Evolutionary Poisson Games for Controlling Large Population Behaviors

Emerging applications in engineering such as crowd-sourcing and (mis)information propagation involve a large population of heterogeneous users or agents in a complex network who strategically make dynamic decisions. In this work, we establish an evolutionary Poisson game framework to capture the random, dynamic and heterogeneous interactions of agents in a holistic fashion, and design mechanisms to control their behaviors to achieve a system-wide objective. We use the antivirus protection challenge in cyber security to motivate the framework, where each user in the network can choose whether or not to adopt the software. We introduce the notion of evolutionary Poisson stable equilibrium for the game, and show its existence and uniqueness. Online algorithms are developed using the techniques of stochastic approximation coupled with the population dynamics, and they are shown to converge to the optimal solution of the controller problem. Numerical examples are used to illustrate and corroborate our results

Large-scale games in large-scale systems

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean field limit and dynamical system viewpoints. Under regularity assumptions and specific time-scaling techniques, the evolution of the mean field limit can be expressed in terms of deterministic or stochastic equation or inclusion (difference or differential). In this paper, we overview recent advances of large-scale games in large-scale systems. We focus in particular on population games, stochastic population games and mean field stochastic games. Considering long-term payoffs, we characterize the mean field systems using Bellman and Kolmogorov forward equations.Comment: 30 pages. Notes for the tutorial course on mean field stochastic games, March 201

Opinion Dynamics in Social Networks through Mean-Field Games

Emulation, mimicry, and herding behaviors are phenomena that are observed when multiple social groups interact. To study such phenomena, we consider in this paper a large population of homogeneous social networks. Each such network is characterized by a vector state, a vector-valued controlled input and a vector-valued exogenous disturbance. The controlled input of each network is to align its state to the mean distribution of other networks’ states in spite of the actions of the disturbance. One of the contributions of this paper is a detailed analysis of the resulting mean field game for the cases of both polytopic and L2 bounds on controls and disturbances. A second contribution is the establishment of a robust mean-field equilibrium, that is, a solution including the worst-case value function, the state feedback best-responses for the controlled inputs and worst-case disturbances, and a density evolution. This solution is characterized by the property that no player can benefit from a unilateral deviation even in the presence of the disturbance. As a third contribution, microscopic and macroscopic analyses are carried out to show convergence properties of the population distribution using stochastic stability theory

Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems

Mixed integer optimal compensation deals with optimization problems with integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls could lead to intractability in problems of large dimensions. To address this challenge, we introduce a decomposition method which turns the original n-dimensional optimization problem into n independent scalar problems of lot sizing form. Each of these problems can be viewed as a two-player zero-sum game, which introduces some element of conservatism. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon, a step that mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent system problem, where each agent seeks to compensate a combination of an exogenous signal and the local state average. We discuss a large population mean-field type of approximation and extend our study to opinion dynamics in social networks as a special case of interest

Individual-based modeling and predictive simulation of fungal infection dynamics

The human-pathogenic fungus Aspergillus fumigatus causes life-threatening infections in immunocompromised patients and poses increasing challenges for the modern medicine. A. fumigatus is ubiquitously present and disseminates via small conidia over the air of the athmosphere. Each human inhales several hundreds to thousands of conidia every day. The small size of conidia allows them to pass into the alveoli of the lung, where primary infections with A. fumigatus are typically observed. In alveoli, the interaction between fungi and the innate immune system of the host takes place. This interaction is the core topic of this thesis and covered by mathematical modeling and computer simulations. Since in vivo laboratory studies of A. fumigatus infections under physiological conditions is hard to realize a modular software framework was developed and implemented, which allows for spatio-temporal agent-based modeling and simulation. A to-scale A. fumigatus infection model in a typical human alveolus was developed in order to simulate and analyze the infection scenario under physiological conditions. The process of conidial discovery by alveolar macrophages was modeled and simulated with different migration modes and different parameter configurations. It could be shown that chemotactic migration was required to find the pathogen before the onset of germination. A second model took advantage of evolutionary game theory on graphs. Here, the course of infection was modeled as a consecutive sequence of evolutionary games related to the complement system, alveolar macrophages and polymorphonuclear neutrophilic granulocytes. The results revealed a central immunoregulatory role of alveolar macrophages. In the case of high infectious doses it was found that the host required fully active phagocytes, but in particular a qualitative response of quantitatively sufficient polymorphonuclear neutrophilic granulocytes.Der human-pathogene Schimmelpilz Aspergillus fumigatus verursacht tödliche Infektionen und Erkrankungen vorrangig bei immunsupprimierten Patienten und stellt die moderne Medizin vor zunehmende Herausforderungen. A. fumigatus ist ubiquitär präsent und verbreitet sich über sehr kleine Konidien durch Luftströmungen in der Athmosphäre. Mehrere Hundert bis Tausende dieser Konidien werden täglich durch jeden Menschen eingeatmet. Die geringe Größe der infektiösen Konidien erlauben es dem Pilz bis in die Alveolen der Lunge des Wirtes vorzudringen,in denen eine Primärinfektionen mit A. fumigatus am häufigsten stattfindet. Die Alveolen sind der zentrale Schauplatz der Interaktion zwischen dem Pilz und dem angeborenen Immunsystem, welche Gegenstand dieser Arbeit ist. Diese Interaktion wird mit Hilfe von mathematischen Modellen und Computersimulationen nachgestellt und untersucht, da eine A. fumigatus Infektion im Nasslabor in vivo unter physiologischen Bedingungen nur sehr schwer realisiert werden kann. Als Grundlage für dieses Vorhaben wurde ein modulares Software-Paket entwickelt, welches agentenbasierte Modellierung und entsprechende Simulationen in Raum und Zeit ermöglicht. Ein maßstabsgetreues mathematisches Infektionsmodell in einer typischen menschlichen Alveole wurde entwickelt und die Suchstrategien von Alveolarmakrophagen unter der Berücksichtigung verschiedener Parameter wie Migrationsgeschwindigkeit, dem Vorhandensein von Chemokinen, dessen Diffusion und Chemotaxis untersucht. Es zeigte sich, dass Chemotaxis, notwendig ist, um die Konidie rechtzeitig finden zu können. In einem weiteren Modell, welches auf das Konzept evolutionärer Spieltheorie auf Graphen zurückgegriff, wurde der Infektionsverlauf als aufeinanderfolgende Serie evolutionärer Spiele mit dem Komplementsystem, Alveolarmakrophagen und Neutrophilen nachgestellt. Aus den Simulationsergebnissen konnte eine zentrale immunregulatorische Rolle von Alveolarmakrophagen entnommen werden

Multi-Scale Modeling of the Innate Immune System: A Dynamic Investigation into Pathogenic Detection

Having a well-functioning immune system can mean the difference between a mild ailment and a life-threatening infection; however, predicting how a disease will progress has proven to be a significant challenge. The dynamics driving the immune system are governed by a complex web of cell types, signaling proteins, and regulatory genes that have to strike a balance between disease elimination and rampant inflammation. An insufficient immune response will induce a prolonged disease state, but an excessive response will cause unnecessary cell dead and extensive tissue damage. This balance is usually self-regulated, but medical intervention is often necessary to correct imbalances. Unfortunately, these therapies are imperfect and accompanied by mild to debilitating side-effects caused by off-target effects. By developing a detailed understanding of the immune response, the goal of this dissertation is to predict how the immune system will respond to infection and determine how new potential therapies could overcome these threats. Computational modeling provides an opportunity to synthesize current immunological observations and predict response outcomes to pathogenic infections. When coupled with experimental data, these models can simulate signaling pathway dynamics that drive the immune response, incorporate regulatory feedback mechanisms, and model inherent biological noise. Taken together, computational modeling can explain emergent behavior that cannot be determined from experiment alone. This dissertation will unitize two computational modeling techniques: ordinary differential equations (ODEs) and agent-based modeling (ABMs). Ultimately, they are combined in a novel way to model cellular immune responses across multiple length scales, creating a more accurate representation of the pathogenic response. TLR4 and cGAS signaling are prominent in a number of diseases and dysregulations including---but not limited to---autoimmunity, cancer, HIV, HSV, tuberculosis, and sepsis. These two signaling pathways are so prevalent because they are activated extremely early and help drive the downstream immune signaling. Modeling how cells dynamically regulate these pathways is critical for understanding how diseases circumvent feedback mechanisms and how new therapies can restore immune function to combat disease progression. By using ODE and ABM techniques, these studies aim to incrementally expand our knowledge of innate immune signaling and understand how feedback mechanisms control disease severity

A statistical mechanics approach to cancer dynamics: a model for multiple myeloma bone disease

L’utilizzo di modelli matematici sta assumendo un ruolo sempre più centrale nella ricerca oncologica. La complessità del cancro ha stimolato gruppi di ricerca interdisciplinare nello sviluppo di modelli quantitativi per rispondere alle numerose domande aperte che riguardano l’insorgenza, la progressione, la diagnosi, la risposta al trattamento terapeutico e l’acquisizione della resistenza ai farmaci dei tumori. La varietà di approcci matematico-fisici ben si adatta allo studio di una materia così eterogenea. In questo lavoro presentiamo innanzitutto gli aspetti biologico-clinici che caratterizzano il cancro, per poi introdurre i modelli che sono stati utilizzati per comprenderli. Abbiamo preso in considerazione il caso del mieloma multiplo, una neoplasia che colpisce le plasmacellule. In particolare proponiamo un modello matematico per lo studio della patogenesi delle lesioni ossee causate dal mieloma. L’insorgere di questo tumore rompe l’equilibrio fisiologico del tessuto osseo, causando un aumento dell’attività degli osteoclasti ed una diminuzione dell’attività degli osteoblasti, fenomeni che, combinati, comportano le caratteristiche fratture. Abbiamo optato per un approccio di tipo ecologico, in cui i diversi tipi di cellule sono considerati come specie interagenti in meccanismi di cooperazione o sfruttamento. Questo fenomeno è stato modellizzato all’interno della classe degli Interacting Particle Systems, che sono sistemi di processi di Markov localmente interagenti. Abbiamo inizialmente studiato il caso dell’osso sano per poi passare a quello in cui sono presenti le cellule del mieloma. Infine, abbiamo svolto simulazioni per delineare l’evoluzione nel tempo delle specie cellulari. Abbiamo riservato una particolare attenzione alla definizione dei parametri del modello: non solo essi ci permettono di riprodurre diversi stadi e forme del mieloma, ma possono descrivere l’intervento terapeutico sul tumore, costituendo un nuovo strumento per la ricerca oncologica

Large networks of dynamic agents: Consensus under adversarial disturbances

This paper studies interactions among homogeneous social groups within the framework of large population games. Each group is represented by a network and the behavior described by a two-player repeated game. The contribution is three-fold. Beyond the idea of providing a novel two-level model with repeated games at a lower level and population games at a higher level, we also establish a mean field equilibrium and study state feedback best-response strategies as well as worst-case adversarial disturbances in that context. © 2012 IEEE