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We consider two neighbouring countries in which a pandemic disease spreads. Countries face a trade-off between the social costs of the epidemic diffusion and the monetary costs in order to avoid the insurgence of pandemics. However, due to migration of people across countries, the treatment efforts by one country generate a positive externality for the neighbouring country. Both countries can negotiate...
Companies or users that want to do advertising on Online Social Networks, need to know in which News Feed it would be more efficient to post, at what time of day the posts would have more visibility and which topic of message they should choose to reach popularity. We propose to answer these questions with the help of the Routing Game Theory, which considers a finite number of players and splittable...
The Colonel Blotto game, proposed by Borel in 1921, is a fundamental model of strategic resource allocation. Two players allocate an exogenously given amount of resources to a fixed number of battlefields with given values. Each battlefield is then won by the player who allocated more resources to it, and each player maximizes the aggregate value of battlefields he wins. This game allows modeling...
Online advertisement through social media is studied in this paper. We describe the combined effect of two mechanisms: the acceleration service offered by online media platforms and the effect of content sharing which occurs in parallel over multiple online channels. In particular, the latter operates by reinforcing the effect of acceleration and may ultimately determine the viral diffusion of the...
We study a local majority algorithm, with two opinions, where nodes poll a subset of their neighbours and update their opinion to the opinion of the majority of the polled neighbours. We derive a condition on the number of neighbours to poll in order to ensure that the nodes end up in the state that was initially held by the majority of nodes. We also derive the time it takes the system to reach consensus...
A distributed framework is considered for resource management in cooperative but distributed peer-to-peer networks, whose aim is a kind of one-versus-rest tit-for-tat (reciprocity), so that the delays experienced by any given peer's messages in the rest of the network are proportional to those experienced by others' messages at that peer. In a Jackson network setting, we describe a novel solution...
We first study a one-dimensional optimal control problem with two controlled different dynamics in two half-lines. This may represent a two-edges node of a network on which we are controlling an evolution with different dynamics on different edges. By the point of view of the dynamic programming, and of the corresponding Hamilton-Jacobi-Bellman equation, the discontinuity of the dynamics at the node...
We study the design of optimal controllers for virus spread dynamics over undirected networks. The network designer is capable of controlling the curing rates of the nodes, and his objective is to reduce infection across the network at minimum cost. We employ Pontryagin's maximum principle to study the switching behavior of optimal controllers. Further, we propose two static control laws and identify...
We study a mean field approximation of the M/M/∞ queuing system. The problem we deal with is quite different from standard games of congestion as we consider the case in which higher congestion results in smaller costs per user. This is motivated by a situation in which some TV show is broadcast so that the same cost is needed no matter how many users follow the show. Using a mean-field approximation,...
An important scenario for smart grids which encompass distributed electrical networks is given by the simultaneous presence of aggregators and individual consumers. In this work, an aggregator is seen as an entity (a coalition) which is able to manage jointly the energy demand of a large group of consumers or users. More precisely, the demand consists in charging an electrical vehicle (EV) battery...
In this paper, we investigate positioning on the mobile market of a Mobile Virtual Network operators (MVNO). We take into account a market segmentation based on brand appeal and look for assumptions that make the the Mobile Virtual Operator (MNO) share the market with the MVNO through the computation of Nash Equilibria (NE).
Log-linear learning algorithm applied to the class of potential games has been proven to converge to system optimal states when these states coincide with potential function maximizers. A theoretical analysis of the algorithm based on the properties of time-inhomogeneous Markov chains provides the method to choose an algorithm parameter guaranteeing the convergence. In this work, we characterize the...
In this paper, we propose an aperiodic formulation of Distributed Model Predictive Control for the cooperation of multi-agent systems under additive bounded disturbances. In the proposed method, each agent solves an Optimal Control Problem only when certain control performances cannot be guaranteed according to certain triggering rules. This could lead to the reduction of energy consumption and the...
This paper proposes a communication-efficient distributed algorithm for solving linear algebraic equations of the form Ax = b among a network of m > 1 agents. Each agent knows only a subset of the rows of the partitioned matrix [A b] and recursively updates its estimate of a solution by utilizing information received only from its neighbors. Neighbor relations are characterized by a time-dependent...
In this paper, we consider the problem of assigning heterogeneous customers to a discriminatory processor sharing (DPS) system with M service classes. A type of a customer is determined by its cost per unit waiting time. In the first part of this paper, we consider the problem of optimally assigning the heterogeneous customers to the service classes to minimize a social cost function. We show that...
In this paper, we characterize the revision sets in different variants of the best response algorithm that guarantee convergence to pure Nash Equilibria in potential games. We prove that if the revision protocol is separable (to be defined in the paper), then the greedy version as well as smoothed versions of the algorithm converge to pure Nash equilibria. If the revision protocol is not separable,...
A unique feature of the botnet security threat is the highly distributed, decentralized network of victims whose compromised computers make up the botnet. These victims are not always the intended target of botnet attacks, yet they play a critical role in the functionality of the botnet. We examine a local mean field game between the operator of a botnet (bat master) and the decentralized, legitimate...
Vehicular networks get high attention nowadays: they are expected to provide both road-safety and entertainment services to mobile users owning a suitable equipment. This new market may attract a number of Internet access providers, aiming to increase their profits by proposing new services. In this work we consider Vehicle to Infrastructure (V2I) communication scenarios, where users pay flat prices...
We address dynamical systems of agents driven by attraction and repulsion forces modelling cohesion and collision avoidance. When the total energy, which is composed of a kinetic part and a geometrical part describing the balance between attraction and repulsion forces, is below a certain threshold, then it is known that the agents will converge to a dynamics where mutual space confinement is guaranteed...
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