My colleague Brad Larsen has an NBER paper that looks at the post-auction bargaining for used cars that didn't reach their reserve price in the market to dealers.
The Efficiency of Real-World Bargaining: Evidence from Wholesale Used-Auto Auctions
Bradley Larsen
This study quantifies the efficiency of a real-world bargaining game with two-sided incomplete information. Myerson and Satterthwaite (1983) and Williams (1987) derived the theoretical efficient frontier for bilateral trade under two-sided uncertainty, but little is known about how well real-world bargaining performs relative to the frontier. The setting is wholesale used-auto auctions, an $80 billion industry where buyers and sellers participate in alternating-offer bargaining when the auction price fails to reach a secret reserve price. Using 270,000 auction/bargaining sequences, this study nonparametrically estimates bounds on the distributions of buyer and seller valuations and then estimates where bargaining outcomes lie relative to the efficient frontier. Findings indicate that the dynamic mechanism attains 80-91% of the surplus which can be achieved on the efficient frontier.
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