Algorithms for Stochastic Games on Interference Channels

We consider a wireless channel shared by multiple transmitter-receiver pairs. Their transmissions interfere with each other. Each transmitter-receiver pair aims to maximize its long-term average transmission rate subject to an average power constraint. This scenario is modeled as a stochastic game. We provide sufficient conditions for existence and uniqueness of a Nash equilibrium (NE). We then formulate the problem of finding NE as a variational inequality (VI) problem and present an algorithm to solve the VI using regularization. We also provide distributed algorithms to compute Pareto optimal solutions for the proposed game

Power Allocation Games on Interference Channels with Complete and Partial Information

We consider a wireless channel shared by multiple transmitter-receiver pairs. Their transmissions interfere with each other. Each transmitter-receiver pair aims to maximize its long-term average transmission rate subject to an average power constraint. This scenario is modeled as a stochastic game under different assumptions. We first assume that each transmitter and receiver has knowledge of all direct and cross link channel gains. We later relax the assumption to the knowledge of incident channel gains and then further relax to the knowledge of the direct link channel gains only. In all the cases, we formulate the problem of finding the Nash equilibrium as a variational inequality (VI) problem and present an algorithm to solve the VI.Comment: arXiv admin note: text overlap with arXiv:1409.755

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

Potential games form a class of non-cooperative games where unilateral improvement dynamics are guaranteed to converge in many practical cases. The potential game approach has been applied to a wide range of wireless network problems, particularly to a variety of channel assignment problems. In this paper, the properties of potential games are introduced, and games in wireless networks that have been proven to be potential games are comprehensively discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on Communications, vol. E98-B, no. 9, Sept. 201

Stochastic Differential Games and Energy-Efficient Power Control

One of the contributions of this work is to formulate the problem of energy-efficient power control in multiple access channels (namely, channels which comprise several transmitters and one receiver) as a stochastic differential game. The players are the transmitters who adapt their power level to the quality of their time-varying link with the receiver, their battery level, and the strategy updates of the others. The proposed model not only allows one to take into account long-term strategic interactions but also long-term energy constraints. A simple sufficient condition for the existence of a Nash equilibrium in this game is provided and shown to be verified in a typical scenario. As the uniqueness and determination of equilibria are difficult issues in general, especially when the number of players goes large, we move to two special cases: the single player case which gives us some useful insights of practical interest and allows one to make connections with the case of large number of players. The latter case is treated with a mean-field game approach for which reasonable sufficient conditions for convergence and uniqueness are provided. Remarkably, this recent approach for large system analysis shows how scalability can be dealt with in large games and only relies on the individual state information assumption.Comment: The final publication is available at http://www.springerlink.com/openurl.asp?genre=article\&id=doi:10.1007/s13235-012-0068-

Distributed Learning Policies for Power Allocation in Multiple Access Channels

We analyze the problem of distributed power allocation for orthogonal multiple access channels by considering a continuous non-cooperative game whose strategy space represents the users' distribution of transmission power over the network's channels. When the channels are static, we find that this game admits an exact potential function and this allows us to show that it has a unique equilibrium almost surely. Furthermore, using the game's potential property, we derive a modified version of the replicator dynamics of evolutionary game theory which applies to this continuous game, and we show that if the network's users employ a distributed learning scheme based on these dynamics, then they converge to equilibrium exponentially quickly. On the other hand, a major challenge occurs if the channels do not remain static but fluctuate stochastically over time, following a stationary ergodic process. In that case, the associated ergodic game still admits a unique equilibrium, but the learning analysis becomes much more complicated because the replicator dynamics are no longer deterministic. Nonetheless, by employing results from the theory of stochastic approximation, we show that users still converge to the game's unique equilibrium. Our analysis hinges on a game-theoretical result which is of independent interest: in finite player games which admit a (possibly nonlinear) convex potential function, the replicator dynamics (suitably modified to account for nonlinear payoffs) converge to an eps-neighborhood of an equilibrium at time of order O(log(1/eps)).Comment: 11 pages, 8 figures. Revised manuscript structure and added more material and figures for the case of stochastically fluctuating channels. This version will appear in the IEEE Journal on Selected Areas in Communication, Special Issue on Game Theory in Wireless Communication