  Mining in the blockchain requires high computing power to solve the hash
puzzle for example proof-of-work puzzle. It takes high cost to achieve the
calculation of this problem in devices of IOT, especially the mobile devices of
IOT. It consequently restricts the application of blockchain in mobile
environment. However, edge computing can be utilized to solve the problem for
insufficient computing power of mobile devices in IOT. Edge servers can recruit
many mobile devices to contribute computing power together to mining and share
the reward of mining with these recruited mobile devices. In this paper, we
propose an incentivizing mechanism based on edge computing for mobile
blockchain. We design a two-stage Stackelberg Game to jointly optimize the
reward of edge servers and recruited mobile devices. The edge server as the
leader sets the expected fee for the recruited mobile devices in Stage I. The
mobile device as a follower provides its computing power to mine according to
the expected fee in Stage. It proves that this game can obtain a uniqueness
Nash Equilibrium solution under the same or different expected fee. In the
simulation experiment, we obtain a result curve of the profit for the edge
server with the different ratio between the computing power from the edge
server and mobile devices. In addition, the proposed scheme has been compared
with the MDG scheme for the profit of the edge server. The experimental results
show that the profit of the proposed scheme is more than that of the MDG scheme
under the same total computing power.
