Mean-Field-Type Games in Engineering

A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201

Joint Channel Selection and Power Control in Infrastructureless Wireless Networks: A Multi-Player Multi-Armed Bandit Framework

This paper deals with the problem of efficient resource allocation in dynamic infrastructureless wireless networks. Assuming a reactive interference-limited scenario, each transmitter is allowed to select one frequency channel (from a common pool) together with a power level at each transmission trial; hence, for all transmitters, not only the fading gain, but also the number of interfering transmissions and their transmit powers are varying over time. Due to the absence of a central controller and time-varying network characteristics, it is highly inefficient for transmitters to acquire global channel and network knowledge. Therefore a reasonable assumption is that transmitters have no knowledge of fading gains, interference, and network topology. Each transmitting node selfishly aims at maximizing its average reward (or minimizing its average cost), which is a function of the action of that specific transmitter as well as those of all other transmitters. This scenario is modeled as a multi-player multi-armed adversarial bandit game, in which multiple players receive an a priori unknown reward with an arbitrarily time-varying distribution by sequentially pulling an arm, selected from a known and finite set of arms. Since players do not know the arm with the highest average reward in advance, they attempt to minimize their so-called regret, determined by the set of players' actions, while attempting to achieve equilibrium in some sense. To this end, we design in this paper two joint power level and channel selection strategies. We prove that the gap between the average reward achieved by our approaches and that based on the best fixed strategy converges to zero asymptotically. Moreover, the empirical joint frequencies of the game converge to the set of correlated equilibria. We further characterize this set for two special cases of our designed game

Non-autonomous random dynamical systems: Stochastic approximation and rate-induced tipping

In this thesis we extend the foundational theory behind and areas of application of non-autonomous random dynamical systems beyond the current state of the art. We generalize results from autonomous random dynamical systems theory to a non-autonomous realm. We use this framework to study stochastic approximations from a different point of view. In particular we apply it to study noise induced transitions between equilibrium points and prove a bifurcation result. Then we turn our attention to parameter shift systems with bounded additive noise. We extend the framework of rate induced tipping in deterministic parameter shifts for this case and introduce tipping probabilities. Finally we perform a case study by developing and applying a numerical method for calculating tipping probabilities and examining the results thereof.Open Acces