Robert Zeithammer

Forward-looking Bidding in Online Auctions

At Internet auction sites like eBay, similar goods are often sold in a sequence of auctions, separated by small amounts of time. Buyers can therefore benefit from forward-looking strategies that take into account available information about future auctions. This paper develops a model of such bidding, and provides empirical evidence of the models relevance to behavior.

The Sealed-Bid Abstraction in Online Auctions

This paper presents five empirical tests of the popular modeling abstraction that assumes bids from online auctions with proxy bidding can be analyzed “as if” they were bids from a second-price sealed-bid auction. The tests rely on observations of the magnitudes and timings of the top two proxy bids, with the different tests stemming from different regularity assumptions about the underlying distribution of valuation signals. We apply the tests to data from three eBay markets---MP3 players, DVDs, and used cars---and we reject the sealed-bid abstraction in all three data sets. A closer examination of these rejections suggests that they are driven by less experienced bidders. This consistent rejection casts doubt on several existing theories of online auction behavior and suggests some demand estimates based on the abstraction can be biased. To assess the direction and magnitude of this bias, we propose and estimate a new model in which some bidders conform to the abstraction while other bidders bid in a reactive fashion. Because reactive bidding can be at least partially detected from the data, we are able to estimate the underlying distribution of demand and compare it to what the sealed-bid abstraction implies. We find that our proposed model fits the data better, and our demand estimates reveal a large potential downward bias were we to assume the second-price sealed-bid model instead.

Research Note---Strategic Bid-Shading and Sequential Auctioning with Learning from Past Prices

This paper analyzes sequential auctioning of single units of an indivisible good to a fluctuating population composed of overlapping generations of unit-demand bidders. Two phenomena emergent in such a market are investigated: forward-looking bidding strategies, and closed-loop selling strategies that involve learning from past prices. The buyers shade their bids down, i.e., bid less than they would in a single isolated auction, whenever they expect the seller to sell another unit of the good in the near future. Unlike in exogenous sequences of auctions, the optimal bidding strategy thus depends on the sellers selling strategy. The converse dependence also occurs: the seller can learn about current demand from past realized prices, and sell only in periods with high-enough demand. Such learning depends on the extent of bid-shading because the seller needs to invert the bidding strategy to learn. In equilibrium, buyer bid-shading persists even when the seller does not sell in every period, but it is self-regulating in that it eventually vanishes when the existence of the market is threatened by low seller profits. In this sense, auction markets have a “self-preservation instinct.” General properties of learning about current demand from past auction prices are also investigated and characterized.

Optimal Reverse-Pricing Mechanisms

Reverse pricing is a market mechanism under which a consumers bid for a product leads to a sale if the bid exceeds a hidden acceptance threshold the seller has set in advance. The seller faces two key decisions in designing such a mechanism. First, he must decide where in the process to collect the revenue---that is, whether to commit to a minimum markup above cost (and thus define the bid-acceptance threshold given cost) and whether to set a fee for the consumers right to bid. Second, the seller must decide whether to facilitate or hinder consumer learning about the current bid-acceptance threshold. We analyze these decisions for a profit-maximizing small intermediary retailer selling to consumers who can also purchase the product in an outside posted-price market. The optimal revenue model is to charge a fee for the right to bid and then accept all bids above cost, rather than to set a positive minimum markup above cost. Avoiding minimum markups in favor of a bidding fee is more profitable because of increased efficiency arising from more entry by consumers and higher bids by the entrants. When consumers learn about the bid-acceptance threshold before they enter the market, efficiency increases further, and generating revenue through a bidding fee can compensate the seller for his loss of information rent when the competition from the outside posted-price firm is relatively weak.

Vertical Differentiation with Variety-Seeking Consumers

We analyze price and quality competition in a vertically differentiated duopoly in which consumers have a preference for variety. The preference for variety is a consequence of diminishing marginal utility for repeated experiences with the same product. We find consumer variety seeking can either soften or intensify price competition, depending on the difference in firm qualities and the strength of consumer preference for variety. When the qualities are similar or the consumer preference for variety is strong, prices and profits are higher than would be obtained in the absence of variety seeking. On the other hand, if qualities differ enough or the preference for variety is weak, stronger preferences for variety are associated with more intense price competition and lower profits. When firms set their qualities before competing on price and the range of feasible qualities is restricted such that variety seeking softens competition, competing firms choose to minimally differentiate themselves from each other. The preference for variety can drive the firms to offer multiunit discounts, and the greater price flexibility from these discounts does not necessarily reduce profits relative to simple unit pricing. This paper was accepted by J. Miguel Villas-Boas, marketing.

The Hesitant Hai Gui: Return-Migration Preferences of U.S. - Educated Chinese Scientists and Engineers

Managers, administrators of research institutions, and policy makers need a greater understanding of the factors that drive return migration decisions of foreign STEM (science, technology, engineering, and mathematics) doctoral graduates of U.S. universities. To address this need, we conducted a large-scale multi-school revealed-preference survey of job preferences among U.S. STEM PhD students and postdocs from China - the source country of the most foreign doctoral students. The survey presents the respondents with choices of potential job offers, and yields individual-level estimates of each respondent’s indirect utility of a job as a function of location, job status, public versus private nature of the employer, and salary. The estimated preferences imply that Chinese doctoral graduates currently tend to remain in the United States because of a large salary disparity between the two countries rather than because of an inherent preference for locating in the United States. The return rate is quite elastic in the salary gap, and many more graduates will return to China if the gap continues to narrow. We provide return-probability estimates for all possible counterfactual levels of the gap. For example, we find that if the gap narrowed to half of today’s level, the return migration would increase threefold to about 27% of graduates. To counteract this potential reverse brain drain, the U.S. managers and policy makers can provide relatively modest monetary incentives and exploit the heterogeneity in job preferences across different student demographics. We also estimate the additional returns due to potential reduced job availability in desirable U.S. coastal cities and due to greater availability of managerial positions in China, and we find that neither change would increase return migration more than a few percentage points.

Optimal Selling in Dynamic Auctions: Information versus Commitment

This paper analyzes optimal selling strategies of a monopolist facing forward-looking patient unit-demand bidders in a sequential auction market. Such a seller faces a fundamental choice between two selling regimes: selling that involves learning about remaining demand from early prices, and selling that forgoes such learning and makes all selling decisions in the beginning of the game. A model of the game between the seller and the bidders is proposed to characterize the optimal regime choice. The model implies that the relative profitability of the two regimes depends on the expected gains from trade: when the expected gains from trade are low, commitment dominates adaptation, and vice versa.

Sequential Auctions with Information About Future Goods

When capacity-constrained bidders have information about a good sold in a future auction, they need to take the information into account in forming todays bids. The capacity constraint makes even otherwise unrelated objects substitutes and creates an equilibrium link between future competition and current bidding strategy. This paper proves the existence and uniqueness of a symmetric pure-strategy equilibrium under mild conditions on the population distribution of valuations, characterizes general properties of the equilibrium bidding strategy, and provides a simple technique for numerically approximating the bidding strategy for arbitrary valuation distributions. The key property of the equilibrium is that almost all bidders submit positive bids in the first stage, thereby ensuring trade with probability one. Even bidders who strongly prefer the second object submit a positive bid in the first auction, because losing the first auction is informative about the remaining competitors who also lost, and losing with a low bid indicates that these competitors are quite strong. Because of the guaranteed trade, the sequential auction with information about future goods is a very efficient trading mechanism, achieving more than 98 percent of the potential gains from trade across a wide variety of settings.

Consumer Preferences for Annuity Attributes: Beyond Net Present Value

Decisions about life annuities are an important part of consumer decumulation of retirement assets, yet they are relatively underexplored by marketing researchers studying consumer financial decision making. In this article, the authors propose and estimate a model of individual preferences for life annuity attributes using a choice-based stated-preference survey. Annuities are presented in terms of consumer-relevant attributes such as monthly income, yearly adjustments, period certain guarantees, and company financial strength. The authors find that these attributes directly influence consumer preferences beyond their impact on the annuitys expected present value. The strength of the direct influence depends on how annuities are described: when annuities are represented only through basic attributes, consumers undervalue inflation protection, and preferences are not monotonically increasing in duration of period certain guarantees. When descriptions of annuities are enriched with cumulative payment information, consumers no longer undervalue inflation protection, but nonlinear preferences for period certain options remain. The authors find that among annuities with the same expected payout but different annual increases and period certain guarantees, the proportion of consumers who choose the annuity over self-management can vary by more than a factor of 2.

Erratum to Optimal Reverse-Pricing Mechanisms by Martin Spann, Robert Zeithammer, and Gerald Häubl

In our paper about optimal reverse pricing mechanisms [Spann M, Zeithammer R, Haubl G 2010 Optimal reverse-pricing mechanisms. Marketing Sci. 296:1058-1070] hereafter, ORPM, some of the mathematical derivations implicitly assume that the name-your-own-price seller interprets the outside-market posted price p differently than the buyers. This note shows that all of the qualitative results in ORPM continue to hold under the more natural assumption of common knowledge that p is the upper bound of wholesale cost. Interestingly, the proofs and algebraic expressions are often simpler than those in ORPM.