4. Home Depot and Lowe\'s are two nationwide hardware stores that compete with e

Question

4. Home Depot and Lowe's are two nationwide hardware stores that compete with each other. Each store can choose whether to charge a high price or a low price for their goods. If both charge high prices, then they both earn a high profit ($100), if both charge a low price, they both earn a modest profit ($10), however if one charges a low price and the other charges a high price, the low price seller will earn huge profits ($200) and the high price seller will get no customers and earn S0 in profits. (a) Draw a payoff matrix for this game (b) What is the Nash Equilibrium for this game? (o) What type of game would you classify this as? Cooperative, Prisoner's Dilemma, or zero-sum? (d) Now assume both businesses decide to offer a coupon that price-matches. The coupon says that if you can find a better price at another store, they will match it. Thus giving each store a chance to match its competitors price if it prices high and the other firm prices low. How does this change the NE for this game? (e) Based on the answers to this question, do you think price-match guarantees are good for consumers?

Explanation / Answer

Solution:

a) As per the given information, the payoff matrix is as follows:

b)To check for Nash Equilibrium, if Home Depot (HD) charges high price, best response for Lowe (L) is to charge low price (100<200), and earn profit of $200. If L charges low price, best response for HD is to charge low price (0<10).

If HD charges low price best response for L is to charge low price (0<10). If L charges low price, best response for HD is to charge low price (0<10).

Thus, (low price, low price) yielding (10,10) is our nash equilibrium.

c) This type of game can be classified under Prisonner's dilemma as it is in the best interest of both hardware stores to cooperate, charging low price and earning $10 but in their self interest, both might choose to charge high price.

d) If price-matches coupons are introduced, none of the stores will lose an entire market on charging higher price, as was the case earlier. Thus, no store has the obligation to stick to the low price strategy. As a result, Nash equilibrium now will be (high price, high price) yielding (100,100) each.

e) Such price-matching is clearly not good for the consumers, as now the stores can charge higher from them. It's like the competition among the stores/firms in general reduces, resulting in higher profits for the firms as consumer surplus declines.

HOME DEPOT (down) LOWE (side) High Price Low Price High Price (100,100) (0,200) Low Price (200,0) (10,10)

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