Text Question 2.5 EQuestion Help Two firms face the following payoff matrix show

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Text Question 2.5 EQuestion Help Two firms face the following payoff matrix shown to the right. Given these profits, Firm 2 wants to match Firm 1's price, but Firm 1 does not want to match Firm 2s price. Firm 1 Does either firm have a dominant strategy? Firm 1's dominant strategy does not exist strategy does not exist Does this game have a unique, pure-strategy Nash equilibrium? O A. The Nash equilibrium is for Firm 1 to pick the low price and for Firm 2 to O B. The Nash equilibrium is for Firm 1 to pick the high price and for Firm 2 to Low Price High Price and Firm 2's dominant $0 $6 Low Price $6 $3 pick the high price. Firm 2 $21 pick the low price. The Nash equilibrium is for both firms to pick the low price. The game does not have a pure-strategy Nash equilibrium. The Nash equilibrium is for both firms to pick the high price. High Price OC. D. O E. $0 $18 Identify all pure- and mixed-strategy Nash equilibria. The mixed-strategy Nash equilibrium is for Firm 1 to pick the low price with response rounded to two decimal places.) probability and Firm 2 to pick the low price with probability(Enter your

Explanation / Answer

There is no domimant strategy as both firms are selecting a strategy that is not consistent with the rival's choice. Also there is no pure strategy Nash equilibrium

Assume that firm 1 selects low price with a probability p and high price with a probability (1 - p). Then firm 2 is indifferent between high price and low price when expected payoffs are same

6*p + 3*(1-p) = 0*p + 18*(1-p)

3p + 3 = 18 - 18p

21p = 15

p = 0.71

Assume that firm 2 selects low price with a probability q and high price with a probability (1 - q). Then firm 1 is indifferent between high price and low price when expected payoffs are same

0*q + 21*(1-q) = 6*q + 18*(1-q)

21 - 21q = 6q + 18 - 18q

3 = 9q

q = 0.33

Hence Mixed strategy NE has firm 1 pick up low price with a probability 0.71 and firm 2 pick up low price with probability 0.33.

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