A Game theoretic approach for competition over visibility in social networks

Social Networks have known an important evolution in the last few years. These structures, made up of individuals who are tied by one or more specific types of interdependency, constitute the window for members to express their opinions and thoughts by sending posts to their own walls or others' timelines. Actually, when a content arrives, it's located on the top of the timeline pushing away older messages. This situation causes a permanent competition over visibility among subscribers who jump on opponents to promote conflict. Our study presents this competition as a non-cooperative game; each source has to choose frequencies which assure its visibility. We model it, exploring the theory of concave games, to reach a situation of equilibrium; a situation where no player has the ultimate ability to deviate from its current strategy. We formulate the named game, then we analyze it and prove that there is exactly one Nash equilibrium which is the convergence of all players' best responses. We finally provide some numerical results, taking into consideration a system of two sources with a specific frequency space, and analyze the effect of different parameters on sources' visibility on the walls of social networks

A Non-cooperative Game-Theoretic Framework for Sponsoring Content in the Internet Market

Data traffic demand over the Internet is increasing rapidly, and it is changing the pricing model between internet service providers (ISPs), content providers (CPs) and end users. One recent pricing proposal is sponsored data plan, i.e., when CP negotiates with the ISP on behalf of the users to remove the network subscription fees so as to attract more users and increase the number of advertisements. As such, a key challenge is how to provide proper sponsorship in the situation of complex interactions among the telecommunication actors, namely, the advertisers, the content provider, and users. To answer those questions, we explore the potential economic impacts of this new pricing model by modeling the interplay among the advertiser, users, and the CPs in a game theoretic framework. The CP may have either a subscription revenue model (charging end-users) or an advertisement revenue model (charging advertisers). In this work, we design and analyze the interaction among CPs having an advertisement revenue as a non-cooperative game, where each CP determines the proportion of data to sponsor and a level of credibility of content. In turn, the end-users demand for the content of a CP depends not only on their strategies but also upon those proposed by all of its competitors. Through rigorous mathematical analysis, we prove the existence and uniqueness of the Nash equilibrium. Based on the analysis of the game properties, we propose an iterative algorithm, which guarantees to converge to the Nash equilibrium point in a distributed manner. Numerical investigation shows the convergence of a proposed algorithm to the Nash equilibrium point and corroborates the fact that sponsoring content may improve the CPs outcome

A game theoretic framework for controlling the behavior of a content seeking to be popular on social networking sites

Over the years, people are becoming more dependent on Online Social Networks, through whom they constitute various sorts of relationships. Furthermore, such areas present spaces of interaction among users; they send more messages and posts showing domains they are interested in to guarantee the level of their popularity. This popularity depends on its own rate, the number of comments the posted topic gets but; also on the cost a user has to pay to accomplish his task on this network. However, the selfish behavior of those subscribers is the root cause of competition over popularity among those users. In this paper, we aim to control the behavior of a social networks users who try their best to increase their popularity in a competitive manner. We formulate this competition as a non-cooperative game. We porpose an efficient game theoretical model to solve this competition and find a situation of equilibrium for the said game

On the Controllability of a Class of Discrete Distributed Systems

We consider a class of linear discrete-time systems controlled by a continuous time input. Given a desired final state x d , we investigate the optimal control which steers the system, with a minimal cost, from an initial state x0 to x d . We consider both discrete distributed systems and finite dimensional ones. We use a method similar to the Hilbert Uniqueness Method (HUM) to determine the control and the Galerkin method to approximate it, we also give an example to illustrate our approach

Joint Beacon Power and Beacon Rate Control Based on Game Theoretic Approach in Vehicular Ad Hoc Networks

In vehicular ad hoc networks (VANETs), each vehicle broadcasts its information periodically in its beacons to create awareness for surrounding vehicles aware of their presence. But, the wireless channel is congested by the increase beacons number, packet collision lost a lot of beacons. This paper tackles the problem of joint beaconing power and a beaconing rate in VANETs. A joint utilitybased beacon power and beacon rate game are formulated as a non-cooperative game and a cooperative game. A three distributed and iterative algorithm (Nash Seeking Algorithm, Best Response Algorithm, Cooperative Bargaining Algorithm) for computing the desired equilibrium is introduced, where the optimal values of each vehicle beaconing power and beaconing rate are simultaneously updated at the same step. Extensive simulations show the convergence of a proposed algorithm to the equilibrium and give some insights on how the game parameters may vary the game outcome. It is demonstrated that the Cooperative Bargaining Algorithm is a fast algorithm that converges the equilibrium

Existence and Uniqueness of Weak Solutions for a New Class of Convex Optimization Problems Related to Image Analysis

This paper proposes a new anisotropic diffusion model in image restoration that is understood from a variational optimization of an energy functional. Initially, a family of new diffusion functions based on cubic Hermite spline is provided for optimal image denoising. After that, the existence and uniqueness of weak solutions for the corresponding Euler–Lagrange equation are proven in an appropriate functional space, and a consistent and stable numerical model is also shown. We complement this work by illustrating some experiments on different actual brain Magnetic Resonance Imaging (MRI) scans, showing the proposed model’s impressive results

Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis

This paper establishes the existence and uniqueness of weak solutions for the initial-boundary value problem of anisotropic nonlinear diffusion partial differential equations related to image processing and analysis. An implicit iterative method combined with a variational approach has been applied to construct approximate solutions for this problem. Then, under some a priori estimates and a monotonicity condition, the existence of unique weak solutions for this problem has been proven. This work has been complemented by a consistent and stable approximation scheme showing its great significance as an image restoration technique

Discounted Markov Decision Processes with Constrained Costs: the decomposition approach

In this paper we consider a constrained optimization of discrete time Markov Decision Processes (MDPs) with finite state and action spaces, which accumulate both a reward and costs at each decision epoch. We will study the problem of finding a policy that maximizes the expected total discounted reward subject to the constraints that the expected total discounted costs are not greater than given values. Thus, we will investigate the decomposition method of the state space into the strongly communicating classes for computing an optimal or a nearly optimal stationary policy. The discounted criterion has many applications in several areas such that the Forest Management, the Management of Energy Consumption, the finance, the Communication System (Mobile Networks) and the artificial intelligence

Predicting Student Success Using Big Data and Machine Learning Algorithms

The prediction of student performance, allows teachers to track student results to react and make decisions that affect their learning and performance, given the importance of monitoring students to fight against academic failure. We realized a system of the prediction of academic success and failure of the students, which is the overall result and the goal of the educational system. We used the personal information of the students, the academic evaluation, the activities of the students in VLE, ​​Psychological, the student environment, and we added practical work and homework, mini projects, and the number of student absences which gives a vision of the quality of the student. Then we applied the methods of artificial intelligence and educational Data mining such as KNN, C4.5 and SVM for the prediction of the academic success of students, but these methods are not sufficient given the progressive number of students, specialties, learning methods and the diversity of data sources as well as student data processing time. To solve this problem, Big Data technology was used to distribute the processing in order to minimize the execution time without losing the efficiency of the algorithms used. In this system we cleaned the data and then applied the property selection algorithms to find the useful properties in order to improve the algorithm prediction rate and also to reduce the execution time. Finally, we stored the data in HDFS and we applied the classification algorithms for the prediction of student success using MAPREDUCE. We compared the results before and after the use of big data and we found that the results after the use of Big Data are very good at execution time and we arrived at a recognition rate of 87.32% by the SVM algorithm

Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem

In many references, both the ill-posed and inverse boundary value problems are solved iteratively. The iterative procedures are based on firstly converting the problem into a well-posed one by assuming the missing boundary values. Then, the problem is solved by using either a developed numerical algorithm or a conventional optimization scheme. The convergence of the technique is achieved when the approximated solution is well compared to the unused data. In the present paper, we present a different way to solve an ill-posed problem by applying the localized and space-time localized radial basis function collocation method depending on the problem considered and avoiding the iterative procedure. We demonstrate that the solution of certain ill-posed and inverse problems can be accomplished without iterations. Three different problems have been investigated: problems with missing boundary condition and internal data, problems with overspecified boundary condition, and backward heat conduction problem (BHCP). It has been demonstrated that the presented method is efficient and accurate and overcomes the stability analysis that is required in iterative techniques