Non-atomic Games for Multi-User Systems

In this contribution, the performance of a multi-user system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). We consider the realistic case of frequency selective channels for uplink CDMA. This scenario illustrates the case of decentralized schemes, where limited information on the network is available at the terminal. Various receivers are considered, namely the Matched filter, the MMSE filter and the optimum filter. The goal of this paper is to derive simple expressions for the non-cooperative Nash equilibrium as the number of mobiles becomes large and the spreading length increases. To that end two asymptotic methodologies are combined. The first is asymptotic random matrix theory which allows us to obtain explicit expressions of the impact of all other mobiles on any given tagged mobile. The second is the theory of non-atomic games which computes good approximations of the Nash equilibrium as the number of mobiles grows.Comment: 17 pages, 4 figures, submitted to IEEE JSAC Special Issue on ``Game Theory in Communication Systems'

Introducing Hierarchy in Energy Games

In this work we introduce hierarchy in wireless networks that can be modeled by a decentralized multiple access channel and for which energy-efficiency is the main performance index. In these networks users are free to choose their power control strategy to selfishly maximize their energy-efficiency. Specifically, we introduce hierarchy in two different ways: 1. Assuming single-user decoding at the receiver, we investigate a Stackelberg formulation of the game where one user is the leader whereas the other users are assumed to be able to react to the leader's decisions; 2. Assuming neither leader nor followers among the users, we introduce hierarchy by assuming successive interference cancellation at the receiver. It is shown that introducing a certain degree of hierarchy in non-cooperative power control games not only improves the individual energy efficiency of all the users but can also be a way of insuring the existence of a non-saturated equilibrium and reaching a desired trade-off between the global network performance at the equilibrium and the requested amount of signaling. In this respect, the way of measuring the global performance of an energy-efficient network is shown to be a critical issue.Comment: Accepted for publication in IEEE Trans. on Wireless Communication

Resource Allocation in a MAC with and without security via Game Theoretic Learning

In this paper a $K$-user fading multiple access channel with and without security constraints is studied. First we consider a F-MAC without the security constraints. Under the assumption of individual CSI of users, we propose the problem of power allocation as a stochastic game when the receiver sends an ACK or a NACK depending on whether it was able to decode the message or not. We have used Multiplicative weight no-regret algorithm to obtain a Coarse Correlated Equilibrium (CCE). Then we consider the case when the users can decode ACK/NACK of each other. In this scenario we provide an algorithm to maximize the weighted sum-utility of all the users and obtain a Pareto optimal point. PP is socially optimal but may be unfair to individual users. Next we consider the case where the users can cooperate with each other so as to disagree with the policy which will be unfair to individual user. We then obtain a Nash bargaining solution, which in addition to being Pareto optimal, is also fair to each user. Next we study a $K$-user fading multiple access wiretap Channel with CSI of Eve available to the users. We use the previous algorithms to obtain a CCE, PP and a NBS. Next we consider the case where each user does not know the CSI of Eve but only its distribution. In that case we use secrecy outage as the criterion for the receiver to send an ACK or a NACK. Here also we use the previous algorithms to obtain a CCE, PP or a NBS. Finally we show that our algorithms can be extended to the case where a user can transmit at different rates. At the end we provide a few examples to compute different solutions and compare them under different CSI scenarios.Comment: 27 pages, 12 figures. Part of the paper was presented in 2016 IEEE Information theory and applicaitons (ITA) Workshop, San Diego, USA in Feb. 2016. Submitted to journa