A note on the paper ‘On dynamical multi-team Cournot game in exploitation of a renewable resource’

In a recent paper (Asker, 2007) [1] a dynamic Cournot oligopoly game is proposed and it is claimed that this model represents competition among firms that exploit a common access natural resource. According to the author’s claim, the feature that relates the model with renewable natural resource harvesting is given by the presence of a particular cost function where the total cost of each fisherman is proportional to the square of the own quantity of harvesting and inversely proportional to the total harvesting quantity. In contrast, the usual function used in the literature on the exploitation of natural resources (such as fisheries) is inversely proportional to the available resource stock, and not to the total harvesting. This, in some sense, assumes exactly the opposite (as the available resource is inversely proportional to the total harvesting). So, we believe that the paper (Asker, 2007) [1] contains an error which is probably due to a misunderstanding or a misreading and misinterpretation of the (well-established) literature on bioeconomic modelling, but nevertheless misleading to researchers interested in bioeconomic modelling. The aim of this short note is to explain the mistake and to summarize the correct derivation and interpretation of the cost function. Our goal is to avoid the propagation of a subtle (but nevertheless misleading) error.     

Is There Still a Place for Independent Research into Issues of Public Policy in England and Wales in the 1980's? A Case Study from the Field of Health Care: Modelling Hospital Costs

This paper is concerned with the viability of independent research into issues of public policy in a climate which is becoming increasingly hostile. The general argument is illustrated by one specific example relating to the development of models of hospital inpatient costs in the National Health Service. In a recent publication by staff of the Operational Research Service of the Department of Health and Social Security a model (denoted the C-G-N model) of hospital costs is put forward. However, no mention is made of an alternative model (denoted the A-B model) published some two years previously and we have therefore decided to compare the two models in terms of general structure, fit to the available observational data and applicability. It is shown that the C-G-N model was applied by its authors in a form which involves an heteroscedastic residual error term. When this model is fitted to a representative data set, with an appropriate weighting factor which produces homoscedastic errors, substantial differences are found in the corresponding parameter estimates. The C-G-N model in its original and modified versions is then compared with the A-B model, and it is shown that the latter is more parsimonious in terms of parameters, is applicable to a wider range of types of hospital and fits the available empirical data somewhat better than either version of the former. Furthermore, there are substantial differences in the conclusions which might be drawn on the basis of the various models in several important classes of application. An outline is given of a more complex model, denoted the component model, which incorporates features of both the C-G-N and A-B models, provides a better fit to the empirical data than either and has a structure which is more satisfactory for a wide range of applications.     

A note on the paper: “Nonlinear integral equations with new admissibility types in <Emphasis Type="Italic">b</Emphasis>-metric spaces”

In this paper we consider, discuss and slightly complement recent fixed point results for mappings in b-metric spaces established by Sintunavarat (J Fixed Point Theory Appl 18:397–416, 2016). Thus, all our results are with shorter proofs. In addition, an application to integral equations is given to illustrate the usability of our approach.