Optimal Pricing Is Hard

We show that computing the revenue-optimal deterministic auction in unit-demand single-buyer Bayesian settings, i.e. the optimal item-pricing, is computationally hard even in single-item settings where the buyer’s value distribution is a sum of independently distributed attributes, or multi-item settings where the buyer’s values for the items are independent. We also show that it is intractable to optimally price the grand bundle of multiple items for an additive bidder whose values for the items are independent. These difficulties stem from implicit definitions of a value distribution. We provide three instances of how different properties of implicit distributions can lead to intractability: the first is a #P-hardness proof, while the remaining two are reductions from the SQRT-SUM problem of Garey, Graham, and Johnson [14]. While simple pricing schemes can oftentimes approximate the best scheme in revenue, they can have drastically different underlying structure. We argue therefore that either the specification of the input distribution must be highly restricted in format, or it is necessary for the goal to be mere approximation to the optimal scheme’s revenue instead of computing properties of the scheme itself.Microsoft Research (Fellowship)Alfred P. Sloan Foundation (Fellowship)National Science Foundation (U.S.) (CAREER Award CCF-0953960)National Science Foundation (U.S.) (Award CCF-1101491)Hertz Foundation (Daniel Stroock Fellowship

Recent Decisions

Comments on recent decisions by Ralph H. Witt, Raymond Brown, Thomas A. McNish, Daniel J. Manelli, Stanley B. Nelson, George A. Pelletier, Jr., David T. Link, and Thomas Kavadas, Jr

Comparison of physics-based, semi-empirical and neural network-based models for model-based combustion control in a 3.0 L diesel engine

A comparison of four different control-oriented models has been carried out in this paper for the simulation of the main combustion metrics in diesel engines, i.e., combustion phasing, peak firing pressure, and brake mean effective pressure. The aim of the investigation has been to understand the potential of each approach in view of their implementation in the engine control unit (ECU) for onboard combustion control applications. The four developed control-oriented models, namely the baseline physics-based model, the artificial neural network (ANN) physics-based model, the semi-empirical model, and direct ANN model, have been assessed and compared under steady-state conditions and over the Worldwide Harmonized Heavy-duty Transient Cycle (WHTC) for a Euro VI FPT F1C 3.0 L diesel engine. Moreover, a new procedure has been introduced for the selection of the input parameters. The direct ANN model has shown the best accuracy in the estimation of the combustion metrics under both steady-state/transient operating conditions, since the root mean square errors are of the order of 0.25/1.1 deg, 0.85/9.6 bar, and 0.071/0.7 bar for combustion phasing, peak firing pressure, and brake mean effective pressure, respectively. Moreover, it requires the least computational time, that is, less than 50 µs when the model is run on a rapid prototyping device. Therefore, it can be considered the best candidate for model-based combustion control applications

Impure Public Goods and Technological Interdependencies

Impure public goods represent an important group of goods. Almost every public good exerts not only effects which are public to all but also effects which are private to the producer of this good. What is often omitted in the analysis of impure public goods is the fact that – regularly – these private effects can also be generated independently of the public good. In our analysis we focus on the effects alternative technologies – independently generating the private effects of the public good – may have on the provision of impure public goods. After the investigation in an analytical impure public good model, we numerically simulate the effects of alternative technologies in a parameterized model for climate policy in Germany

Observation of Top Quark Production in Proton-Nucleus Collisions

Peer reviewe