An augmented first-order approach for incentive problems

Incentive constraints are constraints that are optimization problems themselves. If these problems are non convex then the first order approach fails. We propose an alternative solution method where we use the value function as an additional constraint. This ensures that all solutions are incentive compatible. To get the value function we use a function interpolator like sparse grids. We demonstrate our approach by solving two examples from the literature were it was shown that the first order approach fails

Computing generalized Nash equilibria by polynomial programming

We present a new way to solve generalized Nash equilibrium problems. We assume the feasible set to be compact. Furthermore all functions are assumed to be polynomials. However we do not impose convexity on either the utility functions or the action sets. The key idea is to use Putinar's Positivstellensatz, a representation result for positive polynomials, to replace each agent's problem by a convex optimization problem. The Nash equilibria are then feasible solutions to a system of polynomial equations and inequalities. Our application is a model of the New Zealand electricity spot market with transmission losses based on a real datase

Discrete-Time Dynamic Principal-Agent Models:Contraction Mapping Theorem and Computational Treatment

We consider discrete-time dynamic principal--agent problems with continuous choice sets and potentially multiple agents. We prove the existence of a unique solution for the principal's value function only assuming continuity of the functions and compactness of the choice sets. We do this by a contraction mapping theorem and so we also obtain a convergence result for the value function iteration. To numerically compute a solution for the problem, we have to solve a collection of static principal--agent problems at each iteration. As a result, in the discrete-time setting solving the static problem is the difficult step. If the agent's expected utility is a rational function of his action, then we can transform the bi-level optimization problem into a standard nonlinear program. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal--agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature

Imperfect Thermalizations Allow for Optimal Thermodynamic Processes

Optimal (reversible) processes in thermodynamics can be modelled as step-by-step processes, where the system is successively thermalized with respect to different Hamiltonians by an external thermal bath. However, in practice interactions between system and thermal bath will take finite time, and precise control of their interaction is usually out of reach. Motivated by this observation, we consider finite-time and uncontrolled operations between system and bath, which result in thermalizations that are only partial in each step. We show that optimal processes can still be achieved for any non-trivial partial thermalizations at the price of increasing the number of operations, and characterise the corresponding tradeoff. We focus on work extraction protocols and show our results in two different frameworks: A collision model and a model where the Hamiltonian of the working system is controlled over time and the system can be brought into contact with a heat bath. Our results show that optimal processes are robust to noise and imperfections in small quantum systems, and can be achieved by a large set of interactions between system and bath.Comment: 12 pages + appendix; extended results; accepted in Quantu

Dynamic Principal–Agent Models

This paper contributes to the theoretical and numerical analysis of discrete time dynamic principal-agent problems with continuous choice sets. We first provide a new and simplified proof for the recursive reformulation of the sequential dynamic principal-agent relationship. Next we prove the existence of a unique solution for the principal's value function, which solves the dynamic programming problem in the recursive formulation. By showing that the Bellman operator is a contraction mapping, we also obtain a convergence result for the value function iteration. To compute a solution for the problem, we have to solve a collection of static principal{agent problems at each iteration. Under the assumption that the agent's expected utility is a rational function of his action, we can transform the bi-level optimization problem into a standard nonlinear program. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal-agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature

Machine learning for dynamic incentive problems

We propose a generic method for solving infinite-horizon, discrete-time dynamic incentive problems with hidden states. We first combine set-valued dynamic programming techniques with Bayesian Gaussian mixture models to determine irregularly shaped equilibrium value correspondences. Second, we generate training data from those pre-computed feasible sets to recursively solve the dynamic incentive problem by a massively parallelized Gaussian process machine learning algorithm. This combination enables us to analyze models of a complexity that was previously considered to be intractable. To demonstrate the broad applicability of our framework, we compute solutions for models of repeated agency with history dependence, many types, and varying preferences

Liver surgery in cirrhosis and portal hypertension

The prevalence of hepatic cirrhosis in Europe and the United States, currently 250 patients per 100000 inhabitants, is steadily increasing. Thus, we observe a significant increase in patients with cirrhosis and portal hypertension needing liver resections for primary or metastatic lesions. However, extended liver resections in patients with underlying hepatic cirrhosis and portal hypertension still represent a medical challenge in regard to perioperative morbidity, surgical management and postoperative outcome. The Barcelona Clinic Liver Cancer classification recommends to restrict curative liver resections for hepatocellular carcinoma in cirrhotic patients to early tumor stages in patients with Child A cirrhosis not showing portal hypertension. However, during the last two decades, relevant improvements in preoperative diagnostic, perioperative hepatologic and intensive care management as well as in surgical techniques during hepatic resections have rendered even extended liver resections in higher-degree cirrhotic patients with portal hypertension possible. However, there are few standard indications for hepatic resections in cirrhotic patients and risk stratifications have to be performed in an interdisciplinary setting for each individual patient. We here review the indications, the preoperative risk-stratifications, the morbidity and the mortality of extended resections for primary and metastatic lesions in cirrhotic livers. Furthermore, we provide a review of literature on perioperative management in cirrhotic patients needing extrahepatic abdominal surgery and an overview of surgical options in the treatment of hepatic cirrhosis

Direct-to-Consumer Genetic Testing on Social Media: Topic Modeling and Sentiment Analysis of YouTube Users\u27 Comments

Background: With direct-to-consumer (DTC) genetic testing enabling self-responsible access to novel information on ancestry, traits, or health, consumers often turn to social media for assistance and discussion. YouTube, the largest social media platform for videos, offers an abundance of DTC genetic testing–related videos. Nevertheless, user discourse in the comments sections of these videos is largely unexplored. Objective: This study aims to address the lack of knowledge concerning user discourse in the comments sections of DTC genetic testing–related videos on YouTube by exploring topics discussed and users\u27 attitudes toward these videos. Methods: We employed a 3-step research approach. First, we collected metadata and comments of the 248 most viewed DTC genetic testing–related videos on YouTube. Second, we conducted topic modeling using word frequency analysis, bigram analysis, and structural topic modeling to identify topics discussed in the comments sections of those videos. Finally, we employed Bing (binary), National Research Council Canada (NRC) emotion, and 9-level sentiment analysis to identify users\u27 attitudes toward these DTC genetic testing–related videos, as expressed in their comments. Results: We collected 84,082 comments from the 248 most viewed DTC genetic testing–related YouTube videos. With topic modeling, we identified 6 prevailing topics on (1) general genetic testing, (2) ancestry testing, (3) relationship testing, (4) health and trait testing, (5) ethical concerns, and (6) YouTube video reaction. Further, our sentiment analysis indicates strong positive emotions (anticipation, joy, surprise, and trust) and a neutral-to-positive attitude toward DTC genetic testing–related videos. Conclusions: With this study, we demonstrate how to identify users\u27 attitudes on DTC genetic testing by examining topics and opinions based on YouTube video comments. Shedding light on user discourse on social media, our findings suggest that users are highly interested in DTC genetic testing and related social media content. Nonetheless, with this novel market constantly evolving, service providers, content providers, or regulatory authorities may still need to adapt their services to users\u27 interests and desires