From the following payoff matrix, where the payoffs are the profits or losses of
ID: 1177780 • Letter: F
Question
From the following payoff matrix, where the payoffs are the profits or losses of the two firms, determine (a) whether firm A has a dominant strategy, (b) whether firm B has a dominant strategy, (c) the optimal strategy for each firm, and (d) the Nash equilibrium, if there is one.
Firm B
low price high price
low price (1, 1) (3, -1)
Firm A
high price (-1, 3) (4, 2)
Explanation / Answer
a. Consider the action taken by firm A in response to Firm B%u2019s actions. When B chooses to charge a low price, A will choose to charge a low price as well since it earns a higher payoff from doing so. When B charges a high price, A is better off charging a high price as well. Hence A%u2019s choice of action depends on B%u2019s choice and A does not have a dominant strategy.
b. Consider the action taken by firm B in response to Firm A%u2019s actions. When A chooses to charge a low price, B will choose to charge a low price as well since it earns a higher payoff from doing so. When A charges a high price, B is better off charging a low price as well. Hence B will always choose to charge a low price irrespective of the price charged by A. Therefore charging a low price is a dominant strategy for B.
c. For B, the optimal strategy is to charge a low price irrespective of the action taken by A.
For A, its optimal strategy is to charge a high price if B is also charging a high price and to charge a low price if B is charging a low price.
d. The Nash equilibrium of the game is (low price, low price), i.e. both A and B charge low price. Neither A nor B will want to unilaterally deviate to charging a higher price since it makes them worse off.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.