Making Sense of Non-Binding Retail-Price Recommendations

This paper provides a theoretical rationale for non-binding retail price recommendations (RPRs) in vertical supply relations. Analyzing a bilateral manufacturer-retailer relationship with repeated trade, we show that linear relational contracts can implement the surplusmaximizing outcome. If the manufacturer has private information about production costs or consumer demand, RPRs may serve as a communication device from manufacturer to retailer. We characterize the properties of efficient bilateral relational contracts with RPRs and discuss extensions to settings where consumer demand is affected by RPRs, and where there are multiple retailers or competing supply chains.vertical relationships, relational contracts, asymmetric information, price recommendations

Making Sense of Non-Binding Retail-Price Recommendations

We model non-binding retail-price recommendations (RPRs) as a communication device facilitating coordination in vertical supply relations. Assuming both repeated vertical trade and asymmetric information about production costs, we show that RPRs may be part of a relational contract, communicating private information from manufacturer to retailer that is indispensable for maximizing joint surplus. We show that this contract is self-enforcing if the retailer’s profit is independent of production costs and punishment strategies are chosen appropriately. We also extend our analysis to settings where consumer demand is variable or depends directly on the manufacturer’s RPRs.vertical relationships, relational contracts, asymmetric information, price recommendations

Deregulating Network Industries: Dealing with Price-quality Tradeoffs

This paper examines the effects of introducing competition into monopolized network industries on prices and infrastructure quality. Analyzing a model with reduced-form demand, we first show that deregulating an integrated monopoly cannot simultaneously decrease the retail price and increase infrastructure quality. Second, we derive conditions under which reducing both retail price and infrastructure quality relative to the integrated monopoly outcome increases welfare. Third, we argue that restructuring and setting very low access charges may yield welfare losses, as infrastructure investment is undermined. We provide an extensive analysis of the linear demand model and discuss policy implication

Grid Orientations, (d,d + 2)-Polytopes, and Arrangements of Pseudolines

We investigate the combinatorial structure of linear programs on simple d-polytopes with d + 2 facets. These can be encoded by admissible grid orientations. Admissible grid orientations are also obtained through orientation properties of a planar point configuration or by the dual line arrangement. The point configuration and the polytope corresponding to the same grid are related through an extended Gale transform. The class of admissible grid orientations is shown to contain nonrealizable examples, i.e., there are admissible grid orientations which cannot be obtained from a polytope or a point configuration. It is shown, however, that every admissible grid orientation is induced by an arrangement of pseudolines. This later result is used to prove several nontrivial facts about admissible grid orientation

Multimodal Outcomes in N-of-1 Trials: Combining Unsupervised Learning and Statistical Inference

N-of-1 trials are randomized multi-crossover trials in single participants with the purpose of investigating the possible effects of one or more treatments. Research in the field of N-of-1 trials has primarily focused on scalar outcomes. However, with the increasing use of digital technologies, we propose to adapt this design to multimodal outcomes, such as audio, video, or image data or also sensor measurements, that can easily be collected by the trial participants on their personal mobile devices. We present here a fully automated approach for analyzing multimodal N-of-1 trials by combining unsupervised deep learning models with statistical inference. First, we train an autoencoder on all images across all patients to create a lower-dimensional embedding. In the second step, the embeddings are reduced to a single dimension by projecting on the first principal component, again using all images. Finally, we test on an individual level whether treatment and non-treatment periods differ with respect to the component. We apply our proposed approach to a published series of multimodal N-of-1 trials of 5 participants who tested the effect of creams on acne captured through images over 16 days. We compare several parametric and non-parametric statistical tests, and we also compare the results to an expert analysis that rates the pictures directly with respect to their acne severity and applies a t-test on these scores. The results indicate a treatment effect for one individual in the expert analysis. This effect was replicated with the proposed unsupervised pipeline. In summary, our proposed approach enables the use of novel data types in N-of-1 trials while avoiding the need for manual labels. We anticipate that this can be the basis for further explorations of valid and interpretable approaches and their application in clinical multimodal N-of-1 trials.Comment: 11 pages, 4 figure