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Consider a negotiation between a car buyer and a used-car salesperson. The car salesperson values a car at $10,000 and the buyer values it at $12,000. Suppose the buyer moves first and offers a price p. The car salesperson can accept or reject the offer. If the offer is rejected the buyer can buy an identical car from a different dealer for a price of $5000. In the subgame perfect equilibrium: Group of answer choices Buyer offers $10,000 and the car salesperson rejects Buyer offers $10,000 and the car salesperson accepts Buyer offers $12,000 and the car salesperson rejects. Buyer offers $5000 and the car salesperson rejects Buyer offers $5000 and the car salesperson accepts Buyer offers $12,000 and the car salesperson accepts

Question

Consider a negotiation between a car buyer and a used-car salesperson. The car salesperson values a car at 10,000andthebuyervaluesitat10,000 and the buyer values it at 12,000. Suppose the buyer moves first and offers a price p. The car salesperson can accept or reject the offer. If the offer is rejected the buyer can buy an identical car from a different dealer for a price of $5000. In the subgame perfect equilibrium: Group of answer choices

Buyer offers $10,000 and the car salesperson rejects

Buyer offers $10,000 and the car salesperson accepts

Buyer offers $12,000 and the car salesperson rejects.

Buyer offers $5000 and the car salesperson rejects

Buyer offers $5000 and the car salesperson accepts

Buyer offers $12,000 and the car salesperson accepts

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Solution

The correct answer is: Buyer offers $10,000 and the car salesperson accepts.

Here's the step by step reasoning:

  1. The buyer values the car at 12,000,butknowstheycangetanidenticalcarelsewherefor12,000, but knows they can get an identical car elsewhere for 5,000. Therefore, they would not offer more than $5,000 initially.

  2. The salesperson values the car at 10,000.Ifthebuyeroffers10,000. If the buyer offers 5,000, the salesperson would reject the offer because it's below their valuation.

  3. The buyer, knowing the salesperson's valuation and their own alternative, would then offer 10,000.Thisisbecauseit′swithintheirvaluationrange(between10,000. This is because it's within their valuation range (between 5,000 and $12,000) and it's exactly the salesperson's valuation.

  4. The salesperson would accept the $10,000 offer because it matches their valuation of the car. Rejecting the offer would mean losing the sale, as the buyer has an alternative.

So, in the subgame perfect equilibrium, the buyer offers $10,000 and the car salesperson accepts.

This problem has been solved

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