Generalized Colonel Blotto Game

Competitive resource allocation between adversarial decision makers arises in a wide spectrum of real-world applications such as in communication systems, cyber-physical systems security, as well as financial, political, and electoral competition. As such, developing analytical tools to model and analyze competitive resource allocation is crucial for devising optimal allocation strategies and anticipating the potential outcomes of the competition. To this end, the Colonel Blotto game is one of the most popular game-theoretic frameworks for modeling and analyzing such competitive resource allocation problems. However, in many real-world competitive situations, the Colonel Blotto game does not admit solutions in deterministic strategies and, hence, one must rely on analytically complex mixed-strategies with their associated tractability, applicability, and practicality challenges. In this paper, a generalization of the Colonel Blotto game which enables the derivation of deterministic, practical, and implementable equilibrium strategies is proposed while accounting for the heterogeneity of the battlefields. In addition, the proposed generalized game enables accounting for the consumed resources in each battlefield, a feature that is not considered in the classical Blotto game. For the generalized game, the existence of a Nash equilibrium in pure-strategies is shown. Then, closed-form analytical expressions of the equilibrium strategies, are derived and the outcome of the game is characterized; based on the number of resources of each player as well as the valuation of each battlefield. The generated results provide invaluable insights on the outcome of the competition. For example, the results show that, when both players are fully rational, the more resourceful player can achieve a better total payoff at the Nash equilibrium, a result that is not mimicked in the classical Blotto game.Comment: 8 pages, 5 figure

Deep Learning-Based Dynamic Watermarking for Secure Signal Authentication in the Internet of Things

Securing the Internet of Things (IoT) is a necessary milestone toward expediting the deployment of its applications and services. In particular, the functionality of the IoT devices is extremely dependent on the reliability of their message transmission. Cyber attacks such as data injection, eavesdropping, and man-in-the-middle threats can lead to security challenges. Securing IoT devices against such attacks requires accounting for their stringent computational power and need for low-latency operations. In this paper, a novel deep learning method is proposed for dynamic watermarking of IoT signals to detect cyber attacks. The proposed learning framework, based on a long short-term memory (LSTM) structure, enables the IoT devices to extract a set of stochastic features from their generated signal and dynamically watermark these features into the signal. This method enables the IoT's cloud center, which collects signals from the IoT devices, to effectively authenticate the reliability of the signals. Furthermore, the proposed method prevents complicated attack scenarios such as eavesdropping in which the cyber attacker collects the data from the IoT devices and aims to break the watermarking algorithm. Simulation results show that, with an attack detection delay of under 1 second the messages can be transmitted from IoT devices with an almost 100% reliability.Comment: 6 pages, 9 figure