"This will cause a bank run, so you gotta a make a run on the bank to get your money first."
I mean, I kind of get it. That first 10% could very likely be people who know something you don't. So you use it as an indicator. But then the very perception of instability causes that same instability.
Even if the worst case scenario was only losing 10% of deposits, that's a very good reason to remove your money.
But in reality, everyone knows this will trigger a bank run, which will lose much more, so the only thing that matters is to get out ahead of it.
This is just the inherent logic of the situation, not the fault of whoever realized it first.
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