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Due to the well-known efficiency–rent extraction trade-off, the optimal mechanism in a pure screening environment (e.g., revenue maximization in auctions or cost minimization in procurement) typically calls for distortions in allocative efficiency when agents possess private information at the time of contracting. In this paper we introduce first-stage type-enhancing hidden investment to a standard sequential screening model of procurement, and find that (i) with convex investment cost, mitigation of allocative distortion must arise; and (ii) such mitigation can even be extreme with linear investment cost—procurement cost minimization must require social efficiency when the investment is sufficiently effective. (JEL D44, D82, H57)

Induction motors (IMs) are used extensively as driving actuators in electric vehicles. Motor rotors are prone to defects in the die casting procedure, which can significantly reduce the production quality. Benefitting from the development of Internet of things (IoT) techniques and edge computing, this study designed an instrumentation system for the fast inspection of rotor defects to meet the objectives of efficient and high-quality rotor production. First, an electromagnetic sensing device is designed to acquire the induced voltage signal of the rotor under investigation. Second, a residual multiscale feature fusion convolutional neural network model is designed to extract the hierarchical features of the signal, to facilitate defect recognition. The developed algorithm is deployed into a cost-effective edge computing node that includes a signal acquisition circuit and a Raspberry Pi microcontroller. The conducted experimental studies show that this implementation can achieve an inference time of less than 200 ms and accuracy of more than 99%. It is shown that the designed system exhibits superior performance when compared with conventional methods. The developed, compact and flexible handheld solution with enhanced deep learning techniques shows outstanding potential for use in real-time rotor defect detection.

In this paper, we compare two procedures for allocating a sequence of fixed prizes in multi-stage nested Tullock contests, in which the number of prizes equals the number of contestants. In a winner-leave (loser-leave) procedure, in each stage, the prizes of the stage are allocated to winners (losers) according to their ranks, and prizes in early stages are higher (lower) than those in later stages. Players who obtain prizes leave the contest and the others proceed to the next stage of competition. For both procedures, it is effort-maximizing to allocate one prize in each stage. Provided that the positive prizes in the sequence are homogeneous, the optimally designed loser-leave procedure generates higher total effort if and only if the number of positive prizes is lower than a threshold. If the positive prizes in the sequence are heterogeneous, then the loser-leave procedure may generate higher total effort, even if the number of positive prizes in the sequence is in the high range.

Ultrafast ultrasound imaging remains an active area of interest in the ultrasound community due to its ultra-high frame rates. Recently, a wide variety of studies based on deep learning have sought to improve ultrafast ultrasound imaging. Most of these approaches have been performed on radio frequency (RF) signals. However, in-phase/quadrature (I/Q) digital beamformers are now widely used as low-cost strategies. In this work, we used complex convolutional neural networks for reconstruction of ultrasound images from I/Q signals. We recently described a convolutional neural network architecture called ID-Net, which exploited an inception layer designed for reconstruction of RF diverging-wave ultrasound images. In the present study, we derive the complex equivalent of this network; i.e., the Complex-valued Inception for Diverging-wave Network (CID-Net) that operates on I/Q data. We provide experimental evidence that CID-Net provides the same image quality as that obtained from RF-trained convolutional neural networks; i.e., using only three I/Q images, the CID-Net produces high-quality images that can compete with those obtained by coherently compounding 31 RF images. Moreover, we show that CID-Net outperforms the straightforward architecture that consists of processing the real and imaginary parts of the I/Q signal separately, which thereby indicates the importance of consistently processing the I/Q signals using a network that exploits the complex nature of such signals.

We study how to orchestrate information acquisition in an environment where bidders endowed with original estimates (“types”) about their private values can acquire further information by incurring a cost. We consider both single-round and fully sequential short-listing rules. The optimal single-round shortlisting rule admits the set of most efficient bidders that maximizes expected virtual surplus adjusted by the second-stage signal and information acquisition cost. When shortlisting is fully sequential, at each round, the most efficient remaining bidder is admitted provided that her conditional expected contribution to the virtual surplus is positive. (JEL D44, D82, D83)

Development of docetaxel (TXT) resistance is a major obstacle for triple-negative breast cancer (TNBC) treatment. Additionally, chemoresistant cell-derived exosomes were able to change the chemo-response of chemosensitive recipient cells via transportation of lncRNAs. It has been shown that lncRNA LINC00667 level was significantly elevated in breast cancer tissues. Therefore, we explored whether LINC00667 level is increased in TXT-resistant TNBC cell-derived exosomes. In addition, whether exosomal LINC00667 derived from TXT-resistant TNBC cell could affect TXT sensitivity in TXT-sensitive TNBC cells was investigated as well. In the present study, exosomes were isolated from the TXT-resistant TNBC cells and from TXT-sensitive TNBC cells. Next, the level of LINC00667 in the isolated exosomes was detected with RT-qPCR. We found that LINC00667 expression was obviously elevated in TXT-resistant TNBC cell-derived exosomes compared to that in TXT-sensitive TNBC cell-derived exosomes. In addition, LINC00667 could be transferred from TXT-resistant TNBC cells to TNBC cells via exosomes. Moreover, TXT-resistant TNBC cell secreted exosomal LINC00667 markedly reduced the sensitivity of TNBC cells to TXT via upregulation of Bcl-2. Meanwhile, downregulation of LINC00667 notably enhanced the sensitivity of TXT-resistant TNBC cells to TXT through downregulation of Bcl-2. Additionally, LINC00667 was considered to be a ceRNA to sponge miR-200b-3p, thereby elevating Bcl-2 expression. Collectively, TXT-resistant TNBC cell-derived exosomal LINC00667 could decrease the chemosensitivity of TNBC cells to TXT via regulating miR-200b-3p/Bcl-2 axis. These findings suggested that LINC00667 might serve as a promising target for enhancing sensitivity of TNBC cells to TXT therapy.

DCAF13 is firstly identified as a substrate receptor of CUL4-DDB1 E3 ligase complex. This study disclosed that DCAF13 acted as a novel RNA binding protein (RBP) that contributed to triple-negative breast cancer (TNBC) metastasis. Clinical data obtained from TCGA and our collection showed that DCAF13 was closely correlated with poor clinicopathological characteristics and overall survival, which indicated DCAF13 may serve as a diagnostic marker for TNBC metastasis. Functionally, DCAF13 overexpression or suppression was sufficient to enhance or decrease breast cancer cell migration and invasion. Mechanistically, DCAF13 functioned as an RBP by binding with the AU-rich element (ARE) of DTX3 mRNA 3ʹUTR to accelerate its degradation. Moreover, we identified that DTX3 promoted the ubiquitination and degradation of NOTCH4. Finally, increased DCAF13 expression led to post-transcriptional decay of DTX3 mRNA and consequently activated of NOTCH4 signaling pathway in TNBC. In conclusion, these results identified that DCAF13 as a diagnostic marker and therapeutic target for TNBC treatment. Abbreviation: DCAF13: DDB1 and CUL4-associated factor 13; DDB1: DNA-binding protein 1; CUL4: Cullin 4; CRL4, Cullin-ring finger ligase 4; RBP: RNA binding protein; TNBC: triple-negative breast cancer; ARE: AU-rich element; DTX3: Deltex E3 ubiquitin ligase 3; HER2: human epidermal growth factor receptor 2; ER: estrogen receptor; PR: progesterone receptor; PTEN: phosphatase and tensin homolog deleted on chromosome 10; EMT: epithelial-mesenchymal transition.

Circular RNAs (circRNAs) play an extremely important regulatory role in the occurrence and development of various malignant tumors including papillary thyroid cancer (PTC). circFAT1(e2) is a new type of circRNA derived from exon 2 of the FAT1 gene, which is distributed in the cytoplasm and nucleus of PTC cells. However, so far, the role of circFAT1(e2) in PTC is still unclear. In this study, circFAT1(e2) was found to be highly expressed in PTC cell lines and tissues. circFAT1(e2) knockdown suppressed PTC cell growth, migration, and invasion. Also, circFAT1(e2) acted as a sponge for potential microRNAs (miRNAs) to modulate cancer progression. A potential miRNA target was discovered to be miR-873 which was targeted by circFAT1(e2) in PTC. The dual-luciferase assay conducted later also confirmed that there was indeed a direct interaction between circFAT1(e2) and miR-873. This study also confirmed that circFAT1(e2) inhibited the miR-873 expression and thus promoted the ZEB1 expression, thus affecting the proliferation, metastasis, and invasion of PTC cells. In conclusion, the results of this study indicated that circFAT1(e2) played a carcinogenic role by targeting the miR-873/ZEB1 axis to promote PTC invasion and metastasis, which might become a potential novel target for therapy of PTC.

We study equilibrium player ordering in a dynamic all‐pay contest between two teams. The contest lasts two periods, and each team consists of two players who perform in different periods on behalf of their teams. The team with the higher aggregate output wins the prize, which is a public good to its players. Each team has one stronger player and one weaker player, and the two teams can differ in their values of the prize. The teams maximize their winning odds by strategically assigning their players to different periods. We find that when the intrateam heterogeneity in player ability is not excessive, the teams would allocate their stronger players to the late positions as the “anchormen.” When both the intrateam ability gap and interteam heterogeneity in teams' values become excessively large, the team with high value always places its stronger player in the early position, who will place a large bid to preempt late competition. (JEL C7, D7, D8)

Background:Aberrant expression of eukaryotic translation initiation factor 4E (eIF4E) is common in many types of cancer including acute myeloid leukaemia (AML). Phosphorylation of eIF4E by MAPK-interacting kinases (Mnks) is essential for the eIF4E-mediated oncogenic activity. As such, the pharmacological inhibition of Mnks can be an effective strategy for the treatment of cancer.Methods:A series of N-phenyl-4-(1H-pyrrol-3-yl)pyrimidin-2-amine derivatives was designed and synthesised. The Mnk inhibitory activity of these derivatives as well as their anti-proliferative activity against MV4-11 AML cells was determined.Results:These compounds were identified as potent Mnk2 inhibitors. Most of them demonstrated potent anti-proliferative activity against MV4-11 AML cells. The cellular mechanistic studies of the representative inhibitors revealed that they reduced the level of phosphorylated eIF4E and induced apoptosis by down-regulating the anti-apoptotic protein myeloid cell leukaemia 1 (Mcl-1) and by cleaving poly(ADP-ribose)polymerase (PARP). The lead compound 7k possessed desirable pharmacokinetic properties and oral bioavailability.Conclusion:This work proposes that exploration of the structural diversity in the context of Nphenyl- 4-(1H-pyrrol-3-yl)pyrimidin-2-amine would offer potent and selective Mnk inhibitors.

In this paper, the non-linear viscoelastic-plastic creep models in 1-D and 3-D casesare established. The new non-linear viscoelastic-plastic seepage-creep constitutive models addressed, considering the influence of confining pressure. The proposed models provide the prediction of the creep deformation under the seepage.

This paper studies effort-maximizing prize designs in team contests with an arbitrary number of pairwise battles. The organizer rewards the teams contingent on battle outcomes subject to budget balance constraints. Our analysis fully accommodates heterogeneities across players and battles. We discover an innovative measure of the teams' strengths. The optimal design is a majority-score rule with a headstart score for the weaker team: all battles are assigned team-invariant scores; the team collecting higher total scores from its winning battles wins the entire prize. The optimal design is robust to homogeneity-of-degree-zero contest technologies and contest temporal structure.

We investigate optimal favoritism using identity-contingent prizes in a two-player Tullock model. Besides the usual balance effect, prize allocation has an extra efficiency effect: One additional unit of prize tends to induce more effort, if it is used as the winning prize for the stronger player whose marginal cost is lower. We find that a total-effort-maximizing (contest) designer should offer a larger prize to the strong player if and only if the contest is sufficiently noisy. Our results are in contrast to conventional wisdom obtained from contest models with biased winner selection rules, in which leveling the playing field is always preferable in a two-player setting.

The platelet derived growth factor-D (PDGF-D) plays an important role in breast tumor aggressiveness. However, limited study has investigated the effect of silencing PDGF-D on the biological function of breast cancer. The purpose of this study is to clarify the potential value of PDGF-D as a target for breast cancer treatment.Reverse transcription-polymerase chain reaction and western blot were used to detect PDGF-D expression in 5 different breast cancer cells. The lentiviral vector was usd to silence PDGF-D in MDA-MB-231 cells. Then, Methyl Thiazolyl Tetrazolium was used to detect cell viability, 5-Ethynyl-2'- deoxyuridine and a soft agar assay were used to detect cell proliferation and clonality. Additionally, cell apoptosis after PDGF-D knockdown was measured by Annexin V/ Prodium Iodide staining, and cell migration was detected by trans-well assay. Survival rate and tumor size were measured by nude mice transplantation.The MDA-MB-231 and SK-BR-3 cell lines showed higher PDGF-D expression than the MCF7 cell lines (P.05). After the PDGF-D gene was silenced, the growth and colony forming abilitys ignificantly decreased (P.05) together with the induction of apoptosis in MDA-MB-231 cells (P.05). Moreover, MDA-MB-231 cells with PDGF-D silencing showed significantly diminished aggressive migration and invasion potential compared to other cells (P.05). In vivo experiments also indicated that PDGF-D silencing inhibited tumor growth and improved the survival rate of tumor-bearing mice.Downregulation of PDGF-D had dramatic effects on breast cancer cell proliferation, apoptosis and migration, which indicates that it plays an important role in breast cancer development and progression.

International audience; Single diverging wave (DW) imaging produces ultrasound (US) images at high frame rate (ultrafast) but of low quality. Conventional high-quality DW imaging relies on the coherent compounding of multiple consecutive steered emissions, which in turn reduces the gain in frame rate. Reconstructing high-quality US images for ultrafast imaging using deep learning techniques has recently raised a growing interest in the US community. We recently described a convolutional neural network (CNN) architecture called ID-Net, which exploited an inception layer devoted to the reconstruction of DW ultrasound images using radio frequency (RF) data. We derive in this work the complex equivalent of this network, i.e., the complex inception for DW network (CID-Net), operating on in-phase/quadrature (I/Q) data. We experimentally demonstrate that the CID-Net yields the same image quality as that obtained from the RF-trained CNN, i.e., using only three I/Q images, the CID-Net yields high-quality images competing with those obtained by coherently compounding 31 RF images

Objectives Circular RNAs (circRNAs) are RNA transcripts that belong to non‐coding RNAs (ncRNAs), whose implication in human cancers has been recently demonstrated. However, the specific role of multiple circRNAs in breast cancer remains unidentified. Materials and methods Microarray analysis and bioinformatics analysis were applied to select circRNA and miRNA, respectively. The loop structure of circ‐TFF1 was confirmed using RNase R treatment, divergent primer PCR and Sanger sequencing. qRT‐PCR and Western blot were employed for gene expressions. In vitro and in vivo experiments were conducted to assess the function of circ‐TFF1 in biological processes in breast cancer cells. FISH and subcellular separation indicated circ‐TFF1 cellular distribution. Luciferase reporter and RIP assays and Pearson's correlation analysis were performed to evaluate relationships between genes. Results Circ‐TFF1 and TFF1 were both upregulated and positively associated with each other in breast cancer. Knockdown of circ‐TFF1 hindered breast cancer cell proliferation, migration, invasion and EMT in vitro and controlled tumour growth in vivo. Circ‐TFF1 acted as a ceRNA of TFF1 by sponging miR‐326, and its contribution to breast cancer progression was mediated by miR‐326/TFF1 axis. Conclusions Circ‐TFF1 is a facilitator in breast cancer relying on TFF1 by absorbing miR‐326, providing a novel promising target for BC treatment.

We allow negative prizes and investigate effort-maximizing prize design in rank-order contests. Endogenous participation arises due to less-efficient types' incentive to avoid punishments. If prize sequences are independent of the number of entrants, the optimum features winner-take-all for the best performer coupled with a potential punishment for the worst performer only when all contestants participate. If prize sequences can be contingent on the number of entrants, the optimum integrates winner-take-all and egality: When all contestants participate, all non-top performers are penalized by a budget-augmenting negative prize and the top performer collects the augmented prize budget; otherwise, an egalitarian rule applies.

In this paper, we study score procurement auctions with all-pay quality bids. A supplieris score is the di§erence between his quality and price bids. The supplier with the highest score wins and gets paid his own price bid. The procureris payo§ is the di§erence between the winneris quality and the procureris payments to the suppliers. Equilibrium quality and price bids are solved without Orst obtaining the corresponding equilibrium scores. We Ond that quality bids, the suppliersipayo§s and the procureris payo§ do not depend on whether price bids are made contingent on quality bids. Compared to a benchmark of winner-pay quality bids, in which the losing suppliersi quality bidding costs are reimbursed by the procurer, all-pay quality bids tend to reduce quality provision and suppliersipayo§s, but they tend to increase the total surplus and the procureris payo§.

Jingfeng Lu,1,* Yi Chen,1,* Yanxia Liu,2,* Junbin Ding,1 Zhenhao Piao,1 Weiyan Liu1 1Department of General Surgery, Minhang Hospital, Fudan University, Minhang, Shanghai 201199, People’s Republic of China; 2Department of Nursing, Minhang Hospital, Fudan University, Minhang, Shanghai 201199, People’s Republic of China *These authors contributed equally to this work Background: Postoperative management and survival of gastric cancer is mainly determined by pathologic TNM stage. However, gastric cancer is a heterogeneity group, and the survival is quite different even when they are in the same TNM stage. Moreover, TNM stage system does not grasp other important clinicopathologic factors to determine the survival. The aim of the present study is to propose and validate prognostic score based on age, tumor size, and grade.Materials and methods: Patients diagnosed with gastric cancer in the Surveillance, Epidemiology, and End Results database from 1988 to 2012 were included in the present study. Kaplan–Meier methods were adopted and multivariable Cox regression models were built for the analysis of long-term survival outcomes and risk factors.Results: A total of 26,091 eligible patients diagnosed with noncardia gastric cancer were included in the study. In the univariate and multivariate survival analysis, age at diagnosis, tumor grade, and tumor size were validated as independent prognostic factors (P70), grade (well, moderate, and poor differentiation), and size (≤3, 3–6, ≥7 cm). The prognostic score was verified as independent predictor in both univariate and multivariate survival analyses (P

We study collusion in a second-price auction with two bidders in a dynamic environment. One bidder can make a take-it-or-leave-it collusion proposal, which consists of both an offer and a request of bribes, to the opponent. We show that there always exists a robust equilibrium in which the collusion success probability is one. In the equilibrium, for each type of initiator the expected payoff is generally higher than the counterpart in any robust equilibria of the single-option model ( Eso and Schummer (2004) ) and any other separating equilibria in our model.

This article studies cost‐minimizing two‐stage procurement with Research and Development (R&D). The principal wishes to procure a product from an agent. At the first stage, the agent can conduct R&D to discover a more cost‐efficient production technology. First‐stage R&D efficiency and effort and the realized second‐stage production cost are the agent's private information. The optimal two‐stage mechanism is implemented by a menu of single‐stage contracts, each specifying a fixed provision price and remedy paid by a defaulting agent. A higher delivery price is paired with a higher default remedy, and a more efficient type opts for a higher price and higher remedy.

In this paper, we analyze the role of negative prizes in contest design with a fixed budget, risk-neutral contestants, and independent private abilities. The effort-maximizing prize allocation rule features a threshold. When the highest effort is above the threshold, all contestants with lower efforts receive negative prizes. These negative prizes are used to augment the prize to the contestant with the highest effort, which better incentivizes contestants with higher abilities. When no contestant's effort exceeds the threshold, all contestants equally split the initial budget (or a portion of it) to ensure their participation. We find that allowing negative prizes can increase the expected total effort dramatically. In particular, if no bound is imposed on negative prizes, the expected total effort can be arbitrarily close to the highest possible effort inducible when all contestants have the maximum ability with certainty. The above contest is shown to be the optimal mechanism for a more general class of mechanisms.

Multi-battle competitions are ubiquitous in real life. In this paper, we examine the effort-maximizing reward design in sequentially played multi-battle competitions. The organizer has a fixed prize budget, and rewards players contingent on the number of battles they win in a three-battle contest. Battles are played between two opposing players or between selected pairs of players from two opposing teams. A full spectrum of contest technologies in the Tullock family is accommodated. We find that the optimal design is implemented by a contest prize for the grand winner who wins the majority of battles together with uniform battle prizes to battle winners. For competitions between two individuals, the optimal design varies with the discriminatory power of the contest technology. When it is in the low range, winner-take-all is optimal. For the intermediate range, as discriminatory power increases, the optimal prize structure evolves continuously from winner-take-all to a proportional-division rule due to the need to mitigate the growing momentum/discouragement effect. For the high range, a whole span of prize structures extracts full surplus and thus is optimal. In contrast, winner-take-all is optimal for team competitions, regardless of the contest technology, in which the momentum/discouragement effect does not exist.

Background/Aims: Gastric neuroendocrine tumors (G-NETs) are uncommon neoplasms that can present with or without clinical symptoms. In this study, we evaluated the incidence, prognosis, and temporal trends of G-NETs. Methods: We analyzed all cases of G-NETs registered in the Surveillance, Epidemiology, and End Results (SEER) database from 1973 to 2014. Incidence was estimated by age and joinpoint analyses. Survival rates were calculated and survival trends over time were evaluated. Results: A total of 3740 eligible patients were enrolled in the study. G-NETs incidence increased from 0.31 per 1 000 000 patients in 1975 to 4.85 in 2014, with an annual percentage changes (APCs) of 8.9% (95% confidence interval [CI] = 7.7% to 10.21%, P < 0.001, t test (29) from 1975 to 2001 and 3.6% from 2002 to 2014 (95% CI= 2.3% to 4.9%, P < 0.001). For cases diagnosed between 1973 and 1982, five-year survival was 62.8% ± 7.0% (Standard error, SE) and increased to 86.7% ± 0.7% for cases diagnosed between 2003 and 2012 (P < 0.001). Years of diagnosis, gender, age at diagnosis, marital status, grade, tumor size, tumor stage, and surgery performed or not were the strongest predictors of worse survival in both univariate and multivariate analysis (P

We study optimal dynamic selling mechanisms in a two-stage model where the buyer can search for a better price at the second stage. When this outside price is public, the optimal selling mechanism takes the form of a fixed first-stage price with price matching in the second stage. In contrast, when the outside price is the buyer's private information, the optimal mechanism is a menu of two contracts: a first-stage sale at a higher price with immediate delivery, or a first-stage sale at a lower price with second-stage delivery. Thus the optimal form of search deterrence depends on the observability of the buyer's outside option.

In this paper, we study information disclosure policies in all-pay auctions with incomplete information. Two symmetric players have either high or low private value. The contest organizer observes players' values ex post, and can commit ex ante to four different symmetric information policies exhaustively: She can fully disclose or conceal the players' types, and she can disclose their types if and only if when both are high or if and only if when both are low. We characterize the unique equilibriums, and completely rank the four policies by various criteria. We find the full concealment policy extracts highest aggregate expected effort, followed by the policy of disclosing types if and only if when both are high. The policy of disclosing types if and only if when both are low induces least aggregate expected effort. Players enjoy highest expected payoffs under the policy of disclosing types if and only if when both are low; the other three policies yield the same expected payoffs to players. In terms of prize allocation efficiency, the full concealment policy is ranked highest and the full disclosure policy is ranked lowest. In between, the other two policies' rankings depend on the probability of high type. (JEL C72, D44, D82, D83, J48).

In this paper, we study effort-maximizing contest design under the “reverse” nested lottery contest model of Fu et al. (2014) — which is the “mirror image” of the conventional nested lottery contest of Clark and Riis (1996) . We show that under the reverse-lottery technology, a single-stage winner-take-all grand contest dominates all other feasible designs when the contest is sufficiently noisy. This result is in dramatic contrast to the conventional wisdom on the optimality of multistage elimination contests that is grounded under the conventional nested lottery contest technology in the literature. In the framework of a noisy-performance ranking model, the conventional and reverse models differ only in the noise on players’ performance. Our study therefore reveals the important role that the noise term plays in modeling imperfectly discriminatory contests.

In this paper, we revisit the two-bidder asymmetric all-pay auction of Amann and Leininger (1996) by allowing interdependent values and correlated signals. Both values and signals are distributed on continuous supports. We provide conditions for the existence and uniqueness of a monotone pure-strategy equilibrium (MPSE), and constructively characterize the MPSE when it exists. We find that given the marginal distributions of the signals, the equilibrium allocation is solely determined by how bidders' values depend on their signals. In particular, the equilibrium allocation does not depend on how bidders' signals are correlated.

A contest organizer (e.g., a government regulatory agency) is endowed with the capacity to provide unlimited homogeneous prizes (e.g., medals) that he can use to incentivize contestants to exert productive effort in an all-pay auction with incomplete information. Each agent, at most, wins one prize. We study the optimal number of prizes the organizer should grant in order to induce maximal expected total effort or expected highest effort from agents. Both are single peaked under mild regularity conditions. When players’ abilities follow a family of beta distributions, expected highest effort maximization requires a smaller set of prizes to be awarded; for both goals, the optimal number of prizes weakly increases when the pool of contestants expands or contestant quality improves.