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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?

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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