Put $100 in a bank and it feels like the bank is holding your $100. It isn't. Most of it has been lent out to people buying houses and firms buying machines, and those loans pay back over years. The bank keeps only a slice as ready cash and bets that, on any given day, hardly anyone will ask for their money at the same time.
Your deposit says "withdraw any time". The bank's loans say "wait until 2035". Bridging that gap is the bank's main job, and it is useful: you get savings you can reach, and borrowers get money they can keep. In 1983 Douglas Diamond and Philip Dybvig published the classic model of this arrangement in the Journal of Political Economy. Their uncomfortable finding was that such a deposit contract has more than one stable outcome, and one of them is a bank run.
If everyone waits, the loans pay off and everyone is paid in full. But suppose you think the others are about to line up. Banks pay first come, first served, and to find cash the bank must sell loans early, at a discount, which leaves less behind for whoever is last. So running is the sensible move if you expect others to run. Everyone reasons the same way, and the fear fulfils itself.
Nothing about the loans has to change between the calm outcome and the run. What changes is what people believe about each other.
Below are 100 depositors with $1 each. Tap a few to pick who hears the rumour first (ringed dots). Every other depositor has a private tipping point: "I'll withdraw once this share of everyone else has." The nervousness slider moves those tipping points closer. Press Start the rumour.
Each withdrawal comes first from the vault. Once the vault is empty, the bank has to sell loans, and a $1 loan sold in a panic fetches less than $1. That loss is why even a run that fizzles out leaves the people who stayed with a claim worth less than $1 on the dollar, which gives them a fresh reason to leave. More cash in the vault and smaller fire-sale losses both give the bank room to survive a scare. Higher nervousness does the opposite: the tipping points sit lower and one worried group sets off the next.
The model is deliberately simple. Real depositors don't have clean thresholds, and real banks can borrow from the central bank. It shows the mechanism, not a forecast.
In September 2007 queues formed outside Northern Rock branches in Britain. A UK parliamentary committee described it as the first bank run in the country since Victorian times. In March 2023 Silicon Valley Bank customers tried to withdraw more than $42 billion on 9 March alone, with roughly another $100 billion queued for the next day, together about 81% of the $175 billion it held at the end of 2022 (figures given by the Fed's Michael Barr). Online banking made the line instant. SVB also had real problems, since its bond holdings had lost value, but the speed of the run turned a weakness into a collapse.
Try the insurance box above. If your money is guaranteed, you have no reason to rush, so no one rushes, and the guarantee costs nothing because nobody calls on it. That is the logic behind the US Federal Deposit Insurance Corporation, created in 1933 during the Great Depression and today covering up to $250,000 per depositor, per insured bank, per ownership category. Diamond and Dybvig showed that deposit insurance can, in principle, prevent runs. The price is that insured depositors have less reason to watch what their bank does with the money. In 2022 Diamond and Dybvig shared the economics Nobel with Ben Bernanke for their work on banks and financial crises.
The lesson reaches well beyond banking: sometimes the cause of a collapse is simply everyone's belief that everyone else will leave.