A note on quality choice with an extended Mussa and Rosen's model

We suggest a model derived from the well-known Mussa and Rosen's model, in which two populations of consumers of opposite tastes co-exist: they rank in exactly the reverse order variants sold at the same price. This model may account for linked and contradictory characteristics in products (as for instance nutritional quality and taste), with consumers attaching more importance to one or to the other aspect. The subgame perfect equilibrium is fully characterized for a costless duopoly choosing qualities then prices.opposite tastes.

Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the $n$-sphere, with $n\geq 5$. Using tools from the theory of critical points at infinity, we provide some topological conditions on the level sets of a given positive function under which we prove the existene of a metric, conformally equivalent to the standard metric, with prescribed Paneitz curvature.Comment: 20 page

Predicting financial markets with Google Trends and not so random keywords

We check the claims that data from Google Trends contain enough data to predict future financial index returns. We first discuss the many subtle (and less subtle) biases that may affect the backtest of a trading strategy, particularly when based on such data. Expectedly, the choice of keywords is crucial: by using an industry-grade backtesting system, we verify that random finance-related keywords do not to contain more exploitable predictive information than random keywords related to illnesses, classic cars and arcade games. We however show that other keywords applied on suitable assets yield robustly profitable strategies, thereby confirming the intuition of Preis et al. (2013)Comment: 8 pages, 4 figures. First names and last names swappe

Vertical differentiation, network externalities and compatibility decisions : an alternative approach

We characterize the equilibrium of a game in vertically differentiated market which exhibits network externalities. There are two firms, an incumbent and a potential entrant. Compatibility means in our model that the inherent qualities of the goods are close enough. By choosing its quality, the entrant chooses in the same time to be compatible or not. The maximal quality difference that allows compatibility i.e the compatibility interval is chosen by the incumbent which involves costs increasing with the width of that interval. We show that in order to have two active firms at price equilibrium, the sufficient condition on the market size of a standard vertical differentiation model remains valid under compatibility. However, an additional condition on the firms' qualities is needed under incompatibility. For a small quality segment, the incumbent can block entry choosing an empty compatibility interval. At the subgame perfect equilibrium, incompatibility prevails if the quality segment is large and the compatibility costs are high. Compatibility prevails for sufficiently large quality segments and low costs of compatibility. Finally there is no entry if the quality segment is small and the compatibility costs are high.Vertical differentiation, compatibility, network externalities.

DOPE: Distributed Optimization for Pairwise Energies

We formulate an Alternating Direction Method of Mul-tipliers (ADMM) that systematically distributes the computations of any technique for optimizing pairwise functions, including non-submodular potentials. Such discrete functions are very useful in segmentation and a breadth of other vision problems. Our method decomposes the problem into a large set of small sub-problems, each involving a sub-region of the image domain, which can be solved in parallel. We achieve consistency between the sub-problems through a novel constraint that can be used for a large class of pair-wise functions. We give an iterative numerical solution that alternates between solving the sub-problems and updating consistency variables, until convergence. We report comprehensive experiments, which demonstrate the benefit of our general distributed solution in the case of the popular serial algorithm of Boykov and Kolmogorov (BK algorithm) and, also, in the context of non-submodular functions.Comment: Accepted at CVPR 201