1. A market has only 2 sellers. They are both trying to decide on a pricing stra
ID: 2733079 • Letter: 1
Question
1. A market has only 2 sellers. They are both trying to decide on a pricing strategy. If both firms charge a high price, then each firm will experience a 5% increase in profits. If both firms charge a low price, then each firm will experience a 3% increase in profits. If Firm 1 charges a high price and Firm 2 charges a low price, then Firm 1 will experience a 1% increase in profits and Firm 2 will experience a 6% increase in profits. If Firm 2 charges a high price and Firm 1 charges a low price, then Firm 2 will experience a 2% increase in profits and Firm 1 will experience a 7% increase in profits.
o Construct a payoff matrix for this game.
o Determine whether each firm has a dominant strategy and, if it does, identify the strategy.
o Determine the optimal strategy for each firm.
o Determine the Nash equilibrium. (v) Is this a prisoners’ dilemma? How do you know?
Explanation / Answer
Payoff Matrix
Firm 2
High
Low
Firm 1
High
Increase 5%, Increase 5%
Increase 1%, Increase 6%
Low
Increase 7%, Increase 2%
Increase 3%, Increase 3%
(ii) The dominant strategy for each firm is to charge a low price.
(iii) The dominant strategy is optimal for each firm.
(iv) The Nash equilibrium will hold when both firms choose their dominant strategy.
(v) This is a prisoners’ dilemma because both of the firms would be better off if they cooperated in choosing to charge a high price.
Firm 2
High
Low
Firm 1
High
Increase 5%, Increase 5%
Increase 1%, Increase 6%
Low
Increase 7%, Increase 2%
Increase 3%, Increase 3%
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