  In Aug. 2017, Bitcoin was split into the original Bitcoin (BTC) and Bitcoin
Cash (BCH). Since then, miners have had a choice between BTC and BCH mining
because they have compatible proof-of-work algorithms. Therefore, they can
freely choose which coin to mine for higher profit, where the profitability
depends on both the coin price and mining difficulty. Some miners can
immediately switch the coin to mine only when mining difficulty changes because
the difficulty changes are more predictable than that for the coin price, and
we call this behavior fickle mining.
  In this paper, we study the effects of fickle mining by modeling a game
between two coins. To do this, we consider both fickle miners and some factions
(e.g., BITMAIN for BCH mining) that stick to mining one coin to maintain that
chain. In this model, we show that fickle mining leads to a Nash equilibrium in
which only a faction sticking to its coin mining remains as a loyal miner to
the less valued coin (e.g., BCH), where loyal miners refer to those who conduct
mining even after coin mining difficulty increases. This situation would cause
severe centralization, weakening the security of the coin system.
  To determine which equilibrium the competing coin systems (e.g., BTC vs. BCH)
are moving toward, we traced the historical changes of mining power for BTC and
BCH. In addition, we analyze the recent "hash war" between Bitcoin ABC and SV,
which confirms our theoretical analysis. Finally, we note that our results can
be applied to any competing cryptocurrency systems in which the same hardware
(e.g., ASICs or GPUs) can be used for mining. Therefore, our study brings new
and important angles in competitive coin markets: a coin can intentionally
weaken the security and decentralization level of the other rival coin when
mining hardware is shared between them, allowing for automatic mining.
