  Several attacks have been proposed against Proof-of-Work blockchains, which
may increase the attacker's share of mining rewards (e.g., selfish mining,
block withholding). A further impact of such attacks, which has not been
considered in prior work, is that decreasing the profitability of mining for
honest nodes incentivizes them to stop mining or to leave the attacked chain
for a more profitable one. The departure of honest nodes exacerbates the attack
and may further decrease profitability and incentivize more honest nodes to
leave. In this paper, we first present an empirical analysis showing that there
is a statistically significant correlation between the profitability of mining
and the total hash rate, confirming that miners indeed respond to changing
profitability. Second, we present a theoretical analysis showing that selfish
mining under such elastic hash supply leads either to the collapse of a chain,
i.e., all honest nodes leaving, or to a stable equilibrium depending on the
attacker's initial share.
