Suppose there are two firms in an industry -Alpha and Beta. Each independently c
ID: 1112731 • Letter: S
Question
Suppose there are two firms in an industry -Alpha and Beta. Each independently choses a price for an identical product. The firms choose either a high price or a low price and each aims to maximize its profit. Profits for both firms are affected by the decisions on what price (high or low) each charges. The payoffs are given in the table below.
Alpha’s
Price Strategy
Beta’s
Price Strategy
Alpha’s Profits
($ millions)
Beta’s Profits
($ millions)
low
low
20
40
High
low
200
250
low
high
40
50
High
High
400
200
(7 pts each)
a. Write the above game in normal form. Use the table provided below for that purpose.
Alpha
Beta
low
High
Low
high
b. What is the optimal strategy, if any, for firm Alpha? Justify your answer.
c. What is the optimal strategy, if any, for firm Beta? Justify your answer.
d. What is the Nash equilibrium strategies for this game? Explain.
e. Does the Nash equilibrium outcome maximize the joint profits of the two firms? Explain? If not what other strategies maximizes the joint profits of the firms? Is it possible for the firms to agree to adopt the strategies that result in such outcome? Explain.
Alpha’s
Price Strategy
Beta’s
Price Strategy
Alpha’s Profits
($ millions)
Beta’s Profits
($ millions)
low
low
20
40
High
low
200
250
low
high
40
50
High
High
400
200
Explanation / Answer
a)
Alpha
Beta
low
High
Low
20,40
40,50
high
200,250
400,200
b) The optimal strategy for Alpha will be to pick the strategy of high price as the profit will be maximum in either case irrespective of what Beta selects.
c) The optimal strategy for Beta will be to pick the strategy of low price as the profit will be maximum
d) The nash equilibrium of the game is
400,200 i.e. when both players choose high price strategy.
Yes the nash equilibrium is maximising the joint profits of the two firms.
Yes it is possible for firms to agree to adopt strategy if they both adopt cooperative strategy.
Alpha
Beta
low
High
Low
20,40
40,50
high
200,250
400,200
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