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

Bayesian Persuasion for Containing SIS Epidemic with Asymptomatic Infection

We investigate the strategic behavior of a large population of agents who decide whether to adopt a costly partially effective protection or remain unprotected against the susceptible-infected-susceptible epidemic. In contrast with most prior works on epidemic games, we assume that the agents are not aware of their true infection status while making decisions. We adopt the Bayesian persuasion framework where the agents receive a noisy signal regarding their true infection status, and maximize their expected utility computed using the posterior probability of being infected conditioned on the received signal. We completely characterize the stationary Nash equilibrium of this setting, and identify conditions under which partial information disclosure leads to a smaller proportion of infected individuals at the equilibrium compared to full information disclosure, and vice versa

Economic Development and HIV/AIDS Prevalence

There is a strong negative relationship between economic development and HIV/AIDS prevalence throughout the world. However in Sub-Saharan Africa where the epidemic is worst, this relationship does not hold. Some of the wealthier countries in this region have some of the highest rates of HIV/AIDS prevalence in the world. In order to explain these observations, we set up a two-period model where individuals derive utility from consumption and sexual encounters. Those who expect their second-period consumption to be sufficiently low may engage in unsafe sex, despite the possibility of contracting HIV, if it provides higher instantaneous utility. We show that poorer countries will feature a higher share of the population engaging in unsafe sex, and therefore a higher prevalence of HIV. In economies where the external effect of human capital is high, additional equilibria exist in which even wealthier individuals choose unsafe sex if they expect a large share of the population to do so. This is because if many people engage in unsafe sex, there will be a lower level of aggregate human capital (due to AIDS deaths) and hence lower second-period income, and consumption. Economies featuring multiple equilibria may select one in which a large fraction of the population is engaged in unsafe sex because of beliefs about the transmission of HIV/AIDS. Nous documentons une forte relation négative entre le taux de prévalence du VIH/SIDA et le niveau de développement économique au niveau mondial. Cependant, cette relation ne tient pas en Afrique Sub-Saharienne qui est paradoxalement la région la plus touchée par le VIH/SIDA. Plusieurs pays parmi les plus riches de cette région ont des taux de prévalence très élevés. Afin d'expliquer ce phénomène, nous construisons un modèle où chaque individu vit pendant deux périodes et où son utilité est fonction de sa consommation et de son activité sexuelle. Ceux qui s'attendent à obtenir un revenu relativement faible pendant le reste de leur vie peuvent décider d'avoir des rapports sexuels non protégés en dépit du risque de contracter le VIH. Ce choix est motivé par l'utilité instantanée plus élevée qu'ils obtiennent en ayant un rapport sexuel sans préservatif. Nous démontrons que le taux de prévalence du VIH/SIDA devrait être plus élevé dans les pays pauvres car une plus grande part de la population choisirait d'avoir des rapports sexuels non protégés. Cependant, il peut exister des équilibres multiples dans les économies où les externalités associées au capital humain sont élevées. Dans ce cas, même ceux qui sont relativement riches peuvent choisir d'avoir des relations sexuelles non protégées s'ils anticipent qu'une part importante de la population ferait de même. Si telles sont les anticipations, alors le niveau de capital humain anticipé est faible en raison de la mortalité due au SIDA. Ceci a un effet négatif sur le revenu et la consommation futurs. Ceci explique pourquoi même ceux qui sont relativement riches peuvent choisir d'avoir des relations sexuelles sans préservatif. Si les conditions sont requises pour qu'il y ait des équilibres multiples dans une économie, alors l'équilibre où la prévalence du VIH/SIDA est le plus élevé pourrait être choisi en raison des croyances sur les modes de transmission du VIH/SIDA.HIV/AIDS, human-capital externalities, Sub Saharan Africa, VIH/SIDA, capital humain, Afrique Sub-Saharienne

Inoculation strategies for bounded degree graphs

We analyze a game-theoretic abstraction of epidemic containment played on an undirected graph $G$: each player is associated with a node in $G$ and can either acquire protection from a contagious process or risk infection. After decisions are made, an infection starts at a random node $v$ and propagates through all unprotected nodes reachable from $v$. It is known that the price of anarchy (PoA) in $n$-node graphs can be as large as $\Theta(n)$. Our main result is a tight bound of order $\sqrt{n\Delta}$ on the PoA, where $\Delta$ is the maximum degree of the graph. We also study additional factors that can reduce the PoA, such as higher thresholds for contagion and varying the costs of becoming infected vs. acquiring protection

Global and regional public goods: a prognosis for collective action

This paper applies modern concepts from the theory of public goods to indicate why progress has been made with respect to some global and regional public goods (for example, cutting sulphur emissions) but not with respect to others (for example, cutting greenhouse gases). Factors promoting collective action at the transnational level include the removal of uncertainty, a high share of nation-specific benefits, a limited number of essential participants and the presence of an influential leader nation. The impact of public good aggregation technologies on the future provision of transnational public goods is related to the trend in world-wide income inequality. Principles are presented for designing supranational structures for addressing transnational public good problems.