How Auctioneers Set Ex-Ante and Ex-Post Reserve Prices in English Auctions

We compare two commonly used procurement English auction formats - the ex-ante reserve price and the ex-post reserve price, with symmetric and independently distributed private costs. Both formats are indirect implementations of Myerson's optimal mechanism. Both formats yield the same ex post payoffs when auctioneers optimally choose reserve prices. However, the optimal reserve prices follow two counter-intuitive prescriptions: optimal ex-ante reserve prices do not vary with the number of bidders, and optimal ex-post reserve prices are invariant to the realized auction prices. Anticipated regret, Davis et al (2011), and subjective posterior probability judgement, Shachat and Tan (2015), are two different approaches to rationalize observed auctioneers' choices that violate the two counter-intuitive prescriptions respectively. We generalized the latter model to one of Subjective Conditional Probabilities (SCP) which predicts optimal ex-ante reserve prices decreasing in the number of bidders and also predicts optimal ex-post reserve prices increasing in the realized auction prices. In our first experiment, in which costs follow a uniform distribution, we find two possible explanations to the experimental results. First, the auctioneers use the SCP model for both formats. Second, they use format-specific models. In our second experiment with a left-skewed cost distribution, we finally find that the SCP provides a unified behavioral model of how auctioneer set reserve prices in the two formats

An experimental investigation of auctions and bargaining in procurement

In reverse auctions, buyers often retain the right to bargain further concessions from the winner. The optimal form of such procurement is an English auction followed by an auctioneer's option to engage in ultimatum bargaining with the winner. We study behavior and performance in this procurement format using a laboratory experiment. Sellers closely follow the equilibrium strategy of exiting the auction at their costs and then accepting strictly profitable offers. Buyers generally exercise their option to bargain according to their equilibrium strategy, but their take-it-or-leave-it offers vary positively with auction prices when they should be invariant. We explain this deviation by modeling buyers' subjective posteriors regarding the winners' costs as distortions, calculated using a formulation of probability weighting, of the Bayesian posteriors. We show alternative models based upon risk aversion and anticipated regret can't explain these price dependencies

How Auctioneers Set Ex-Ante and Ex-Post Reserve Prices in English Auctions

We compare two commonly used procurement English auction formats - the ex-ante reserve price and the ex-post reserve price, with symmetric and independently distributed private costs. Both formats are indirect implementations of Myerson's optimal mechanism. Both formats yield the same ex post payoffs when auctioneers optimally choose reserve prices. However, the optimal reserve prices follow two counter-intuitive prescriptions: optimal ex-ante reserve prices do not vary with the number of bidders, and optimal ex-post reserve prices are invariant to the realized auction prices. Anticipated regret, Davis et al (2011), and subjective posterior probability judgement, Shachat and Tan (2015), are two different approaches to rationalize observed auctioneers' choices that violate the two counter-intuitive prescriptions respectively. We generalized the latter model to one of Subjective Conditional Probabilities (SCP) which predicts optimal ex-ante reserve prices decreasing in the number of bidders and also predicts optimal ex-post reserve prices increasing in the realized auction prices. In our first experiment, in which costs follow a uniform distribution, we find two possible explanations to the experimental results. First, the auctioneers use the SCP model for both formats. Second, they use format-specific models. In our second experiment with a left-skewed cost distribution, we finally find that the SCP provides a unified behavioral model of how auctioneer set reserve prices in the two formats

An experimental investigation of auctions and bargaining in procurement

In reverse auctions, buyers often retain the right to bargain further concessions from the winner. The optimal form of such procurement is an English auction followed by an auctioneer's option to engage in ultimatum bargaining with the winner. We study behavior and performance in this procurement format using a laboratory experiment. Sellers closely follow the equilibrium strategy of exiting the auction at their costs and then accepting strictly profitable offers. Buyers generally exercise their option to bargain according to their equilibrium strategy, but their take-it-or-leave-it offers vary positively with auction prices when they should be invariant. We explain this deviation by modeling buyers' subjective posteriors regarding the winners' costs as distortions, calculated using a formulation of probability weighting, of the Bayesian posteriors. We show alternative models based upon risk aversion and anticipated regret can't explain these price dependencies

Robust Optimization using a new Volume-Based Clustering approach

We propose a new data-driven technique for constructing uncertainty sets for robust optimization problems. The technique captures the underlying structure of sparse data through volume-based clustering, resulting in less conservative solutions than most commonly used robust optimization approaches. This can aid management in making informed decisions under uncertainty, allowing a better understanding of the potential outcomes and risks associated with possible decisions. The paper demonstrates how clustering can be performed using any desired geometry and provides a mathematical optimization formulation for generating clusters and constructing the uncertainty set. In order to find an efficient solution to the problem, we explore different approaches since the method may be computationally expensive. This contribution to the field provides a novel data-driven approach to uncertainty set construction for robust optimization that can be applied to real-world scenarios

Amorphous 1-D nanowires of calcium phosphate/pyrophosphate : A demonstration of oriented self-growth of amorphous minerals

Amorphous inorganic solids are traditionally isotropic, thus, it is believed that they only grow in a non-preferential way without the assistance of regulators, leading to the morphologies of nanospheres or irregular aggregates of nanoparticles. However, in the presence of (ortho)phosphate (Pi) and pyrophosphate ions (PPi) which have synergistic roles in biomineralization, the highly elongated amorphous nanowires (denoted ACPPNs) form in a regulator-free aqueous solution (without templates, additives, organics, etc). Based on thorough characterization and tracking of the formation process (e.g., Cryo-TEM, spherical aberration correction high resolution TEM, solid state NMR, high energy resolution monochromated STEM-EELS), the microstructure and its preferential growth behavior are elucidated. In ACPPNs, amorphous calcium orthophosphate and amorphous calcium pyrophosphate are distributed at separated but close sites. The ACPPNs grow via either the preferential attachment of ∼2 nm nanoclusters in a 1-dimension way, or the transformation of bigger nanoparticles, indicating an inherent driving force-governed process. We propose that the anisotropy of ACPPNs microstructure, which is corroborated experimentally, causes their oriented growth. This study proves that, unlike the conventional view, amorphous minerals can form via oriented growth without external regulation, demonstrating a novel insight into the structures and growth behaviors of amorphous minerals

Isolation, characterization, and genomic analysis of a lytic bacteriophage, PQ43W, with the potential of controlling bacterial wilt

Bacterial wilt (BW) is a devastating plant disease caused by the soil-borne bacterium Ralstonia solanacearum species complex (Rssc). Numerous efforts have been exerted to control BW, but effective, economical, and environmentally friendly approaches are still not available. Bacteriophages are a promising resource for the control of bacterial diseases, including BW. So, in this study, a crop BW pathogen of lytic bacteriophage was isolated and named PQ43W. Biological characterization revealed PQ43W had a short latent period of 15 min, 74 PFU/cell of brust sizes, and good stability at a wide range temperatures and pH but a weak resistance against UV radiation. Sequencing revealed phage PQ43W contained a circular double-stranded DNA genome of 47,156 bp with 65 predicted open reading frames (ORFs) and genome annotation showed good environmental security for the PQ43W that no tRNA, antibiotic resistance, or virulence genes contained. Taxonomic classification showed PQ43W belongs to a novel genus of subfamily Kantovirinae under Caudoviricetes. Subsequently, a dose of PQ43W for phage therapy in controlling crop BW was determined: 108 PFU*20 mL per plant with non-invasive irrigation root application twice by pot experiment. Finally, a field experiment of PQ43W showed a significantly better control effect in crop BW than the conventional bactericide Zhongshengmycin. Therefore, bacteriophage PQ43W is an effective bio-control resource for controlling BW diseases, especially for crop cultivation