Exclusive dealing through resellers in auctions with stochastic bidder participation.

• Author: Bose, Subir

1. Introduction

   This paper considers a private values auction in which some of an item's potential consumers compete for its possession against professional resellers (or intermediaries). If the resellers win, they market the item to the general public, which includes the consumers who participated in the auction. We show that prohibiting the participation of these potential consumers in the auction can have direct revenue-enhancing effects. In particular, we show that a risk-neutral seller prefers to exclude final consumers from an auction and sell the item exclusively to resellers when these resellers can gain access, at a cost, to a sufficiently bigger market than the seller himself.

   This result might at first appear counterintuitive, as increasing the number of bidders increases expected revenue in private values bidding models. Seemingly, a seller could not profit from excluding any set of bidders. The intuition behind our result is that the resellers recoup their expenses for buying the item by reselling it to the final consumers. If some final consumers participate in the first auction and are outbid by the resellers, this is an indication that their values for the item are relatively low. Outbidding part of their customer base is "bad news" for resellers, so their bids are depressed if final consumers compete with them. Indeed, the resellers are less aggressive when competing against a subset of the final consumers even if, by observing the valuation of the participating consumers, they cannot make any inference about the valuations of the nonparticipating consumers, that is, even when consumer valuations are completely independent.

   This paper also characterizes the social welfare implications of restricting the participation of consumers. The socially optimal and revenue-maximizing choices of auction format do not necessarily coincide. Even though restricting the participation of consumers may be both socially and privately (for the seller) optimal, it is also possible that restricting participation is socially optimal but privately suboptimal, and vice-versa.

   Further, the results of this paper have implications for seller strategy, implications that are particularly relevant in a world where electronic trading is shrinking transactions costs. In Internet auctions, for instance, bids for an item can now be submitted electronically by potential consumers. Sellers who were hitherto unable to sell directly to consumers can now do so through these electronic auctions. However, it appears likely that Internet auctions fail to attract the entire set of possible consumers, as up to 50% of the auctions in some major sites do not result in a sale (see Lucking-Reiley 2000). The results of this paper suggest that if indeed only a small fraction of the potential customers participate directly in the electronic/Internet auction, the seller may find it optimal to exclude them altogether and, instead, sell the item in a dealer auction. Furthermore, such a direct exclusion of final consumers from an auction may not be driven by the desire to reduce transaction costs. In real estat e auctions, for example, it is frequently observed that properties that could be sold separately are sold in large batches. Indeed, in some cases the seller explicitly announces that only wholesalers are welcome to participate. Although such exclusions and sales of items in large batches might economize on transactions costs, they also result in more aggressive bidding from wholesalers. In other words, the results of our paper endogenize the distribution channel in auction markets, without an appeal to transactions costs.

   This paper is related to two different strands of the literature that are discussed in the next section. The first strand considers common or affiliated value bidding environments in which preventing the participation of certain bidders can increase seller revenue. The second strand studies auctions with the possibility of postauction resale, and considers both private and common value environments. Our work integrates these two strands by considering the impact that the possibility of resale has on the incentives of the seller to forbid the participation of certain bidders in the auction. Our paper shows that a seller can profitably exclude some bidders from the auction even in a private values environment when the set of bidders is partitioned to those who purchase for their own consumption and those who purchase for the explicit purpose of resale.

   Section 2 of the paper summarizes the related literature, whereas section 3 describes the modeling framework and a simple, tractable, benchmark model. The following section solves the seller's problem for the benchmark model, and section 5 analyzes the welfare implications of his choice. Section 6 generalizes the benchmark model to markets of arbitrary size and shows that the key results are robust to different assumptions about bidder entry and seller reserve. Finally, the paper ends with a few concluding remarks. All long proofs are contained in an Appendix.

2. Related Literature

   This paper is related to two different lines of research. The first one studies auctions in which resale can arise in equilibrium. The other studies the possibility that the exclusion of some bidders from the auction can actually be revenue increasing. In this section we provide a brief overview of this research and how it relates to our work.

   There has been a recent flurry of research on models of auctions that incorporate the possibility of profitable resale. One strand of the literature pursues explanations for resale on the basis of the existence of further gains from trade available after the object is sold via an auction. A potential source of these gains can arise from the nonparticipation of a subset of the buyers in the first auction. The winner in the first auction may then find it profitable to reauction the item (see Haile 1996). Another potential source of gains from trade arises from the existence of uncertainty about the private value of the object, which is resolved after the first auction. A bidder who expects to value the object most highly wins it in the first auction. When uncertainty about private values is resolved, he may find it profitable to sell the object to one of the other bidders (see Haile 2000, 2001, 2002). A third possibility of gains from trade occurs if bidder asymmetry results in an inefficient allocation in the first-price auction. The winner may find it profitable to resell the item to one of the losing bidders (see Gupta and Lebrun 1997, 1999). The results in Gupta and Lebrun (1997) are very interesting in the context of this work because they show that it may be profitable for the seller to forbid resale of the good. Limiting what the buyers can do with the item, which seemingly reduces its value, can actually yield higher expected revenue. In our work, forbidding consumption of the item, that is, limiting the buyers to purchasing for resale, can actually increase expected revenue.

   In all of the above models, all participants are potentially "final consumers": They directly value the object that is put up for sale. Another strand of the literature considers participants of two types: The first type consists of participants in the first auction who compete for the object with the intention of reselling it. The second type consists of the final consumers who compete among themselves to purchase the items from the resellers. Bikhchandani and Huang (1989), for instance, analyze a common value auction in which an exogenous number of bidders competes in a multiple object auction to acquire items that will then be resold to consumers. In that paper, the policy question is which auction format to use to award the objects to the resellers rather than to exclude or not to exclude the final consumers from the auction.

   This paper adopts the exogenous partition of the players into resellers and final consumers. Unlike the model in Bikhchandani and Huang (1989), ours is a private values model where some or all of the final consumers can be present in the first auction. Furthermore, the policy question we analyze is whether or not the initial seller should allow the participation of the final consumers. Bose and Deltas (1999) is the precursor to this work. In that paper, unlike this one, consumer and reseller participation is deterministic with a single out of N final consumers participating in a seller auction. That paper shows that the seller is never better off by allowing the single consumer to compete for the item. In contrast, in this paper the participation of both types of buyers is stochastic. Under this framework, the optimal seller policy depends on the probabilities of participation and the relative, to the bidder valuations, size of the marketing costs. Furthermore, we are here able to fully analyze the welfare im plications of the exclusion of the final consumers from the seller's auction, derive the comparative statics of the revenue (or welfare)-maximizing auction format, and discuss the robustness of the results to the posting of reserve prices and how stochastic consumer participation can arise endogenously by analyzing the consumer participation decision.

   There is a relatively small literature that considers the profitability of exclusionary practices in auctions. Krishna and Morgan (1997) demonstrate that, when consumer valuations are the average of all bidders' signals, excluding one of the bidders at random can potentially result in higher revenue. Bulow and Klemperer (1998) provide a similar example when bidder valuations have a common and a private component. Finally, an example in Haile (1996) shows that when competing buyers know each other's type with probability that becomes arbitrarily close to 1, and all competing buyers have some intrinsic value for the auctioned object, the seller can profitably exclude one of the buyers from...