  Future IoT networks consist of heterogeneous types of IoT devices (with
various communication types and energy constraints) which are assumed to belong
to an IoT service provider (ISP). To power backscattering-based and
wireless-powered devices, the ISP has to contract with an energy service
provider (ESP). This article studies the strategic interactions between the ISP
and its ESP and their implications on the joint optimal time scheduling and
energy trading for heterogeneous devices. To that end, we propose an economic
framework using the Stackelberg game to maximize the network throughput and
energy efficiency of both the ISP and ESP. Specifically, the ISP leads the game
by sending its optimal service time and energy price request (that maximizes
its profit) to the ESP. The ESP then optimizes and supplies the transmission
power which satisfies the ISP's request (while maximizing ESP's utility). To
obtain the Stackelberg equilibrium (SE), we apply a backward induction
technique which first derives a closed-form solution for the ESP. Then, to
tackle the non-convex optimization problem for the ISP, we leverage the block
coordinate descent and convex-concave procedure techniques to design two
partitioning schemes (i.e., partial adjustment (PA) and joint adjustment (JA))
to find the optimal energy price and service time that constitute local SEs.
Numerical results reveal that by jointly optimizing the energy trading and the
time allocation for heterogeneous IoT devices, one can achieve significant
improvements in terms of the ISP's profit compared with those of conventional
transmission methods. Different tradeoffs between the ESP's and ISP's profits
and complexities of the PA/JA schemes can also be numerically tuned.
Simulations also show that the obtained local SEs approach the socially optimal
welfare when the ISP's benefit per transmitted bit is higher than a given
threshold.
