Prices versus auctions in large markets
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Prices versus auctions in large markets Hanzhe Zhang1 Received: 25 April 2019 / Accepted: 17 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper studies the use of posted prices and auctions in a large dynamic market with many short-lived sellers and long-lived buyers. Although a reserve-price auction maximizes the expected revenue, the optimal revenue decreases when the market becomes more buyer-friendly; namely, when buyers survive longer, face fewer competitors, and become more patient. As the market becomes more buyer-friendly, the revenue advantage of a reserve-price auction over posting a price also decreases, but using posted prices would lead to sale and allocative inefficiencies. Keywords Optimal mechanism · Reserve price · Auction · Posted price JEL Classification D44 · C73 · C78
1 Introduction In theory and practice, a standard auction with a well-chosen reserve price is a desirable revenue-enhancing choice for unit-supply sellers who face buyers with independent private valuations. This paper confirms the revenue optimality of the reserve-price auction in dynamic markets, but the optimal revenue decreases when the market becomes more competitive for sellers. I study the steady-state equilibrium of a dynamic market in which infinitely many short-lived sellers and long-lived buyers who potentially have many chances to obtain a good are matched randomly. When sellers have no fixed cost of running any mechanism, a reserve-price auction is expected-revenue maximizing. The reserve price is
This paper is a revised version of Chapter 4 of my Ph.D. dissertation at the University of Chicago. Financial support by Yahoo! Key Scientific Challenges Fellowship and the National Science Foundation is gratefully acknowledged.
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Hanzhe Zhang [email protected] Department of Economics, Michigan State University, 486 W Circle Drive, East Lansing, MI 48824, USA
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shown to indicate market competitiveness: The equilibrium reserve price and auction revenue are lower in a more buyer-friendly market; a market is said to be more buyerfriendly if buyers survive longer, face fewer competitors, and become more patient. I generalize the monopolist’s problem of Myerson (1981) by introducing a market in which buyers may have subsequent opportunities to buy a perfect substitute of the good. Along the way, I generalize virtual utility (Myerson 1981), which is interpreted as the auction marginal revenue curve (Bulow and Roberts 1989). Although in theory an auction with an optimally chosen reserve price generates the highest expected revenue, in practice there is increasing use of alternative mechanisms in many markets of goods with close substitutes. This is because these alternative mechanisms have other operational advantages while, at the same time, achieving revenues close to optimal. For example, used car dealers use secret reserve-price auctions followed by bargaining (Larsen 2020); central banks offer liquidity loans via price menus and only use auctions during special ti
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