Robust power allocation games under channel uncertainty and time delays

In this paper, we focus on robust power allocation strategies, against the imperfectness of the channel state information at the transmitters in discrete power allocation games. Considering imperfectness in term of payoff measurement and time delays at the transmitters, we propose a Delayed Combined fully DIstributed Payoff and Strategy Reinforcement Learning (Delayed-CODIPAS-RL) in which each transmitter learns its payoff function as well as its associated optimal strategies. Under the Delayed-CODIPAS-RL, the transmitter can use different learning patterns (heterogeneous learning) and different learning rates. Exploiting the specific structure of the power allocation game under channel uncertainty, a global convergence of the ordinary differential equation to one the equilibrium is obtained for small time delays and for almost all initial conditions.