Multi-unit Setting Research Articles

Learning Strong Substitutes Demand via Queries

This article addresses the computational challenges of learning strong substitutes demand when given access to a demand (or valuation) oracle. Strong substitutes demand generalises the well-studied gross substitutes demand to a multi-unit setting. Recent work by Baldwin and Klemperer shows that any such demand can be expressed in a natural way as a finite list of weighted bid vectors. A simplified version of this bidding language has been used by the Bank of England. Assuming access to a demand oracle, we provide an algorithm that computes the unique list of weighted bid vectors corresponding to a bidder’s demand preferences. In the special case where their demand can be expressed using positive bids only, we have an efficient algorithm that learns this list in linear time. We also show super-polynomial lower bounds on the query complexity of computing the list of bids in the general case where bids may be positive and negative. Our algorithms constitute the first systematic approach for bidders to construct a bid list corresponding to non-trivial demand, allowing them to participate in “product-mix” auctions.

A generalized interrupted time series model for assessing complex health care interventions.

Assessing the impact of complex interventions on measurable health outcomes is a growing concern in health care and health policy. Interrupted time series (ITS) designs borrow from traditional case-crossover designs and function as quasi-experimental methodology able to retrospectively analyze the impact of an intervention. Statistical models used to analyze ITS designs primarily focus on continuous-valued outcomes. We propose the "Generalized Robust ITS" (GRITS) model appropriate for outcomes whose underlying distribution belongs to the exponential family of distributions, thereby expanding the available methodology to adequately model binary and count responses. GRITS formally implements a test for the existence of a change point in discrete ITS. The methodology proposed is able to test for the existence of and estimate the change point, borrow information across units in multi-unit settings, and test for differences in the mean function and correlation pre- and post-intervention. The methodology is illustrated by analyzing patient falls from a hospital that implemented and evaluated a new care delivery model in multiple units.

Impacts of electronic cigarettes usage on air quality of vape shops and their nearby areas

With the rapid growth of the electronic cigarette (e-cig) market, there is an increasing number of vape shops that exclusively sell e-cigs. The use of e-cigs in the vape shop is a primary source of indoor particles, which might transport to its nearby indoor spaces in the multiunit setting. In this study, six pairs of vape shops and neighboring businesses in Southern California were recruited for real-time measurements of particulate pollutants between February 2017 and October 2019. The mean (SD) particle number concentration (PNC) and PM2.5 concentration in the studied vape shops were 2.8 × 104 (2.3 × 104) particles/cm3 and 276 (546) μg/m3, which were substantially higher than those in neighboring businesses and outdoor areas. In addition, 24-h time-weighted average (TWA) nicotine sampling was conducted in the six pairs and three additional pairs. Nicotine was detected in the air of all the studied vape shops and neighboring businesses, in which the mean (SD) concentration was 2.59 (1.02) and 0.17 (0.13) μg/m3, respectively. Inside vape shops, the dilution-corrected vaping density (puffs/h/100 m3) is a strong predictor of the particle concentration, and nicotine concentration highly depends on the air exchange rate (AER). Out of the six studied pairs, PNCs in five vape shops and PM2.5 in two vape shops were significantly correlated with those in their neighboring businesses. This correlation was stronger when the door of the vape shop was closed. When the door was open, environmental electronic vaping (EEV) aerosols, especially smaller particles, could transport from the vape shop to the outdoor environment. Overall, e-cig usage in the vape shop impacts both its own and nearby air quality, raising concerns regarding the risk of exposure to EEV aerosols in the surrounding environments.

Prior-free multi-unit auctions with ordered bidders

Prior-free auctions are robust auctions that assume no distribution over bidders' valuations and provide worst-case (input-by-input) approximation guarantees. In contrast to previous work on this topic, we pursue good prior-free auctions with non-identical bidders.Prior-free auctions can approximate meaningful benchmarks for non-identical bidders only when sufficient qualitative information about the bidder asymmetry is publicly known. We consider digital goods auctions where there is a total ordering of the bidders that is known to the seller, where earlier bidders are in some sense thought to have higher valuations. We use the framework of Hartline and Roughgarden (STOC'08) to define an appropriate revenue benchmark: the maximum revenue that can be obtained from a bid vector using prices that are nonincreasing in the bidder ordering and bounded above by the second-highest bid. This monotone-price benchmark is always as large as the well-known fixed-price benchmark F(2), so designing prior-free auctions with good approximation guarantees is only harder. By design, an auction that approximates the monotone-price benchmark satisfies a very strong guarantee: it is, in particular, simultaneously near-optimal for essentially every Bayesian environment in which bidders' valuation distributions have nonincreasing monopoly prices, or in which the distribution of each bidder stochastically dominates that of the next. Even when there is no distribution over bidders' valuations, such an auction still provides a quantifiable input-by-input performance guarantee.In this paper, we design a simple O(1)-competitive prior-free auction for digital goods with ordered bidders. We also extend the monotone-price benchmark and our O(1)-competitive prior-free auction to multi-unit settings with limited supply.

Using the Knowledge‐to‐Action Framework to understand experiences of breastfeeding guideline implementation: A qualitative study

To examine the perceptions and experiences of health care professionals and mothers in relation to the implementation of a breastfeeding clinical practice guideline (CPG). Breastfeeding CPG applications remain limited, and qualitative studies have indicated the need to overcome the perception by professionals of difficulties in applying recommendations. A qualitative study was conducted in a Spanish public hospital that implemented the Registered Nurses´ Association of Ontario breastfeeding CPG from 2012 through 2015. Between May and August 2017, 27 semi-structured interviews were conducted with managers, with professionals in maternity and paediatric departments and with mothers. Deductive content analysis was performed following the stages in the Knowledge-To-Action (KTA) Framework. We obtained five main categories: (a) problem as opportunity; (b) adequate context and adapted recommendations; (c) extent of implementation; (d) impact of results; and (e) knowledge use normalization. The KTA Framework assists understanding of the participation of the main actors in breastfeeding CPG implementation. The nature of the interventions and the participation of managers, different professionals and mothers in a multi-unit setting generate a complex implementation process that reveals key factors to be taken into account in future CPG implementations.

Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms

We study revenue maximization through sequential posted-price (SPP) mechanisms in single-dimensional settings with n buyers and independent but not necessarily identical value distributions. We construct the SPP mechanisms by considering the best of two simple pricing rules: one that imitates the optimal/Myersonian mechanism via the taxation principle and the other that posts a uniform price. Our pricing rules are rather generalizable and yield the first improvement over long-established approximation factors in several settings. We design factor-revealing mathematical programs that crisply capture the approximation factor of our SPP mechanism. In the single-unit setting, our SPP mechanism yields a better approximation factor than the state of the art prior to our work (Azar et al. 2018). In the multi-unit setting, our SPP mechanism yields the first improved approximation factor over the state of the art after over nine years (Yan (2011) and Chakraborty et al. (2010)). Our results on SPP mechanisms immediately imply improved performance guarantees for the equivalent free-order prophet inequality problem. In the position auction setting, our SPP mechanism yields the first higher-than 1 − 1/e approximation factor. In eager second-price (ESP) auctions, our two simple pricing rules lead to the first improved approximation factor that is strictly greater than what is obtained by the SPP mechanism in the single-unit setting

Multiunit Facility Location Games

Facility location games have been a topic of major interest in economics, operations research, and computer science, starting from the seminal work by Hotelling [Hotelling H (1929) Stability in competition. Econom. J. 39(153):41–57]. In the classical pure location Hotelling game, businesses compete for maximizing customer attraction by strategically locating their facilities, assuming no price competition, and customers are attracted to their closest facilities. Surprisingly, very little rigorous work has been presented on multiunit facility location games, where the classical pure location Hotelling games are extended to contexts where each player is to locate several facilities. In this paper, we present two major contributions to the study of multiunit pure location Hotelling games. In the first part of this paper, we deal with the two-player multiunit setting and fully characterize its equilibria. In the second part of this paper, we deal with multiunit facility location games, with [Formula: see text] players; our main result in this part is the full characterization of the settings where pure strategy equilibria exist. Our results also extend classical results on necessary and sufficient conditions for a strategy profile to be in equilibrium in a pure location (single-unit) Hotelling game to multiunit pure location games.

Pareto Efficient Auctions with Interest Rates

We consider auction settings in which agents have limited access to monetary resources but are able to make payments larger than their available resources by taking loans with a certain interest rate. This setting is a strict generalization of budget constrained utility functions (which corresponds to infinite interest rates). Our main result is an incentive compatible and Pareto-efficient auction for a divisible multi-unit setting with 2 players who are able to borrow money with the same interest rate. The auction is an ascending price clock auction that bears some similarities to the clinching auction but at the same time is a considerable departure from this framework: allocated goods can be de-allocated in future and given to other agents and prices for previously allocated goods can be raised.

Online Random Sampling for Budgeted Settings

We study online multi-unit auctions in which each agent’s private type consists of the agent’s arrival and departure times, valuation function and budget. Similarly to secretary settings, the different attributes of the agents’ types are determined by an adversary, but the arrival process is random. We establish a general framework for devising truthful random sampling mechanisms for online multi-unit settings with budgeted agents. We demonstrate the applicability of our framework by applying it to different objective functions (revenue and liquid welfare), and a range of assumptions about the agents’ valuations (additive or general) when selling identical divisible items. Our main result is the design of mechanisms for additive bidders with budget constraints that extract a constant fraction of the optimal revenue (under a standard large market assumption). We also show a mechanism that extracts a constant fraction of the optimal liquid welfare for general valuations.

Sequential Posted-Price Mechanisms with Correlated Valuations

We study the revenue performance of sequential posted-price mechanisms and some natural extensions for a setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted-price mechanisms are conceptually simple mechanisms that work by proposing a “take-it-or-leave-it” offer to each buyer. We apply sequential posted-price mechanisms to single-parameter multiunit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers. For standard sequential posted-price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted-price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the case of a continuous valuation distribution when various standard assumptions hold simultaneously (i.e., everywhere-supported, continuous, symmetric, and normalized (conditional) distributions that satisfy regularity , the MHR condition , and affiliation ). In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted-price mechanism is proportional to the ratio of the highest and lowest possible valuation. We prove that a simple generalization of these mechanisms achieves a better revenue performance; namely, if the sequential posted-price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a Ω (1/max { 1, d }) fraction of the optimal revenue can be extracted, where d denotes the degree of dependence of the valuations, ranging from complete independence ( d =0) to arbitrary dependence ( d = n -1).

Equilibrium in a Uniform-Price Auction with Private Values

In a model incorporating bidders with private information bidding for multiple units of a homogeneous good, I show that the equilibrium bid functions can be completely characterized, sometimes in closed form. The equilibrium bid functions can be considered aggregated bid functions from first-price single unit bidders. This property allows one to extend results from the single-unit auction literature to this multi-unit setting.

Bidding behaviour in the multi-unit Vickrey and uniform price auctions

Theory provides limited understanding of auctions in complex, multi-unit settings. This absence became apparent when performance concerns were raised over wholesale electric power auctions in England and California. This research used experiments involving 234 subjects to partially bridge the gap in knowledge with regard to bidding behaviour. Using a complex procurement setting motivated by power markets, bidding in the last accepted and first rejected uniform price auctions and the multi-unit Vickrey were examined across group sizes of 2, 4, and 6. To allow opportunity for tacit collusion, constant cost and demand conditions were maintained for 75 periods. Group size and experience were found to be most significant in explaining the differences between bids and costs. For groups of 2, this difference was significantly higher than with the other sizes, suggesting market power. Across sizes, after experience there was no significant difference in bidding behaviour between the uniform price auctions, with subjects in both bidding well above costs. Differences in the multi-unit Vickrey decreased after experience but, unexpectedly, bids were often below costs. Under no combinations did bids equal costs as would be desired by market designers. Results should give concern to policy analysts, and research suggestions to theorists.

Evaluating surrogate endpoints

The validation of surrogate endpoints has been studied by Prentice, who presented a definition as well as a set of criteria that are equivalent if the surrogate and true endpoints are binary. Freedman et al. supplemented these criteria with the so-called proportion explained. Buyse and Molenberghs proposed to replace the proportion explained by two quantities: (1) the relative effect, linking the effect of treatment on both endpoints, and (2) the adjusted association, an individual-level measure of agreement between both endpoints. In a multiunit setting, these quantities can be generalized to a trial-level measure of surrogacy and an individual-level measure of surrogacy. In this paper, we argue that such a multiunit approach should be adopted because it overcomes difficulties that necessarily surround validation efforts based on a single trial. These difficulties are highlighted.

Statistical challenges in the evaluation of surrogate endpoints in randomized trials

The validation of surrogate endpoints has been studied by Prentice, who presented a definition as well as a set of criteria that are equivalent if the surrogate and true endpoints are binary. Freedman et al. supplemented these criteria with the so-called proportion explained. Buyse and Molenberghs proposed to replace the proportion explained by two quantities: (1) the relative effect, linking the effect of treatment on both endpoints, and (2) the adjusted association, an individual-level measure of agreement between both endpoints. In a multiunit setting, these quantities can be generalized to a trial-level measure of surrogacy and an individual-level measure of surrogacy. In this paper, we argue that such a multiunit approach should be adopted because it overcomes difficulties that necessarily surround validation efforts based on a single trial. These difficulties are highlighted.

Multiunit Auctions in Which Almost Every Bid Wins

1. Introduction Recent work suggests that multiunit auctions are much more complicated than their singleunit counterparts (Back and Zender 1993; Katzman 1995; Noussair 1995; Ausubel and Cramton 1996; Chakraborty 1997; Engelbrecht-Wiggans and Kahn 1998a). Because multiunit auctions are of such importance in economics and finance applications-treasury auctions, auctions for electromagnetic spectrum, electric power, privatizations, procurement-it becomes important for economic theorists to be able to make legitimate predictions about the performance of various commonly used auction forms. This is an enormous task. To date, only certain natural but extreme cases have yielded to analysis, for example restriction to auctions in which purchasers only want one or two units (Engelbrecht-Wiggans and Kahn 1998a, b; Katzman 1995). Other results have been demonstrated asymptotically,1 a problematic case since expanding the number of bidders eliminates the very feature that generates a need for organized auctions: a limited number of purchasers. Thus, to have a comprehensive understanding of the behavior of multiunit auctions, it will likely be necessary to devote attention to a large variety of cases. As part of that process, this paper examines a different sector of the parameter space, one unexamined thus far, but one that is readily amenable to solution by simple analytic techniques without resort to asymptotic approximations. We consider auctions in which the number of units available is so large that every bid but one wins a unit. We examine, in the case of independent private values, three different auctions: the pay-your-bid auction (section 3) and two different forms of uniform-price auction (sections 4 and 5). We find that when all but one bid wins, the three auctions are efficient. In section 6, we use a multiunit revenue equivalence result of Engelbrecht-Wiggans (1988) to calculate their expected revenue by comparison to a Vickrey auction (Vickrey 1961, 1962). In most previously studied cases, specifically those in which each bidder wins at most one object, Vickrey auctions turn out to be uniform-price auctions. In the case where all but one bid wins, the Vickrey auction differs significantly from uniform-price auctions. For example, in the case of two bidders and a reservation price of zero, efficiency implies that each bidder in the Vickrey auction wins approximately half of the units. Nonetheless, we show that all the revenue from the Vickrey auction comes from one bidder; the other pays nothing. The analysis of the Vickrey auction shows the importance of the reserve price in a multiunit setting. We also find that the bids from the two forms of uniform-price auction are identical, providing some justification for the common practice of using one as a proxy for the other in theoretical work. Section 8 shows that this equivalence continues to hold for some cases beyond the pure private values setting of the rest of the paper. Of course, the case where every bid but one wins is an extreme example. Nonetheless, as we briefly argue in the final section, the equivalence of the two uniform-price auctions in this case is still significant, since the extreme example we consider is in important ways biased against similarity of the two auction forms. The final section also provides some conjectures about when the two forms of uniform-price auction are likely to yield similar bids. 9. Summary In this paper we have used the case of auctions in which almost every bid wins as a natural laboratory for comparison of different auction rules. We have seen three useful points. The first is extremely simple: If a player is guaranteed to win a unit, the reserve price plays a central role in determining revenue. In single-unit auctions with more than one bidder, reserve prices play no role, as long as they are below the support of the bidders' valuations. In contrast, when some bidder is assured of winning at least one unit no matter what that bidder bids, we need a lower limit on the bids to keep revenue from drifting to minus infinity. …