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There are three types of cars, the good G, the bad B, and the ugly U.A G car is worth $40, a B car is worth $20, and a U car is worth $15.The seller knows the precise quality of his car, but the buyer cannot distinguish the difference in the quality of a car offered for sale.There is an equal probability of a car being G, B, or U.
-A possible warranty scheme that can ensure incentive compatibility in question 20 is $g, $b, $u
A)$50, $45, $5
B)$45, $15, $0
C)$45, $35, $0
D)$50, $5, $0
E)$25, $12.5, $0

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There are three types of cars, the good G, the bad B, and the ugly U.A G car is worth $40, a B car is worth $20, and a U car is worth $15.The seller knows the precise quality of his car, but the buyer cannot distinguish the difference in the quality of a car offered for sale.There is an equal probability of a car being G, B, or U.
-A possible warranty scheme that can ensure incentive compatibility in question 20 is $g, $b, $u
A)$50, $45, $5
B)$45, $15, $0
C)$45, $35, $0
D)$50, $5, $0
E)$25, $12.5, $0

Quizplus · Accepted Answer

Given the setup, the warranty scheme must ensure that each seller is incentivized to truthfully reveal the quality of their car. For incentive compatibility, the net payoff (car value plus warranty minus any cost of lying) for being truthful must be at least as high as the payoff for misrepresenting the car's quality. Option C, with warranties of $45 for G, $35 for B, and $0 for U, ensures that:- A G car seller gets $40 (value) + $45 (warranty) = $85, which is higher than claiming it's B ($20 + $35) or U ($15).- A B car seller gets $20 (value) + $35 (warranty) = $55, which is higher than claiming it's U ($15).- A U car seller gets $15 (value) + $0 (warranty) = $15, and there's no incentive to lie since claiming it to be B or G would not increase the net payoff without the corresponding warranty.This scheme ensures that each type of seller is best off when truthfully revealing the quality of their car, making it incentive compatible.

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