Non-LTE radiative transfer in cool stars. Theory and applications to the abundance analysis for 24 chemical elements

The interpretation of observed spectra of stars in terms of fundamental stellar properties is a key problem in astrophysics. For FGK-type stars, the radiative transfer models are often computed using the assumption of local thermodynamic equilibrium (LTE). Its validity is often questionable and needs to be supported by detailed studies, which build upon the consistent framework of non-LTE. In this review, we outline the theory of non-LTE. The processes causing departures from LTE are introduced qualitatively by their physical interpretation, as well as quantitatively by their impact on the models of stellar spectra and element abundances. We also compile and analyse the most recent results from the literature. In particular, we examine the non-LTE effects for 24 chemical elements for six late-studied FGK-type stars.Comment: 19 pages, accepted for publication as a chapter in "Determination of Atmospheric Parameters of B, A, F and G Type Stars", Springer (2014), eds. E. Niemczura, B. Smalley, W. Pyc

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

Information Structures in Optimal Auctions

A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. These properties imply that the optimal selling strategy of a seller can be implemented by a sequence of exclusive take-it or leave-it offers.Optimal Auction, Private Values, Information Structures, Partitions

Efficient Search by Committee

This note constructs an efficient mechanism for finding the best candidate for a committee from a sequence of potential candidates. Committee members have independent private values information about the quality of the candidate. The mechanism selects the best candidate according to the standard utilitarian welfare criterion. Furthermore, the mechanism can be modified to have a balanced budget.Search, Committtees, Voting, Mechanism design, Dynamic pivot mechanism