secure strategy.
Answer: Both firms have a secure strategy to play low price.