Question

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.

Answer 1

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.