List pricing and pure strategy outcomes in a Bertrand-Edgeworth duopoly

Non-existence of a pure strategy equilibrium in a Bertrand-Edgeworth duopoly model is analyzed. The standard model is modified to include a list pricing stage and a subsequent price discounting stage. Both firms first simultaneously choose a maximum list price and then decide to lower the price, or not, in a subsequent discounting stage. List pricing works as a credible commitment device that induces the pure strategy outcome. It is shown that for a general class of rationing rules there exists a sub-game perfect equilibrium that involves both firms playing pure strategies. This equilibrium payoff dominates any other sub-game perfect equilibrium of the game. Further unlike the dominant firm interpretation of a price leader, we show that the small firm may have incentives to commit to a low price and in this sense assume the role of a leader

Non-detection of magnetic fields in the central stars of the planetary nebulae NGC 1360 and LSS 1362

The presence of magnetic fields is an attractive hypothesis for shaping PNe. We report on observations of the central star of the two Planetary Nebulae NGC1360 and LSS1326. We performed spectroscopy on circularly polarized light with the FOcal Reducer and low dispersion Spectrograph at the Very Large Telescope of the European Southern Observatory. Contrary to previous reports (Jordan et al. 2005, A&A, 432, 273), we find that the effective magnetic field, that is the average over the visible stellar disk of longitudinal components of the magnetic fields, is null within errors for both stars. We conclude that a direct evidence of magnetic fields on the central stars of PNe is still missing --- either the magnetic field is much weaker (< 600 G) than previously reported, or more complex (thus leading to cancellations), or both. Certainly, indirect evidences (e.g., MASER emission) fully justify further efforts to study the strength and morphology of such magnetic fields.Comment: Published in ApJ letters: Leone et al. 2011, ApJ, 731, 33

Estimation of mean form and mean form difference under elliptical laws

The matrix variate elliptical generalization of [30] is presented in this work. The published Gaussian case is revised and modified. Then, new aspects of identifiability and consistent estimation of mean form and mean form difference are considered under elliptical laws. For example, instead of using the Euclidean distance matrix for the consistent estimates, exact formulae are derived for the moments of the matrix B = Xc(Xc)T; where Xcis the centered landmark matrix. Finally, a complete application in Biology is provided; it includes estimation, model selection and hypothesis testing. © 2017, Institute of Mathematical Statistics. All rights reserved

LIST PRICING AND PURE STRATEGY OUTCOMES IN A BERTRAND-EDGEWORTH DUOPOLY

Non-existence of a pure strategy equilibrium in a Bertrand-Edgeworth duopoly model is analyzed. The standard model is modified to include a list pricing stage and a subsequent price discounting stage. Both firms first simultaneously choose a maximum list price and then decide to lower the price, or not, in a subsequent discounting stage. List pricing works as a credible commitment device that induces the pure strategy outcome. It is shown that for a general class of rationing rules there exists a sub-game perfect equilibrium that involves both firms playing pure strategies. This equilibrium payoff dominates any other sub-game perfect equilibrium of the game. Further unlike the dominant firm interpretation of a price leader, we show that the small firm may have incentives to commit to a low price and in this sense assume the role of a leader.