Ashish R. Hota

Fragility of the commons under prospect-theoretic risk attitudes

We study a common-pool resource game where the resource experiences failure with a probability that grows with the aggregate investment in the resource. To capture decision making under such uncertainty, we model each players risk preference according to the value function from prospect theory. We show the existence and uniqueness of a pure Nash equilibrium when the players have heterogeneous risk preferences and under certain assumptions on the rate of return and failure probability of the resource. Greater competition, vis-a-vis the number of players, increases the failure probability at the Nash equilibrium; we quantify this effect by obtaining bounds on the ratio of the failure probability at the Nash equilibrium to the failure probability under investment by a single user. We further show that heterogeneity in attitudes towards loss aversion leads to higher failure probability of the resource at the equilibrium.

Interdependent Security Games on Networks Under Behavioral Probability Weighting

We consider a class of interdependent security games on networks where each node chooses a personal level of security investment. The attack probability experienced by a node is a function of her own investment and the investment by her neighbors in the network. Most of the existing work in these settings considers players who are risk neutral. In contrast, studies in behavioral decision theory have shown that individuals often deviate from risk-neutral behavior while making decisions under uncertainty. In particular, the true probabilities associated with uncertain outcomes are often transformed into perceived probabilities in a highly nonlinear fashion by the users, which then influence their decisions. In this paper, we investigate the effects of such behavioral probability weightings by the nodes on their optimal investment strategies and the resulting security risk profiles that arise at the Nash equilibria of interdependent network security games. We characterize graph topologies that achieve the largest and smallest worst case average attack probabilities at Nash equilibria in Total Effort games, and equilibrium investments in Weakest Link and Best Shot games.

Optimal and Game-Theoretic Deployment of Security Investments in Interdependent Assets

We introduce a game-theoretic framework to compute optimal and strategic security investments by multiple defenders. Each defender is responsible for the security of multiple assets, with the interdependencies between the assets captured by an interdependency graph. We formulate the problem of computing the optimal defense allocation by a single defender as a convex optimization problem, and establish the existence of a pure Nash equilibrium of the game between multiple defenders. We apply our proposed framework in two case studies on interdependent SCADA networks and distributed energy resources, respectively. In particular, we investigate the efficiency loss due to decentralized defense allocations.

Interdependent Security Games Under Behavioral Probability Weighting

We consider a class of interdependent security games where the security risk experienced by a player depends on her own investment in security as well as the investments of other players. In contrast to much of the existing work that considers risk neutral players in such games, we investigate the impacts of behavioral probability weighting by players while making security investment decisions. This weighting captures the transformation of objective probabilities into perceived probabilities, which influence the decisions of individuals in uncertain environments. We show that the Nash equilibria that arise after incorporating probability weightings have much richer structural properties and equilibrium risk profiles than in risk neutral environments. We provide comprehensive discussions of these effects on the properties of equilibria and the social optimum when the players have homogeneous weighting parameters, including comparative statics results. We further characterize the existence and uniqueness of pure Nash equilibria in Total Effort games with heterogeneous players.

Controlling human utilization of shared resources via taxes

We study a general resource sharing game where overutilization by selfish decision makers leads to possible failure of the resource. Our goal is to understand the effectiveness of a taxation mechanism in reducing the utilization and fragility of the resource when players have behavioral risk preferences. In particular, we incorporate risk preferences drawn from prospect theory, an empirically validated behavioral model of human decision making. We first identify counter-intuitive behavior under prospect theory, where utilization (and hence fragility) can increase under taxation, depending on the resource characteristics. We then identify conditions under which taxation is effective in reducing the fragility of the resource. We also show that homogeneous sensitivities to taxes leads to smaller failure probability compared to the case where players have heterogeneous (player-specific) sensitivities to taxes.

Optimal network topologies for mitigating security and epidemic risks

We consider networked environments under security and epidemic risks, where the probability of successful attack or infection at each vertex depends on the actions or states of its neighbors. In such settings, we consider the problem of designing an optimal network topology with a given number of vertices and edges in order to minimize the expected fraction of attacked or infected vertices. We show that such problems can be cast as minimizing the sum of a concave function of the vertex degrees, and generalize existing results on network design to obtain insights about the optimal network topologies. We first consider a class of interdependent security games where each vertex represents a user that invests in security to protect herself. The probability of successful attack at any given vertex is a function of the security investments in the neighborhood of that vertex. We introduce the notion of behavioral risk-attitudes, where each user perceives the security risks in a skewed manner (as prescribed by established models from the behavioral economics literature). We characterize an upper bound on the expected number of vertices that are successfully attacked under the Nash equilibrium security investments in such settings, and identify the network topologies that minimize this bound. We then consider the N-intertwined approximation of SIS epidemic dynamics, and characterize graphs that minimize (bounds on) the fraction of infected vertices in steady state.

A Game-Theoretic Framework for Securing Interdependent Assets in Networks.

Large-scale networked systems, such as the power grid, are comprised of a large number of interconnected assets managed by multiple self-interested stakeholders. The interdependencies between the assets play a critical role in the security of the overall system, especially against strategic attackers who exploit these interdependencies to target valuable assets. In this work, we develop a general game-theoretic framework to model the security investments of resource-constrained stakeholders against targeted attacks. We consider two complementary problems: (i) where defenders are given a budget to minimize expected loss due to attacks and (ii) where defenders minimize security investment cost subject to a maximum security risk they are willing to tolerate per each valuable asset. For both problems, we establish the existence of Nash equilibria and show that the problem of computing the optimal defense allocation by a central authority and the (decentralized) problem of computing the best response for a single defender can be formulated as convex optimization problems. We then show that our framework can be applied to determine deployment of moving target defense (MTD) in networks. We first apply the game-theoretic framework on the IEEE 300 bus power grid network and compare the optimal expected loss (respectively, security investment cost) under centralized and Nash equilibrium defense allocations. We then show how our framework can be used to compute optimal deployment of MTD on an e-commerce system.

The Superposition-Traffic Game

We consider a queuing game where a set of sources or players strategically send jobs to a single shared server. The traffic sources have disparate coefficients of variation of the interarrival times, and the sources are strategic in their choice of mean inter-arrival times (or the arrival rates). For every job completion, each player receives a benefit that potentially depends on the number of other players using the server (capturing network effects due to using the same server). However, the players experience a delay due to their jobs waiting in the queue. Assuming the service times have a general distribution with a finite second moment, we model the delay experienced by the superposed traffic using a Brownian approximation. In our first contribution, we show that the total rate of job arrivals at a Nash equilibrium with n sources is larger when the sources have heterogeneous coefficients of variation, while the average delay experienced by a job is smaller, compared to the equilibrium with an equal number of homogeneous sources. In the second contribution, we characterize the equilibrium behavior of the queuing system when the number of homogeneous sources scales to infinity in terms of the rate of growth of the benefits due to network effects.