Question

Dell and Sony compete primarily by price. Each firm must choose either a high price or a low price simultaneously. Use the following information to create the profit matrix:

1. If Dell and Sony both set high prices, Dell’s profit is $40 million and Sony’s profit is $35 million.
2. If Dell sets high price and Sony sets low price, Dell’s profit is $25 million and Sony’s profit is $40 million.
3. If Dell sets low price and Sony sets high price, Dell’s profit is $50 million and Sony’s profit is $10 million.
4. If Dell and Sony set low prices, Dell has $20 million and Sony has $15 million.

Please answer the following questions:

1. Does Sony have a dominant strategy? Dell? If so, which one?
2. If Dell and Sony maximize their profits non-cooperatively, what is the Nash-equilibrium for this profit matrix?
3. Instead, if Dell and Sony maximize their joint profits cooperatively, what is the equilibrium? Assume they keep their agreements.

Answer 1

Dell / Sony	High	low
High	(40,35)	(25*,40•)
Low	(50*,10)	(20,15•)

A) Sony does have a dominant strategy

set low price is dominant strategy

bcoz Sony gets higher payoff , from low option , for any choice of other player Dell.

as if Dell sets high, Sony gets higher payoff from low.

if Dell sets low price, Sony gets higher payoff from low .

Dell doesn't have any dominant strategy

b) NE : ( Dell sets high price, Sony sets low)

C) if both behave Cooperatively

Then joint profit is maximum when both charge high price, then joint profit = 40+35 = 75

Where as in NE, joint profit = 25+40 = 65

So eqm : ( high price , high price )

both sets high prices