Containing epidemic outbreaks by message-passing techniques

The problem of targeted network immunization can be defined as the one of finding a subset of nodes in a network to immunize or vaccinate in order to minimize a tradeoff between the cost of vaccination and the final (stationary) expected infection under a given epidemic model. Although computing the expected infection is a hard computational problem, simple and efficient mean-field approximations have been put forward in the literature in recent years. The optimization problem can be recast into a constrained one in which the constraints enforce local mean-field equations describing the average stationary state of the epidemic process. For a wide class of epidemic models, including the susceptible-infected-removed and the susceptible-infected-susceptible models, we define a message-passing approach to network immunization that allows us to study the statistical properties of epidemic outbreaks in the presence of immunized nodes as well as to find (nearly) optimal immunization sets for a given choice of parameters and costs. The algorithm scales linearly with the size of the graph and it can be made efficient even on large networks. We compare its performance with topologically based heuristics, greedy methods, and simulated annealing

Robust Price of Anarchy for Atomic Games with Altruistic Players

We study the inefficiency of equilibria for various classes of games when players are (partially) altruistic. We model altruistic behavior by assuming that player i's perceived cost is a convex combination of 1-\beta_i times his direct cost and \beta_i times the social cost. Tuning the parameters \beta_i allows smooth interpolation between purely selfish and purely altruistic behavior. Within this framework, we study altruistic extensions of linear congestion games, fair cost-sharing games and valid utility games. We derive (tight) bounds on the price of anarchy of these games for several solution concepts. Thereto, we suitably adapt the smoothness notion introduced by Roughgarden and show that it captures the essential properties to determine the robust price of anarchy of these games. Our bounds reveal that for congestion games and cost-sharing games the worst-case robust price of anarchy increases with increasing altruism, while for valid utility games it remains constant and is not affected by altruism. We also show that the increase in price of anarchy is not a universal phenomenon: for symmetric singleton linear congestion games we derive a bound on the price of anarchy for pure Nash equilibria that decreases as the level of altruism increases. Since the bound is also strictly lower than the robust price of anarchy, it exhibits a natural example in which Nash equilibria are more efficient than more permissive notions of equilibrium

Negotiation Based Resource Allocation to Control Information Diffusion

Study of diffusion or propagation of information over a network of connected entities play a vital role in understanding and analyzing the impact of such diffusion, in particular, in the context of epidemiology, and social and market sciences. Typical concerns addressed by these studies are to control the diffusion such that influence is maximally (in case of opinion propagation) or minimally (in case of infectious disease) felt across the network. Controlling diffusion requires deployment of resources and often availability of resources are socio-economically constrained. In this context, we propose an agent-based framework for resource allocation, where agents operate in a cooperative environment and each agent is responsible for identifying and validating control strategies in a network under its control. The framework considers the presence of a central controller that is responsible for negotiating with the agents and allocate resources among the agents. Such assumptions replicates real-world scenarios, particularly in controlling infection spread, where the resources are distributed by a central agency (federal govt.) and the deployment of resources are managed by a local agency (state govt.). If there exists an allocation that meets the requirements of all the agents, our framework is guaranteed to find one such allocation. While such allocation can be obtained in a blind search methods (such as checking the minimum number of resources required by each agent or by checking allocations between each pairs), we show that considering the responses from each agent and considering allocation among all the agents results in a “negotiation” based technique that converges to a solution faster than the brute force methods. We evaluated our framework using data publicly available from Stanford Network Analysis Project to simulate different types of networks for each agents

Better Vaccination Strategies for Better People

In this paper, we study the vaccination of graphs against the outbreak of infectious diseases, in the following natural model generalizing a model by Aspnes et al.: An infectious disease breaks out at a random node of the graph and propagates along the edges of the graph. Vaccinated nodes cannot be infected, nor pass on the infection, whereas all other nodes do. The decisions on which nodes get vaccinated must be made before the random outbreak location is known. There is a cost associated with vaccination and a different cost with getting infected. In this model, we provide two results. First, we improve the approximation guarantee for finding the best vaccination strategy from O(log 1.5 n) to O(log z) (where z is the support size of the outbreak distribution), by rounding a natural linear program with region-growing techniques. Second, we analyze the impact of autonomy on the part of the nodes: while a benevolent authority may suggest which nodes should be vaccinated, nodes may opt out after being chosen. We analyze the “Price of Opting Out ” in this sense under partially altruistic behavior. Individuals base their decisions on their own cost and the societal cost, the latter scaled by some factor β. If the altruism parameter is β = 0, it is known that the Price of Anarchy and Price of Stability can be Θ(n). We show that with positive altruism, Nash Equilibria may not exist, but the Price of Opting Out is at most 1/β (whereas the Price of Anarchy can remain at Θ(n))