Learning Equilibria of a Stochastic Game on Gaussian Interference Channels with Incomplete Information

Abstract

We consider a wireless communication system in which N transmitter-receiver pairs want to communicate with each other. Each transmitter transmits data at a certain rate using a power that depends on the channel gain to its receiver. If a receiver can successfully receive the message, it sends an acknowledgement (ACK), else it sends a negative ACK (NACK). Each user aims to maximize its probability of successful transmission. We formulate this problem as a stochastic game and propose a fully distributed learning algorithm to find a correlated equilibrium (CE).In addition, we use a no regret algorithm to find a coarse correlated equilibrium (CCE) for our power allocation game.We also propose a fully distributed learning algorithm to find a Pareto optimal solution. In general Pareto points do not guarantee fairness among the users, therefore we also propose an algorithm to compute a Nash bargaining solution which is Pareto optimal and provides fairness among users. Finally, under the same game theoretic setup, we study these equilibria and Pareto points when each transmitter sends data at multiple rates rather than at a fixed rate. We compare the sum rate obtained at the CE, CCE, Nash bargaining solution and the Pareto point and also via some other well known recent algorithms. KeywordsPart of this paper is presented

Distributed learning of equilibria for a stochastic game on interference channels

“…At the end of T slots, user i, with probability ǫ, chooses an action randomly with uniform probability from A (i) other than k (i) , and with probability 1 − ǫ it chooses an action other than k (i) randomly from a neighborhood of the current strategy which may increase the probability of success (see details in [21]). Let this new action bek (i) .…”