A market has only two 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.
(a) Construct a payoff matrix for this game.
(b) Determine whether each firm has a dominant strategy and, if it does, identify the strategy.
(c) Determine the optimal strategy for each firm.
(d) Determine the Nash equilibrium.
(e) Is this a prisoners' dilemma? How do you know?
(a) The payoff matrix will be the following, where the first value is Firm 1's payoff, and the second value is Firm 2's payoff.
High Price Low Price
High Price (5, 5) (1,6)
Low Price ...
Prisoner's Dilemma is exemplified.
The Prisoner's Dilemma and the Nash Equilibrium
Explain the Prisoner's Dilemma game, the notion of dominant strategy, and the concept of Nash equilibrium and cooperation. Using these concepts, then, analyze the following duopoly game.
Philip Morris and R.J. Reynolds spend huge sums of money each year to advertise their tobacco products in an attempt to steal customers from each other. Suppose each year Philip Morris and R.J. Reynolds have to decide whether or not they want to spend money on advertising. If neither firm advertises, each will earn a profit of $2 million. If they both advertise, each will earn a profit of $1.5 million. If one firm advertises and the other does not, the firm that advertises will earn a profit of $2.8 million and the other firm will earn $1 million.
• If the two companies decide to collude to maximize profits, what will each company do? What profit will each company earn?
• What is the dominant strategy for each company, and what profit will each company earn if they follow those strategies?
• Is the solution you found in the first question a Nash equilibrium?
• Is the solution you found in the second question a Nash equilibrium?
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