Fundamental stellar parameters and metallicities from Bayesian spectroscopy. Application to low- and high-resolution spectra

We present a unified framework to derive fundamental stellar parameters by combining all available observational and theoretical information for a star. The algorithm relies on the method of Bayesian inference, which for the first time directly integrates the spectroscopic analysis pipeline based on the global spectrum synthesis and allows for comprehensive and objective error calculations given the priors. Arbitrary input datasets can be included into our analysis and other stellar quantities, in addition to stellar age, effective temperature, surface gravity, and metallicity, can be computed on demand. We lay out the mathematical framework of the method and apply it to several observational datasets, including high- and low-resolution spectra (UVES, NARVAL, HARPS, SDSS/SEGUE). We find that simpler approximations for the spectroscopic PDF, which are inherent to past Bayesian approaches, lead to deviations of several standard deviations and unreliable errors on the same data. By its flexibility and the simultaneous analysis of multiple independent measurements for a star, it will be ideal to analyse and cross-calibrate the large ongoing and forthcoming surveys, like Gaia-ESO, SDSS, Gaia and LSST.Comment: 20 pages, 18 figures, 2 tables, accepted for publication in MNRA

Correlated Equilibrium in Games with Incomplete Information

We define a notion of correlated equilibrium for games with incomplete information in a general setting with finite players, finite actions, and finite states, which we call Bayes correlated equilibrium. The set of Bayes correlated equilibria of a fixed incomplete information game equals the set of probability distributions over actions, states and types that might arise in any Bayes Nash equilibrium where players observed additional information. We show that more information always shrinks the set of Bayes correlated equilibria.Correlated equilibrium, Incomplete information, Robust predictions, Information structure

Entry and Vertical Differentiation

This paper analyzes the entry of new products into vertically differentiated markets where an entrant and an incumbent compete in quantities. The value of the new product is initially uncertain and new information is generated through purchases in the market. We derive the (unique) Markov perfect equilibrium of the infinite horizon game under the strong long run average payoff criterion. The qualitative features of the optimal entry strategy are shown to depend exclusively on the relative ranking of established and new products based on current beliefs. Superior products are launched relatively slowly and at high initial prices whereas substitutes for existing products are launched aggressively at low initial prices. The robustness of these results with respect to different model specifications is discussed. Classification-JEL: C72, C73, D43, D83 Keywords: Entry, Duopoly, Quantity Competition, Vertical Differentiation, Bayesian Learning,Markov Perfect Equilibrium, Experimentation, Experience Goods

Monopoly Pricing of Experience Goods

We develop a dynamic model of experience goods pricing with independent private valuations. We show that the optimal paths of sales and prices can be described in terms of a simple dichotomy. In a mass market, prices are declining over time. In a niche market, the optimal prices are initially low followed by higher prices that extract surplus from the buyers with a high willingness to pay. We consider extensions of the model to integrate elements of social rather than private learning and turnover among buyers.Monopoly, dynamic pricing, learning, experience goods, continuous time, Markov perfect equilibrium

Robust Mechanism Design: An Introduction

This essay is the introduction for a collection of papers by the two of us on "Robust Mechanism Design" to be published by World Scientific Publishing. The appendix of this essay lists the chapters of the book. The objective of this introductory essay is to provide the reader with an overview of the research agenda pursued in the collected papers. The introduction selectively presents the main results of the papers, and attempts to illustrate many of them in terms of a common and canonical example, the single unit auction with interdependent values. In addition, we include an extended discussion about the role of alternative assumptions about type spaces in our work and the literature, in order to explain the common logic of the informational robustness approach that unifies the work in this volume.Mechanism design, Robust mechanism design, Common knowledge, Universal type space, Interim equilibrium, Ex post equilibrium, Dominant strategies, Rationalizability, Partial implementation, Full implementation, Robust implementation

Robust Implementation in General Mechanisms

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.Mechanism design, Implementation, Robustness, Common knowledge, Interim equilibrium, Dominant strategies