Question

The following payoff matrix depicts two companies, Lowe's and Home Depot, in an advertising game. The companies will be playing the same game several times. Each company makes its decision without knowing what the other chooses. The payoffs for each firm

The following payoff matrix depicts two companies, Lowe's and Home Depot, in an advertising game. The companies will be playing the same game several times. Each company makes its decision without knowing what the other chooses. The payoffs for each firm represent economic profits.



Imagine that at the beginning of each week, Home Depot and Lowe's play the game described in the payoff matrix above. Assume there is no known end to the game, so Home Depot and Lowe's will effectively be playing an infinite number of rounds. The possible payoffs are the same in all rounds played.
 
In the first week, neither Home Depot nor Lowe's offered a coupon, and each earned $150 million. In the second week, Home Depot offered a 10% off coupon and Lowe's did not offer a coupon. From the third round onward, assume that both players will play a strict tit-for-tat strategy.
 
In the third week, Home Depot earns a profit of 

 and Lowe's earns a profit of 

 .

In the fourth week, Home Depot earns a profit of 

 and Lowe's earns a profit of 

 .

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Answer #1

1. Tit for tat strategy: The tit for tat strategy in a game theory is the repeated series of the same games. Here in the first week the both do not offer a coupon and earn $150 million each. In the second week, the Home depot offer 10% off coupon and lower did not offer a coupon. So in the second week Homo depot earn $200 million and Lowes earn S50 million. Third week profit of Home depot and Lowes: Since, they follow the tit for tat strategy, Home depot do not offer and Lowes offer 10% of coupon, so the Home depot profit is S50 million and Lowes profit S200 million Fourth week profit of Home depot and Lowes: Again in the fourth week, Home depot offer 10% of coupon and Lowes do not offer, so Home depot profit S200 million and Lowes profit is S50 million

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The following payoff matrix depicts two companies, Lowe's and Home Depot, in an advertising game. The companies will be playing the same game several times. Each company makes its decision without knowing what the other chooses. The payoffs for each firm
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