The Diamond-Dybvig model uses game theory to provide a mathematical explanation of the provision of liquidity by a bank, and of the circumstances under which the demand for liquidity can lead to a bank run.
For the purpose of the model, a bank is treated as an intermediary between borrowers who want long-term loans for the purpose of investment, and savers who have unpredictable needs for immediate access to cash, and which is paid for that service by charging a higher interest rate on loans than it pays to depositors. Since the undredictable needs of different savers are unlikely to coincide, a small proportion of its receipts is normally sufficient to meet those needs. However if enough depositors attempt to make simultaneous withdrawals the bank may be unable to pay them all.
The findings of the model
Among the findings of the model is the conclusion that the provision of of deposit insurance is a more efficient way of preventing bank runs than the alternative of suspending withdrawals until sufficient funds can be raised to pay them.  .