On Cournot-Nash equilibria with exogenous uncertainty

A large body of literature has accumulated which examines how the optimal solution of an agent maximizing the expectation of a real-valued function, depending on a random parameterp and the agent's behaviorx, reacts to perturbations in the first and second moments ofp. Here, by an approximation valid for small uncertainty, we allow many agents and consider their behavior in a Cournot-Nash equilibrium. We also allowp to depend on the behaviors of the participating agents. We apply the analysis to two models, one of a Cournot oligopoly, the other of a cooperative of individuals where there is uncertainty in the return to communal work

Bargaining over a finite set of alternatives

We analyze bilateral bargaining over a finite set of alternatives. We look for “good” ordinal solutions to such problems and show that Unanimity Compromise and Rational Compromise are the only bargaining rules that satisfy a basic set of properties. We then extend our analysis to admit problems with countably infinite alternatives. We show that, on this class, no bargaining rule choosing finite subsets of alternatives can be neutral. When rephrased in the utility framework of Nash (1950), this implies that there is no ordinal bargaining rule that is finite-valued

Prakash and Sertel's theory of non-cooperative equilibria in social systems - twenty years later

Cataloged from PDF version of article.This paper is intended as a companion to the paper 'Existence of non-cooperative equilibria in social systems by Prakash and Sertel (1974b) appearing in this volume. It aims to perform two tasks: (1) to give the reader a glimpse at the literature relevant to the existence of equilibria in social systems as it has developed since the writing of the Prakash and Sertel (PS) paper; and (2) to provide a class of examples illustrating where the PS notions of a social system and the non-cooperative equilibrium of a social system generalize the well-known concepts of games, abstract economies and their associated equilibria, showing how the existence theory of PS even today bears economic results beyond where alternative theories are applicable

Evaluation of apertura piriformis and related cranial anatomical structures through computed tomography: golden ratio

Background: The purpose of study was to evaluate normal morphometric measurements of piriform aperture (PA) by limiting the age range in genders to show the morphometry of the relevant and close proximal cranial structures; and also to investigate whether these are in compliance with the golden ratio. Materials and methods: Our study was performed on 83 (42 female, 41 male) multidetector computed tomography images obtained from patients. A total of 14 morphological measurements were performed including the height of PA, the width of PA and 12 cranial structures; and these measurements were evaluated for compliance with the golden ratio. The differences of 14 parameters between the genders and age groups, and also the interaction of these two factors were analysed. Results: In our morphometric study, significant difference between the genders was found in all measurements except for the distance between vertex and rhinion (V~Rh), between rhinion and right foramen supraorbitalis (Rh~FSOR), between rhinion and left FSO (Rh~FSOL), and the width of PA on the level between the right and left foramen infraorbitalis (PAW~FIO) with the difference valid for both age subgroups (p < 0.05). When the differences between the age subgroups were evaluated, there was significant difference only at the widest distance of cranium (CW; p = 0.008); and it was observed that the average has increased with age in both genders. When the golden ratio was examined, the ratio of the distance between anterior nasal spine and nasion to the height of piriform aperture (NSA~N:PAH) was found to be within the limits of the golden ratio in males (p = 0.074). No golden ratio has been found in females. Conclusions: In our study, significant differences were detected between genders in all parameters of PA and in some parameters of the close cranial structures in the age group we examined. The effect of age was detected only in the CW parameter, and the PA and close cranial structures were not affected. In our study, the averages of the morphometric measurements of 13 parameters of young adults were determined. The PA and surrounding cranial structures are important for the area and related surgical procedures; however, gender differences must be considered in this respect. In addition to this, in the PA, which is the anterior limit of the skeletal nose in males, the NSA~N:PAH ratio having the ideal golden ratio limits is valuable in aesthetical terms and due to its position of the PA in the face

Land use and land cover mapping using deep learning based segmentation approaches and VHR Worldview-3 images

Deep learning-based segmentation of very high-resolution (VHR) satellite images is a significant task providing valuable information for various geospatial applications, specifically for land use/land cover (LULC) mapping. The segmentation task becomes more challenging with the increasing number and complexity of LULC classes. In this research, we generated a new benchmark dataset from VHR Worldview-3 images for twelve distinct LULC classes of two different geographical locations. We evaluated the performance of different segmentation architectures and encoders to find the best design to create highly accurate LULC maps. Our results showed that the DeepLabv3+ architecture with an ResNeXt50 encoder achieved the best performance for different metric values with an IoU of 89.46%, an F-1 score of 94.35%, a precision of 94.25%, and a recall of 94.49%. This design could be used by other researchers for LULC mapping of similar classes from different satellite images or for different geographical regions. Moreover, our benchmark dataset can be used as a reference for implementing new segmentation models via supervised, semi- or weakly-supervised deep learning models. In addition, our model results can be used for transfer learning and generalizability of different methodologies

The basic approval voting game

We survey results about Approval Voting obtained within the standard framework of game theory. Restricting the set of strategies to undominated and sincere ballots does not help to predict Approval Voting outcomes, which is also the case under strategic equilibrium concepts such as Nash equilibrium and its usual refinements. Strong Nash equilibrium in general does not exist but predicts the election of a Condorcet winner when one exists