Consider a model of two firms (Firm 1 and Firm 2) competing against each other a

Question

Consider a model of two firms (Firm 1 and Firm 2) competing against each other and setting prices simultaneously. Suppose they have a choice of setting either P = $5 or P = $8. If both of them set the lower price they split the total profits of $44 equally(i.e. each of them gets $22). If they both set the higher price, they split the total profits of $82 equally (i.e. each of them gets $41). However, if one of them charges the lower price while the other firm charges the higher price, the lower price firm earns a profit of $60, while the other firm earns a profit of $14. The payoff matrix is given below. Does Firm 1 and 2 have a dominant strategy each? What is the Nash Equilibrium in this game? Explain briefly.

                         $5           $8

Strategies $5 (22, 22) (60, 14)

for Firm 1   $8 (14, 60) (41, 41)

Explanation / Answer

Following is the Payoff Matrix based on the information given:

Dominant strategy is the best course of action for firm irrespective of action of rival firm. Here is the Low price strategy is best strategy for both firms payoff of from low price strategy is maximum for both firms since the (22,60) > (14,41)

Hence the Nash equilibrium is (Low Price, Low Price) or (22,22)

Firm 2 Low Price ($5) High Price ($8) Firm 1 Low Price ($5) $22 ,$ 22 $60 ,$14 High Price ($8) $14, $60 $41, $41

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