  Deploying mobile edge computing (MEC) server in the mobile blockchain-enabled
Internet of things (IoT) system is a promising approach to improve the system
performance, however, it imposes a significant challenge on the trust of MEC
server. To address this problem, we first propose an untrusted MEC proof of
work scheme in mobile blockchain network where plenty of nonce hash computing
demands can be offloaded to MEC server. Then, we design a nonce ordering
algorithm for this scheme to provide fairer computing resource allocation for
all mobile IoT devices/users. Specifically, we formulate the user's nonce
selection strategy as a non-cooperative game, where the utilities of individual
user are maximized in the untrusted MEC-aided mobile blockchain network. We
also prove the existence of Nash equilibrium and analyze that the cooperation
behavior is unsuitable for the blockchain-enabled IoT devices by using the
repeated game. Finally, we design the blockchain's difficulty adjustment
mechanism to ensure stable block times during a long period of time.
