Two-Sided Competition and Differentiation (with an Application to Media)

We model a duopoly in which two-sided platforms compete on both sides of a two-sided market. Platforms (or intermediaries) select the quality they offer consumers, and the prices they charge to consumers and firms. In this model, non-trivial competition on both sides induces non-quasiconcave payoffs in one subgame. All equilibria are characterized. Under well-defined conditions, the unique equilibrium in pure strategies can be computed. Prices entail a discount on one side, a premium on the other one and the quality offered to consumers is distorted downward. When the pure-strategy equilibrium fails to exist, a mixed-strategy equilibrium is shown to always exist and the distributions are characterized. In this case, the market may be preempted ex post. The model may find applications in the media, internet trading platforms, the software industry or even the health care industry (HMO/PPO).Two-Sided Market; Vertical Differentiation; Industrial Organization; Platform Competition

Platform Pricing Structure and Moral Hazard

We study pricing by a monopoly platform that matches buyers and sellers in an environment with cross-market externalities. Said platform has no private information, does not set the commodity's price and can only charge trading parties for the transaction. Our innovation consists in introducing moral hazard on the sellers' side and an equilibrium notion of platform reputation in an infinite horizon model. With linear fees the platform can mitigate, but not eliminate, the loss of reputation induced by moral hazard. If lump-sum fees (registration fees) can be levied, moral hazard can be overcome. The upfront payment determines the participation threshold of sellers and extracts them, while (lower) transactions fees provide incentives for good behavior. This breaks the equivalence of lump-sum payments and linear fees (Rochet and Tirole (2006)). We draw implications for the role of subsidies (Caillaud and Jullien (2003)).Platforms; Two-Sided Markets; Reputation; Moral Hazard

Two-sided competition with vertical differentiation

This paper studies duopoly in which two-sided platforms compete in differentiated products in a two-sided market. Direct competition on both sides leads to results that depart from much of the current literature. Under some conditions the unique equilibrium in pure strategies can be computed. It features discounts on one side and muted differentiation as the cross-market externality intensifies competition. Less standard, that equilibrium fails to exist when the externality is too powerful (that side becomes too lucrative). A mixed-strategy equilibrium always exists and is characterized. These results are robust to variations in the extensive form. The model may find applications in the media, internet trading platforms, search engine competition, social media or even health insurance (HMO/PPO)

EEG inverse problem solution with minimal influence of the conductivity

In this paper, we propose a novel method that improves the accuracy of the estimation of neural electrical dipoles when solving the EEG inverse problem. A spherical head model is used where we limit the influence of the unknown conductivity brain-skull ratio on the inverse problem.We redefine the cost function that is used in the EEG problem where only useful information is used as input in the inverse problem. In contrast to previous approaches, weighting factors are used where the electrodes are strategically chosen so to reduce the error made on EEG dipole source localization. The proposed method enhances the source localization accuracy from approximately 9mm to 1mm for dipoles near the edge and from 2.1mm to 0.4mm for dipoles near the center of the brain

Au large d’Arromanches-les-Bains – Le port Mulberry B ou Winston-Churchill

Dans le cadre du projet d’inscription au patrimoine mondial de l’Unesco des plages du débarquement, la région Basse-Normandie souhaite connaître l’état de conservation du port artificiel, dernier vestige du génie militaire maritime de la Seconde Guerre mondiale. Elle souhaite en outre connaître les phénomènes liés à la dégradation du site, son évolution prévisible et voir estimer différents scénarii de gestion. La région Basse-Normandie a confié cette mission d’expertise à la société Antea Gr..

MPI+X: task-based parallelization and dynamic load balance of finite element assembly

The main computing tasks of a finite element code(FE) for solving partial differential equations (PDE's) are the algebraic system assembly and the iterative solver. This work focuses on the first task, in the context of a hybrid MPI+X paradigm. Although we will describe algorithms in the FE context, a similar strategy can be straightforwardly applied to other discretization methods, like the finite volume method. The matrix assembly consists of a loop over the elements of the MPI partition to compute element matrices and right-hand sides and their assemblies in the local system to each MPI partition. In a MPI+X hybrid parallelism context, X has consisted traditionally of loop parallelism using OpenMP. Several strategies have been proposed in the literature to implement this loop parallelism, like coloring or substructuring techniques to circumvent the race condition that appears when assembling the element system into the local system. The main drawback of the first technique is the decrease of the IPC due to bad spatial locality. The second technique avoids this issue but requires extensive changes in the implementation, which can be cumbersome when several element loops should be treated. We propose an alternative, based on the task parallelism of the element loop using some extensions to the OpenMP programming model. The taskification of the assembly solves both aforementioned problems. In addition, dynamic load balance will be applied using the DLB library, especially efficient in the presence of hybrid meshes, where the relative costs of the different elements is impossible to estimate a priori. This paper presents the proposed methodology, its implementation and its validation through the solution of large computational mechanics problems up to 16k cores

Large Deviation Theory for a Homogenized and "Corrected" Elliptic ODE

We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a "pointwise" large deviation principle (LDP) for the full solution and approximate this LDP with a more tractable form. These results allow one to access the limits of Gaussian correctors. In general, the corrector does not capture the large deviation behavior. Applications to uncertainty quantification are considered

Combustion in microgravity: The French contribution

AbstractMicrogravity (drop towers, parabolic flights, sounding rockets and space stations) are particularly relevant to combustion problems given that they show high-density gradients and in many cases weak forced convection. For some configurations where buoyancy forces result in complex flow fields, microgravity leads to ideal conditions that correspond closely to canonical problems, e.g., combustion of a spherical droplet in a far-field still atmosphere, Emmons' problem for flame spreading over a solid flat plate, deflagration waves, etc. A comprehensive chronological review on the many combustion studies in microgravity was written first by Law and Faeth (1994) and then by F.A. Williams (1995). Later on, new recommendations for research directions have been delivered. In France, research has been managed and supported by CNES and CNRS since the creation of the microgravity research group in 1992. At this time, microgravity research and future activities contemplated the following:–Droplets: the “D2 law” has been well verified and high-pressure behavior of droplet combustion has been assessed. The studies must be extended in two main directions: vaporization in mixtures near the critical line and collective effects in dense sprays.–Flame spread: experiments observed blue flames governed by diffusion that are in accordance with Emmons' theory. Convection-dominated flames showed significant departures from the theory. Some theoretical assumptions appeared controversial and it was noted that radiation effects must be considered, especially when regarding the role of soot production in quenching.–Heterogeneous flames: two studies are in progress, one in Poitiers and the other in Marseilles, about flame/suspension interactions.–Premixed and triple flames: the knowledge still needs to be complemented. Triple flames must continue to be studied and understanding of “flame balls” still needs to be addressed

A subspace fitting method based on finite elements for fast identification of damages in vibrating mechanical systems

International audienceIn this paper, a method based on subspace fitting is proposed for identification of faults in mechanical systems. The method uses the modal information from an observability matrix, provided by a stochastic subspace identification. It is used for updating a Finite Element Model through the Variable Projection algorithm. Experimental example aims to demonstrate the ability and the efficiency of the method for diagnosis of structural faults in a mechanical system