# 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?

https://brainmass.com/economics/applied-economics/prisoner-s-dilemma-298594

#### 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.