Bank Runs: Fractional Reserve Banking, Diamond-Dybvig and Contagion

Fractional reserve: why the bank doesn't have your money

A fractional-reserve bank does not hold every depositor's money in a vault; it lends most of it out, keeping only a fraction — the reserve ratio — on hand to meet ordinary day-to-day withdrawals. This is the entire economic function of banking: it channels idle savings into loans that fund productive activity, and it is only viable because, under normal conditions, not everyone wants their money back at the same time. A reserve ratio of 10% means the bank keeps $10 in reserve for every $100 in deposits and has lent the other $90 out, typically for terms (mortgages, business loans) far longer than a depositor's money is nominally 'on demand.'

reserves held = reserve ratio × total deposits
if (withdrawal requests) > (reserves held):  bank must sell/call in illiquid assets fast
                                              — often at a loss, if it can at all

The Diamond-Dybvig model: two equilibria, same bank

Douglas Diamond and Philip Dybvig's 1983 model formalised why bank runs happen even to fundamentally solvent banks. The bank's core service — turning illiquid long-term loans into liquid demand deposits — is a genuine social good in normal times, but it creates exactly two self-fulfilling equilibria for depositor behaviour: in the good equilibrium, depositors withdraw only when they actually need the money, the bank meets those withdrawals from its reserve, and the arrangement works precisely as intended. In the bad equilibrium, depositors withdraw simply because they expect everyone else to withdraw — and that expectation is entirely rational and self-confirming, because if enough other depositors are about to withdraw, the bank genuinely will run out of reserves, so getting in line early really is individually optimal even though it destroys value for the group as a whole.

This is the key insight the model is famous for: a bank run is not necessarily evidence the bank was insolvent or mismanaged. A perfectly solvent bank, with assets that would cover all deposits if given time to mature or be sold in an orderly way, can still fail purely because depositors coordinated — through panic, rumour, or simple observation of other depositors queuing — on the bad equilibrium instead of the good one.

Deposit insurance: making the bad equilibrium irrational

Deposit insurance (like the FDIC in the US, established directly in response to the runs of the Great Depression) is the standard fix, and it works by changing depositor incentives rather than by changing the bank's actual reserve position. If deposits are guaranteed up to some limit regardless of what happens to the bank, an individual depositor has no rational reason to rush to withdraw early — their money is safe whether they withdraw today or next month — which eliminates the self-fulfilling panic dynamic at its root and, in the Diamond-Dybvig framework, removes the bad equilibrium from the game entirely rather than just making it less likely.

Contagion: why one bank's run becomes many banks' run

Real banking systems are not isolated single banks; they are networks connected by interbank lending — banks routinely lend reserves to each other overnight to smooth out short-term liquidity mismatches. That interconnection is efficient in normal times but becomes a transmission mechanism for distress: if Bank A fails or is forced into a fire sale of assets, every bank that lent to Bank A, or that holds assets similar enough to be repriced by Bank A's distressed sale, takes a hit. Depositors at those exposed banks, observing Bank A's failure and knowing (or suspecting) their own bank's interbank exposure, may rationally reassess their own bank's safety and start withdrawing — turning an idiosyncratic, single-bank problem into a systemic one purely through the network of interlocking claims, even among banks with no fundamental problems of their own.

What this simulation lets you probe

The model on this page combines these three pieces: adjustable reserve ratios set how much of a genuine withdrawal shock any single bank can absorb before needing to liquidate assets; a panic trigger lets you push depositor confidence into the bad Diamond-Dybvig equilibrium directly, independent of any real change in bank solvency; and an interbank network lets a shock at one bank propagate probabilistically to its lending partners. Toggling deposit insurance on removes the self-fulfilling panic channel while leaving the underlying reserve mechanics untouched, which is exactly the comparison the model is built to let you run: does a given shock cause a contained, orderly liquidity event, or a cascading systemic run — and how much of the difference is explained by reserves alone versus by confidence and contagion.

Frequently asked questions

Try it live

Everything above runs in your browser — open Bank Run and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.