Return to the Lemons game, and consider the same structure, except suppose there are just two quality levels: low and high. The buyer initially assigns probability q to a car’s being of high quality and probability 1 - q to its being of low quality. If the seller sells the car, then her payoff is the price the buyer paid. If the car is not sold, assume that it is worth $10,000 to the seller if it is of high quality and $6,000 if it is of low quality; those are the payoffs. The value of the car to the buyer is $12,000 if it is of high quality and $7,000 if it is of low quality. If the buyer purchases the car, then the buyer’s payoff is the car’s value—which is $12,000 or $7,000—less the price paid; his payoff is zero if he does not buy the car. Find values for q such that there is a PBNE with pooling.
Return to the Lemons game, and consider the same structure, except suppose there are just two quality levels: low and high. The buyer initially assigns probability q to a car’s being of high quality and probability 1 - q to its being of low quality. If the seller sells the car, then her payoff is the
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