# Economic Classroom Experiments/Diamond Dybvig Experiment

Small investors panic and lose money in a bank run because the bank has insufficient liquidity to pay them all at the same time.

## Overview

Any level

None

Any

### Intended learning outcomes

1. Explanation of bank runs (multiple equilibria).
2. Possible preventative measures.

## Computerized Version

There is a computerized version of this experiment available on the Exeter games site.

You can quickly log in as a subject to try out this group participation experiment, by pretending to be one of the original participants in a real session. You may also find the sample instructions helpful.

### Abstract

Students play together as a group of small investors who all have money on deposit at the same bank. Each investor has to decide whether to withdraw his/her money today or wait until tomorrow. Some investors are 'impatient' and have a higher utility today, whereas others are 'patient' and have a higher utility tomorrow.

The bank has kept some of the money as cash in hand but the rest is invested in an illiquid asset that does not pay out until tomorrow, with a penalty for early withdrawal today. There is enough money to pay everyone in full provided sufficient of the patient investors decide to wait until tomorrow. Otherwise the money runs out and the bank pays as many investors as it can, with priority being given to those who decided to withdraw today. There is an equilibrium where the patient investors all wait until tomorrow and a second one where they all withdraw today, this latter being a bank run when some investors are not paid because they all try to withdraw early.

### Discussion of Likely Results

In the default setup, 5 impatient investors and 5 patient investors each invest £1, total £10. Investors choose between withdrawing £1 today or £2 tomorrow. Payoffs represent the investors' utility. Receiving £1 today is worth £1 to both impatient and patient investors. Receiving £2 tomorrow is worth £0.50 to impatient investors and £2 to patient investors. The bank has £5 in cash and £5 invested, with a return on each £1 invested of £0.50 today or £2 tomorrow. There is still some money left to pay investors tomorrow provided no more than two patient investors decide to withdraw today.

 Withdrawals Today Investors Paid Impatient Patient Today Tomorrow 5 0 5 5 5 1 6 3 5 2 7 1 5 3 *7.5 0 5 4 *7.5 0 5 5 *7.5 0 (*) One investor is not paid in full.

A bank run is almost inevitable if the bank gets only £0.20 today and £1.10 tomorrow for each £1 invested. Now the money runs out altogether if only one patient investor panics and decides to withdraw today.

 Withdrawals Today Investors Paid Impatient Patient Today Tomorrow 5 0 5 5 5 1 6 0 5 2 6 0 5 3 6 0 5 4 6 0 5 5 6 0

The bank can prevent a run by suspending payments for today once 5 investors have been paid. If more than 5 investors decide to withdraw today, the bank picks 5 of them at random to be paid; all others who wanted their money today are made to come back tomorrow instead, when they are paid alongside those who preferred to wait originally. So it is possible that some impatient investors will be paid tomorrow if one or more patient investors decide to withdraw today.

### Discussion of Application

There was a 'bank run' on hedge funds due to the problems with subprime mortgages. See Paul Krugman: It's A Miserable Life.

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