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In Aug. 2017, Bitcoin was split into the original Bitcoin (BTC) and BitcoinCash (BCH). Since then, miners have had a choice between BTC and BCH miningbecause they have compatible proof-of-work algorithms. Therefore, they canfreely choose which coin to mine for higher profit, where the profitabilitydepends on both the coin price and mining difficulty. Some miners canimmediately switch the coin to mine only when mining difficulty changes becausethe difficulty changes are more predictable than that for the coin price, andwe call this behavior fickle mining.  In this paper, we study the effects of fickle mining by modeling a gamebetween 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 thatchain. In this model, we show that fickle mining leads to a Nash equilibrium inwhich only a faction sticking to its coin mining remains as a loyal miner tothe less valued coin (e.g., BCH), where loyal miners refer to those who conductmining even after coin mining difficulty increases. This situation would causesevere 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 andBCH. In addition, we analyze the recent "hash war" between Bitcoin ABC and SV,which confirms our theoretical analysis. Finally, we note that our results canbe 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 newand important angles in competitive coin markets: a coin can intentionallyweaken the security and decentralization level of the other rival coin whenmining hardware is shared between them, allowing for automatic mining.

Bitcoin vs. Bitcoin Cash: Coexistence or Downfall of Bitcoin Cash?