Two men’s clothing stores that compete for most of the market in a small town in
ID: 1114902 • Letter: T
Question
Two men’s clothing stores that compete for most of the market in a small town in Ohio must choose their average price levels simultaneously. The following payoff table facing the two firms, Arbuckle & Son and Baldwin Apparel, shows the weekly profit outcomes for the various price level combinations.
Baldwin Apparel
LOW HIGH
Low
Arbuckle & Sons
High
$9,000 , $6,000
$7,000 , $4,000
$8,000 , $9,000
$10,000 , $8,000
a. Does Arbuckle & Sons have a dominant strategy? If so, what is it?
b. Does Baldwin Apparel have a dominant strategy? If so, what is it?
c. Does Arbuckle & Sons have a dominated strategy? If so, what is it?
d. Does Baldwin Apparel have a dominated strategy? If so, what is it?
e. What is the Nash (strategically stable) equilibrium?
Low
Arbuckle & Sons
High
$9,000 , $6,000
$7,000 , $4,000
$8,000 , $9,000
$10,000 , $8,000
Explanation / Answer
a) Dominant strategy is a strategy for a player i.e. best response to all strategy profile of other player. If all players in a game have a dominant strategy then we say that Game has dominant strategy equilibrium.
Arbuckle and Sons does not have a dominant strategy because payoff of Arbuckle depends on the decision of Baldwin Apparel. If Abuckle chooses to charge low price then payoff will be more when Baldwin choose Low price. On the other hand, if Abuckle chooses to charge high price then payoff will be more when Baldwin choose to charge high price.
b) Baldwin Apparel has a dominant strategy of choosing low price because payoff of Baldwin does not depends on the decision of Abuckle and Sons. Baldwin Apparel earns higher payoff when it chooses to charge low price irrespective of decision of Abuckle and Sons.
c) Nash equilibrium is a strategy profile such that for each player given strategy, it is best response. Nash equilibrium is a set of strategies such that each player is doing their best given the strategy of other player.
If Baldwin chooses to charge low price then best response of Abuckle is to charge Low price.
If Abuckle charges low price then best response of Baldwin is to charge low price.
So, (Low price; Low price) is the nash equilibrium.
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