  Eyal and Sirer's selfish mining strategy has demonstrated that Bitcoin system
is not secure even if 50% of total mining power is held by altruistic miners.
Since then, researchers have been investigating either to improve the
efficiency of selfish mining, or how to defend against it, typically in a
single selfish miner setting. Yet there is no research on a selfish mining
strategies concurrently used by multiple miners in the system. The
effectiveness of such selfish mining strategies and their required mining power
under such multiple selfish miners setting remains unknown.
  In this paper, a preliminary investigation and our findings of selfish mining
strategy used by multiple miners are reported. In addition, the conventional
model of Bitcoin system is slightly redesigned to tackle its shortcoming:
namely, a concurrency of individual mining processes. Although a theoretical
analysis of selfish mining strategy under this setting is yet to be
established, the current findings based on simulations is promising and of
great interest. In particular, our work shows that a lower bound of power
threshold required for selfish mining strategy decreases in proportion to a
number of selfish miners. Moreover, there exist Nash equilibria where all
selfish miners in the system do not change to an honest mining strategy and
simultaneously earn their unfair amount of mining reward given that they
equally possess sufficiently large mining power. Lastly, our new model yields a
power threshold for mounting selfish mining strategy slightly greater than one
from the conventional model.
