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Prisoner's Dilemma

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?

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Solution Preview

(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.

Firm 2
High Price Low Price
High Price (5, 5) (1,6)
Firm 1
Low Price ...

Solution Summary

Prisoner's Dilemma is exemplified.

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