Estimating an Auction Platform Game with Two-Sided Entry

Estimating an auction platform game with two-sided entry Marleen Marra∗ January 1, 2021 Abstract I study endogenous entry of bidders and sellers in an auction platform, and how they respond to platform fee changes. As the platform is more valuable to bidders when more sellers enter, and vice versa, welfare impacts of fee changes are theoretically ambiguous. I exploit equilibrium outcomes of the auction platform game to quantify such network effects and estimate the model with data from a wine auction platform. A particular novel element of the model is that it captures entry of heterogeneous sellers and its relation to bidder entry: higher- value sellers exit when raising fees, increasing the platform's attractiveness to buyers anticipating lower (reservation) prices. I show that relevant model primitives are identified from variation in reserve prices, transaction prices, and the number of bidders. Results highlight the role of selection in redesigning platforms with listing heterogeneity and reveal pricing strategies to increase both platform profitability and user welfare. JEL codes: D44, C57, L10 Keywords: Ascending auctions, Auctions with entry, Seller selection ∗Sciences Po, Department of Economics, 28 Rue des Saints-Pères, 75007 Paris, France. E-mail: [email protected]. Tel: +33 (0)695 526 146. 1 How should a peer-to-peer auction platform allocate fees between buyers and sellers? What antitrust damages should be awarded when the platform raises fees anticompetitively? Auction platforms facilitating trade between users necessarily generate indirect network effects as they are more valuable to potential bidders when more sellers enter, and vice versa. The theoretical two-sided market literature high- lights that both 1) the platform revenue-maximizing fee structure, and 2) welfare impacts of those fees are theoretically ambiguous and depend on the magnitude of network effects.1 This ambiguity has also proved a bottleneck for antitrust policy. Increasing the seller's listing fee, for instance, could for some magnitudes be beneficial for all parties when paired with a reduction in bidder cost, if bidders exert a larger indirect network effect than sellers. In this paper, I exploit an original data set of online wine auctions and develop a structural model that allows me to quantify network effects arising from endogenous bidder and seller entry. Specifically, I leverage the transparency of payoffs and actions in the auction game to characterize the value to sellers of an additional bidder, and vice versa.2 After recovering the value distributions of potential bidders and sellers and their entry cost, network effects can be estimated directly for any counterfactual fee structure. This approach maps out the platform's two-sidedness and allows me to provide a tight quantitative analysis of how fee changes affect both platform profitability and user welfare.3 Accounting for seller selection in the auction game furthermore allows me to cap- ture an important interaction effect of this platform. Bidders expect lower (reservation) prices when lower-value sellers are attracted to the platform, so bidder entry depends both on the expected number and type of sellers that enter.4 As the first empirical auction paper to address selective entry of sellers, a separate contribution is therefore my empirically tractable auction platform game with two-sided entry. Conditional on observed auction-level heterogeneity, values are assumed to be of idiosyncratic, private values nature and independent both across bidders and between 1See e.g. Evans(2003), Rochet and Tirole(2006), and Rysman(2009). 2Empirical two-sided market papers have used quasi-experimental designs (e.g. Cullen and Far- ronato(2020) and Li and Netessine(2020)) or demand models where functional form restrictions play a larger role (e.g. Ackerberg and Gowrisankaran(2006) and Lee(2013)) to estimate network effects. 3Fees: buyer / seller commission, buyer entry fee, seller listing fee, and reserve price fee. 4The importance of this dynamic for auction platform profitability was first postulated in Ellison, Fudenberg and Mobius(2004), but never implemented empirically. 2 bidders and sellers. I show how the model's equilibrium distributions of reserve prices, transaction prices and number of bidders per listing are endogenous to the fee structure through optimal entry, bidding and reserve pricing strategies. Observed variation in these outcomes allow for the recovery of model primitives needed to estimate fee impacts. It is highly compelling that sellers enter selectively given that they own the so- called “fine, rare, and vintage wine" before listing. Reduced form evidence supports this idea. Specifically, estimates from a Heckman(1976) selection model suggest that lower value (marginal cost) sellers enter first and also optimally sort into setting a zero reserve price. Initial regression analysis also suggests that listings are independent of each other and that bidders learn their values after entering, consistent with the presence of listing inspection cost. This is a meaningful departure from search models previously applied to homogeneous-good auction platform data.5 Estimates from the structural model indeed reveal significant listing inspection cost between 5-9 percent of the second-highest bid.6 Besides fitting my empirical setting, seller selection and listing inspection cost contribute to the empirical tractability of the auction platform game. I show that the model generates a unique entry equilibrium despite its two-sidedness, character- ized by a fixed point in seller value space with nested an equilibrium bidder entry threshold. The auction platform game generates the following network effects, where an (indirect) network effect describes the change in expected surplus for a user when an additional user on the same (other) side enters the platform.7 As such, positive indirect network effects on both sides result from the expected sale price and prob- ability being endogenous to the number of bidders per listing. Due to the constant listing inspection cost the game's equilibrium entry conditions dictate that this type of platform exhibits no scale effects in the number of listings. Specifically, holding 5See e.g. Backus and Lewis(2016), Hendricks and Sorensen(2018), Bodoh-Creed, Boehnke and Hickman(2020), and Coey, Larsen and Platt(2019). 6Listing inspection cost are associated with understanding the wine's many idiosyncracies such as its provenance, ullage, delivery cost, storage-, insurance-, and return conditions. 7This follows the definition in e.g. Katz and Shapiro(1985) and Evans and Schmalensee(2013) and crucially it captures changes in expected surplus before any entry equilibrium responses arise. The ex-post change in surplus will be different, especially because the entry equilibrium is dictated by zero-profit conditions on both sides. Network effects in this paper are non-linear depending on the baseline platform composition, are driven by latent value distributions and entry costs, and are different for each of the heterogeneous (potential) sellers. Rochet and Tirole(2006) refer to indirect network effects as cross-group externalities. 3 seller types constant, doubling the number of listings doubles the number of bidders on the platform. Seller selection diminishes the indirect network effect on potential bidders. This is because attracting additional sellers, for instance by lowering the listing fee, results in a platform that is populated with higher-reserve setting sellers. These model predictions are consistent with empirical patterns in the data.8 Counterfactual simulations reveal the magnitude of network effects driven by the estimated latent value distributions and entry costs, by exogenously increasing the number of bidders or sellers. Adding one additional bidder is about twice as prof- itable for the marginal seller as the reverse. Furthermore, 62 (38) percent of potential bidders' surplus of adding 100 (10) additional listings evaporates because those sellers set higher reserve prices. On the whole, my empirical results underscore the importance of accounting for seller selection when evaluating mechanism design changes in auction platforms. Perhaps the most telling result is that the negative own-side externality of the selection of higher-value sellers makes that, for sellers who remain on the platform, the reduction in surplus of a unit fee increase is less than one as it excludes \lemons" from the platform.9 In the wine auction platform this effect arises because bidders enter based on the expected distribution of secret reserve prices. For example, I estimate that a one pound increase in the listing fee only lowers expected surplus for sellers who remain on the platform by 77-89 pence. This lemons effect is stronger for lower-value sellers and when sellers are more heterogeneous. In fact, it can be exploited to make all users better off by pairing the one pound higher listing fee with a budget-neutral bidder entry subsidy. These results are of interest beyond the studied setting given that many important two-sided markets feature heterogeneous sellers offering idiosyncratic goods.10 The model also facilitates estimation of currently hard to measure antitrust dam- 8Recent quasi-experimental evidence by Cullen and Farronato(2020) and Li and Netessine(2020) support constant and decreasing returns to scale in other peer-to-peer platforms. The listing inspection cost in my auction platform provide a micro-foundation for the absence of positive scale

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