The bank run game: will your class wait, or run?

A bank run is a rush of depositors asking for their money at once, because each fears the bank cannot pay everyone. Every bank keeps only part of its deposits as cash and lends the rest out, so even a sound bank cannot repay every depositor on the same day. The classic model is Douglas W. Diamond and Philip H. Dybvig, “Bank Runs, Deposit Insurance, and Liquidity”, Journal of Political Economy 91 (1983). The Diamond–Dybvig model shows that such a bank has two outcomes: if those who can wait do, its loans pay off and everyone is paid; if enough of them expect a run, withdrawing first is each one's best answer, and the run happens. Deposit insurance, which promises every depositor their money, removes the reason to run.

In this lesson your class is the bank's depositors. Everyone has £100 in one small bank, which sets aside cash in its vault for 3 in every 10 of them and lends the rest out for a year. Each student chooses: withdraw £100 today, or wait for £110 next year. If no more ask than the vault has cash for, the bank holds, and both are paid as promised. If more ask, the bank shuts and sells its loans early for what they fetch: £50 to each person who asked, and nothing to whoever waited. Waiting pays more only if few others ask, so each choice is a forecast of the room.

Your class plays it as “One small bank”. The phones open on a rumour that the bank has lent too much, and everyone chooses while the screen shows the rule and how many have answered, never how many chose either way. Then the big screen deals the answers onto a tally of who asked for their money, and a pen ticks the vault's cash across the Withdraw lane. Its tag says whether the bank held, and if it failed, by how many askers.

A note for the teacher: the vault is worked out from the room. It holds cash for 3 in every 10 depositors who answered, rounded down and never fewer than 1, and the bank fails when more ask than that. In a room of 30 the vault holds cash for 9, so 9 askers leave the bank standing and the 10th breaks it. The £50 is the lesson's rule whatever the number of askers: at 30 depositors it is at most £1,500, the vault's £900 and £600 from loans that cost £2,100 to make, sold early at under a third of their worth.

Then deposit insurance: same bank, same vault, same rumour, and one rule changed. If the bank fails, an insurer pays every depositor their £100, so waiting never pays less than asking, and the run has no reason to start. The room chooses again, and the last step compares the rounds: round 1 whole on the left, the insured round on the right, a ribbon for the people who kept or changed their answer, each as thick as its people, and a headline that says whether the insured bank held.

Counts only: the screen never names a student or a seat. Each phone shows the same counts and the bank's line, and each student reads their own payout from the answer they gave. Try the screen-and-phone preview: the phone is yours, and fictional classmates choose through the same runtime as the lesson; they are illustrative, not observations of a real class.