Nash equilibrium

Towards a Nash game strategy approach to blind image deconvolution: a fractional-order derivative variational framework

Image restoration is a critical process aimed at recovering degraded images, often impacted by factors including motion blur, sensor blurring, defocused photography, optical aberrations, atmospheric distortions, and noise-induced blur.  The inherent challenge lies in the typical scenario where both the original image and the blur kernel (Point Spread Function, PSF) are unknown.  This restorative process finds applications in various fields, including sensing, medical imaging, astronomy, remote sensing, and criminal investigations.  This paper introduces an innovative ap

Architecture and Formal-mathematical Justification of Generative Adversarial Networks

The purpose of the work is to analyze the features of generative adversarial networks. The object of research is the process of machine learning algorithmization. The subject of the research is mathematical methods used in the generation of semantically related text. This article explores the architecture and mathematical justification of such a type of generative models as generative adversarial networks. Generative adversarial networks are a powerful tool in the field of artificial intelligence, capable of generating realistic data, including photos, videos, sounds, etc.

Image retrieval using Nash equilibrium and Kalai-Smorodinsky solution

In this paper, we propose a new formulation of Nash games for solving a general multi-objectives optimization problems.  The objective of this approach is to split the optimization variables, allowing us to determine numerically the strategies between two players.  The first player minimizes his function cost using the variables of the first table P and the second player, using the second table Q.  The original contribution of this work concerns the construction of the two tables of allocations that lead to a Nash equilibrium on the Pareto front.  The second proposition of this paper is to

Modeling behavioral strategies competitive companies in the market of tourist service

We have considered the peculiarities of mathematical models construction, which describe different strategies of the competitive companies` behavior at the market of tourist services. We have found that at the market of service provision any subject must act in accordance with the established rules of behavior and interaction of participants of this market. We have developed mathematical models of behavioral strategies and interaction between two competing companies when providing one travel service.