We investigate competition in a delegation framework, with a coarsely informed principal. Two imperfectly informed and biased experts simultaneously propose action choices. A principal with a diffuse prior, and only being able to ordinally compare the two proposals, has to choose one of them. The selected expert might receive a bonus payment. We show that having a second expert benefits the principal, even if the two experts have the same biases and the bonus of the winner is zero. In contrast with other models of expertise, in our setting the principal prefers experts with equal rather than opposite biases. Increasing the bonus brings experts closer to truthful reporting, but this only benefits the principal up to a threshold level, with further increases in the bonus strictly decreasing her payoffs. A methodological contribution of our paper is characterizing restrictions on the set of strategies which allows a formal generalization of ex ante expected payoffs to games with diffuse prior.

A new DeteRmInAtIOn methOD FOR COAL metAmORPhISm DeGRee Purpose. Development and approbation of a new method for determining the degree of coal metamorphism by the index of gray shade intensity of macerals for microphotographs of lump sections of coal samples. methodology. Optical spectroscopy using a videooptical complex: MBI-11, HB 200, followed by digital com puter processing (Scope photo software) of microphotographs of coal substance samples upon lump sections. Findings. A new method is proposed for determining the degree of coal substance metamorphism, the essence of which is the use of optical microscopy of lump sections of coal samples, followed by digital processing of the obtained data. The method was tested on coal samples of various ranks-from longflame to anthracite. To characterize the degree of coal metamorphism, a new index of the gray shade intensity of macerals was applied on the photographic images of the lump sections of coal samples microscopically. Correlation of the proposed index with the classical ones of the degree of coal metamorphism-vitrinite reflectance is shown. Originality. For the first time, a digital processing of photographic images of the lump sections of coal samples using a new index of gray shade intensity of macerals was applied to characterize the degree of coal metamorphism. Practical value. The proposed method can be used for practical application in order to assess the degree of coal metamorphism. This method differs by its operability and simplicity from the currently widely used one for determin ing the degree of coal metamorphism by vitrinite reflectance. The method can also be applied to assess the recover ability of coals and calculation of their maceral composition.

This paper reports determining the grayscale intensity of macerals in the coal lump polished sections oriented along and across the layering of three main groups of sub-bituminous, high volatile bituminous, low volatile bituminous coals. All measurements have been performed in white, red, yellow, green, blue light. The influence of all selected factors and most of their combinations on grayscale intensity is reliable; the most pronounced effects are established for the optical filter color and the maceral type. Comparative analysis of the grayscale intensity data array with the spectra of full reflectance in the visible region and the coefficient of diffuse reflection in the white light of fine powders of the same samples has been carried out. Green light yields a very dark image of vitrinite and liptinite with the grayscale intensity approaching zero. In two of the six samples, the reflectance level of inertinite in yellow light is significantly higher than the grayscale intensity of white light. This anomaly is associated with a hypsochromic shift in the inertinite maximum absorption. The approach used is an alternative method for quantifying the relative changes in reflectivity and position of the diffuse spectral minimum without applying a microspectrometer.

The article focuses on a quasistable electrical potential registered on samples of highly-metamorphic and high-ash coal in normal laboratory conditions. The purpose of the study is to determine the possible conditions for the appearance of their effect in the coal and carbon-like argillite and the parameters of its structure. The appearance of an uncompensated charge is not associated with thermoelectric and electrokinetic phenomena and it has not been previously described. Most samples are characterized by an uneven distribution of charges along the surface in the form of a polydomain structure. Polarized samples have a layered coal-mineral structure. The charge magnitude depends on the thickness and density of the layers. In heterogeneous and heterophase substances the Maxwell-Wagner polarization is realized, arising on the boundary layers of dielectric micrograins of various substances, as well as between the areas of one dielectric with an amorphous and crystalline phase. Microinclusions and anthracite layers, which increase the potential ability of mineral components to their own polarization, can be conductors. Charged samples may have a stable, non-compensated monodomain residual charge under constant external conditions, which is characteristic of the electrets. The detected effect can be useful when creating alternative devices accumulating electricity.