  In the paper, we present a cross-layer perspective on data transmission in
energy harvesting cognitive radio networks (CRNs). The delay optimal power
allocation is studied while taking into account the randomness of harvested
energy, data generation, channel state and the grid price. To guarantee primary
user (PU)'s transmission, its Signal-Interference-Ratio (SIR) should be no less
than a threshold. Each user, including PU as well as secondary user (SU), has
energy harvesting devices, and the PU can also purchases the grid power. Each
user is rational and selfish to minimize its own the buffer delay. We formulate
a stochastic Stackelberg game in a bilevel manner. After decoupling via
rewriting the objective and constraints, an equivalent tractable reconstruction
is derived. First, we give a distributive algorithm to obtain the Nash
equilibrium (NE) of the lower level SUs' noncooperative stochastic game.
Thereafter, the stochastic Stackelberg game is discussed under the
circumstances that there is no information exchange between PU and SU.
Distributed iterative algorithms are designed. Furthermore, a distributive
online algorithm is proposed. Finally, simulations are carried out to verify
the correctness and demonstrate the effectiveness of proposed algorithms.
