Welfare and Revenue Guarantees for Competitive Bundling Equilibrium

We study equilibria of markets with $m$ heterogeneous indivisible goods and $n$ consumers with combinatorial preferences. It is well known that a competitive equilibrium is not guaranteed to exist when valuations are not gross substitutes. Given the widespread use of bundling in real-life markets, we study its role as a stabilizing and coordinating device by considering the notion of \emph{competitive bundling equilibrium}: a competitive equilibrium over the market induced by partitioning the goods for sale into fixed bundles. Compared to other equilibrium concepts involving bundles, this notion has the advantage of simulatneous succinctness ($O(m)$ prices) and market clearance. Our first set of results concern welfare guarantees. We show that in markets where consumers care only about the number of goods they receive (known as multi-unit or homogeneous markets), even in the presence of complementarities, there always exists a competitive bundling equilibrium that guarantees a logarithmic fraction of the optimal welfare, and this guarantee is tight. We also establish non-trivial welfare guarantees for general markets, two-consumer markets, and markets where the consumer valuations are additive up to a fixed budget (budget-additive). Our second set of results concern revenue guarantees. Motivated by the fact that the revenue extracted in a standard competitive equilibrium may be zero (even with simple unit-demand consumers), we show that for natural subclasses of gross substitutes valuations, there always exists a competitive bundling equilibrium that extracts a logarithmic fraction of the optimal welfare, and this guarantee is tight. The notion of competitive bundling equilibrium can thus be useful even in markets which possess a standard competitive equilibrium

LP-based Covering Games with Low Price of Anarchy

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3]

Local cryotherapy on the pancreas with pancreatic necrosis: Results of the experimental study

Background. Acute pancreatitis retains its leading position in the structure of urgent abdominal pathology, maintaining a high postoperative mortality, despite the emergence of new methods of surgical treatment.The aim of the study: to evaluate pathomorphological changes in the pancreas, surrounding organs and tissues, clinical manifestations in dynamics after local cryotherapy on the pancreas in animals with experimental pancreatic necrosis for subsequent use of the method in clinical practice.Material and methods. An experimental study was performed on Wistar rats, in the main group, pancreatic necrosis was simulated with subsequent cryotherapy, in the control group, pancreatic necrosis was simulated and simple pancreatic mobilization was performed, in the third group, cryotherapy was performed on an unchanged gland. With the help of modern statistical methods, the effectiveness and safety of cryotherapy techniques were evaluated.Results. The optimal duration of cryoapplication is an interval of 3–4  seconds at a temperature of –195.75 °C, it is not accompanied by the formation of a cryonecrosis zone, promotes the regeneration of acinuses, does not damage the accumulation of endocrine cells, interrupting the course of pancreonecrosis, does not lead to a fatal outcome, a pronounced adhesive process, other serious intraabdominal complications.Conclusion. Cryotherapy on the pancreas in experimental pancreatic necrosis in  the  optimal temperature-time regime is accompanied by significantly lower mortality, is a safe technique and can be tested in clinical practice for the treatment of patients with this pathology

Heterogeneity and the dynamics of technology adoption

We estimate the demand for a videocalling technology in the presence of both network effects and heterogeneity. Using a unique dataset from a large multinational firm, we pose and estimate a fully dynamic model of technology adoption. We propose a novel identification strategy based on post-adoption technology usage to disentangle equilibrium beliefs concerning the evolution of the network from observed and unobserved heterogeneity in technology adoption costs and use benefits. We find that employees have significant heterogeneity in both adoption costs and network benefits, and have preferences for diverse networks. Using our estimates, we evaluate a number of counterfactual adoption policies, and find that a policy of strategically targeting the right subtype for initial adoption can lead to a faster-growing and larger network than a policy of uncoordinated or diffuse adoption

Structure and regulation of the Asr gene family in banana

Abscisic acid, stress, ripening proteins (ASR) are a family of plant-specific small hydrophilic proteins. Studies in various plant species have highlighted their role in increased resistance to abiotic stress, including drought, but their specific function remains unknown. As a first step toward their potential use in crop improvement, we investigated the structure and regulation of the Asr gene family in Musa species (bananas and plantains). We determined that the MusaAsr gene family contained at least four members, all of which exhibited the typical two exons, one intron structure of Asr genes and the “ABA/WDS” (abscisic acid/water deficit stress) domain characteristic of Asr genes. Phylogenetic analyses determined that the MusaAsr genes were closely related to each other, probably as the product of recent duplication events. For two of the four members, two versions corresponding to the two sub-genomes of Musa, acuminata and balbisiana were identified. Gene expression and protein analyses were performed and Asr expression could be detected in meristem cultures, root, pseudostem, leaf and cormus. In meristem cultures, mAsr1 and mAsr3 were induced by osmotic stress and wounding, while mAsr3 and mAsr4 were induced by exposure to ABA. mASR3 exhibited the most variation both in terms of amino acid sequence and expression pattern, making it the most promising candidate for further functional study and use in crop improvement