Two home-improvement stores (Lopes and HomeMax) in a growing urban area are inte
ID: 1120835 • Letter: T
Question
Two home-improvement stores (Lopes and HomeMax) in a growing urban area are interested in expanding their market share. Both are interested in expanding the size of their store and parking lot to accommodate potential growth in their customer base. The following game depicts the strategic outcomes that result from the game. Increases in annual profits of the two home-improvement stores are shown in the table below.
Increase the size of store and parking lot
Do not increase the size of
Increase the size
of store and
Lopes = $1.0 million
Lopes = $0.4 million
Do not increase
the size of store
Lopes = $3.2 million
Lopes = $2.0 million
a) What is the dominant strategy for both the firms?
b) What will be the Nash equilibrium of the game?
Lopes HomeMaxIncrease the size of store and parking lot
Do not increase the size of
store and parking lotIncrease the size
of store and
parking lotLopes = $1.0 million
HomeMax = $1.5 millionLopes = $0.4 million
HomeMax = $3.4 millionDo not increase
the size of store
and parking lotLopes = $3.2 million
HomeMax = $0.6 millionLopes = $2.0 million
HomeMax = $2.5 millionExplanation / Answer
a) Dominant strategy is the strategy of player which maximises his payoff regardless of his competitors decision.
Dominant strategy of HomeMax is to increase the size of store because it gives it higher payoff.
Dominant strategy of lopes is also to increase the size of store.
b) If Home Max chooses to increase size of store than best response of lopes is to increase its shop size because it maximizes lopes payoff.
If lopes chooses to increase its shop size then best response of HomeMax is to increase its size also.
Therefore, (Increase in size;Increase in size) is the nash equilibrium.
If homemax chooses to Do not increase size then the best response of lopes is to increase its size.
If lopes chooses to increase its size then best response of homemax is to increase size of shop.
So, (do not increase, increase size) is not nash equilibrium.
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