Optimal Auctions with Financially Constrained Bidders

We consider an environment where potential buyers of an indi- visible good have liquidity constraints, in that they cannot pay more than their `budget' regardless of their valuation. A buyer's valuation for the good as well as her budget are her private information. We derive constrained-efficient and revenue maximizing auctions for this setting. In general, the optimal auction requires `pooling' both at the top and in the middle despite the maintained assumption of a mono- tone hazard rate. Further, the auctioneer will never¯find it desirable to subsidize bidders with low budgets.the universal type space, the strategic topology; the uniform strategic topology; the uniform-weak topology; interim correlated rationalizable actions

Geometry of mixed states and degeneracy structure of geometric phases for multi-level quantum systems. A unitary group approach

We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same method in the case of SU(3) we study the effect of degeneracies on geometric phases for three-level systems. This is shown to lead to a highly nontrivial generalization of the result for two-level systems in which degeneracy results in a "monopole" structure in parameter space. The rich structures that arise are related to the geometry of adjoint orbits in SU(3). The limiting case of a two-level degeneracy in a three-level system is shown to lead to the known monopole structure.Comment: Latex, 27 p

The Strange Case of Privacy in Equilibrium Models

We study how privacy technologies affect user and advertiser behavior in a simple economic model of targeted advertising. In our model, a consumer first decides whether or not to buy a good, and then an advertiser chooses an advertisement to show the consumer. The consumer's value for the good is correlated with her type, which determines which ad the advertiser would prefer to show to her---and hence, the advertiser would like to use information about the consumer's purchase decision to target the ad that he shows. In our model, the advertiser is given only a differentially private signal about the consumer's behavior---which can range from no signal at all to a perfect signal, as we vary the differential privacy parameter. This allows us to study equilibrium behavior as a function of the level of privacy provided to the consumer. We show that this behavior can be highly counter-intuitive, and that the effect of adding privacy in equilibrium can be completely different from what we would expect if we ignored equilibrium incentives. Specifically, we show that increasing the level of privacy can actually increase the amount of information about the consumer's type contained in the signal the advertiser receives, lead to decreased utility for the consumer, and increased profit for the advertiser, and that generally these quantities can be non-monotonic and even discontinuous in the privacy level of the signal

The centralizing effects of private order flow on proposer-builder separation

The current Proposer Builder Separation (PBS) equilibrium has several builders with different backgrounds winning blocks consistently. This paper considers how this equilibrium will shift when transactions are sold privately via order flow auctions (OFAs) rather than forwarded directly to the public mempool. We discuss a novel model that highlights the augmented value of private order flow for integrated builder searchers. We show that private order flow is complementary to top-of-block opportunities, and therefore integrated builder-searchers are more likely to participate in OFAs and outbid non integrated builders. They will then parlay access to these private transactions into an advantage in the PBS auction, winning blocks more often and extracting higher profits than non-integrated builders. To validate our main assumptions, we construct a novel dataset pairing post-merge PBS outcomes with realized 12-second volatility on a leading CEX (Binance). Our results show that integrated builder-searchers are more likely to win in the PBS auction when realized volatility is high, suggesting that indeed such builders have an advantage in extracting top-of-block opportunities. Our findings suggest that modifying PBS to disentangle the intertwined dynamics between top-of-block extraction and private order flow would pave the way for a fairer and more decentralized Ethereum

Patelloplasty with and without circumpatellar denervation in reducing anterior knee pain in primary total knee arthroplasty: a comparative prospective study

Background: Anterior knee pain (AKP) following total knee arthroplasty (TKA) ­­­­­­is one of the complication which cause dissatisfaction in patients. Incidence estimated to be 4-49%. The aim of our study is to know the efficacy of patelloplasty with circumpatellar denervation with diathermy in reducing AKP in primary TKA.Methods: A total of 130 unilateral TKAs’ are divided into 2 groups. Group I (control) includes 65 patients in which only patelloplasty was done. Group II (intervention) includes 65 patients in which both patelloplasty and circumpatellar denervation with diathermy was done and analysed. Mean follow up period was 18 months. Patients were assessed both preoperatively and postoperatively at final follow up.Results: The overall incidence of AKP at follow up (18 months) was 16.9%, with 7.7% in the intervention group and 26.1% in the control group (p<0.05).  Western Ontario and McMaster Universities osteoarthritis index scores were significantly  better in intervention group when compared to control group (28.71±3.948 vs 31.40±3.860). Better results were also found in knee society scores for intervention group compared to control group (166.57±7.941 vs 161.23±11.219); Feller patellar score of  intervention group was significantly better when compared to control group (23.28±2.546 vs 20.69±3.729); the range of knee flexion was similar in both the groups (94.62±12.6 vs 93.54±10.7). In terms of pain referred by the patient at 72 hrs postoperatively, there was statistically significant difference observed according to visual analogue scale.Conclusions: There is statistically significant difference with respect to AKP in patients who have undergone patelloplasty with circumpatellar denervation using diathermy compared with patelloplasty alone.

Effect of Methylprednisolone in Periarticular Infiltration for Primary Total Knee Arthroplasty on Pain and Rehabilitation

Background: Optimal pain management after total knee arthroplasty (TKA) is important to ensure timely rehabilitation and patient satisfaction. This study examines the efficacy of adding corticosteroid in periarticular infiltration cocktail with relation to postoperative pain management and rehabilitation in patients undergoing simultaneous bilateral TKA. Methods: Fifty patients with symptomatic end-stage bilateral knee osteoarthritis undergoing bilateral TKA under the same anesthetic were recruited. More painful knee was operated first, and the study solution containing ropivacaine, clonidine, epinephrine, and ketorolac with methylprednisolone was infiltrated in one knee and an identical mixture but without methylprednisolone was infiltrated in the second knee. Outcome measures included comparison of visual analogue scale on movement of each knee and range of motion achieved during the first three days after surgery. Results: Differences in visual analogue scale score and range of motion at day one and three between the two groups of knees were significant (P < .05). Postoperative inflammation and the ability to straight leg raise showed better trends in the knees receiving prednisolone although this did not reach statistical significance. Conclusion: Addition of methylprednisolone to periarticular infiltration cocktail for patients undergoing TKA has significant influence on reduction of pain in the early postoperative period and patients are able to regain knee flexion more quickly