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Bank Run

Game Description

Each player in a group deposits $100 at a bank, which is used to make a loan which will certainly be repaid. Each day until repayment (or bank failure), each player simultaneously chooses whether to withdraw, and the number of withdrawals is announced to all. The bank can honor a certain number of withdrawals, but if too many withdraw, the bank fails and those who have not withdrawn lose their investment. If the bank does not fail, then all who have not withdrawn receive a return on their investment.

Learning Objective 1: Fractional Banking and Bank Runs

With fractional banking, a bank run may become self-fulfilling. Early withdrawals may lead to fear of bank failure, spurring others to withdraw and hastening failure.

Learning Objective 2: Deposit Insurance and Bank Runs

By removing the risk of deposit loss, deposit insurance makes bank runs less likely, and thus decreases the likelihood of the event it was created to insure against.

Brief Instructions

It is implicitly assumed that the bank receives interest-free loans—up to the liquidation value of its investment—to cover early withdrawals. Therefore, the Liquidation Rate determines the number of safe withdrawals (displayed to students) as well as how withdrawals are processed if the bank fails.

Assume ten $100-depositors with a 35% liquidation rate. On day 1, there are two withdrawals. The bank honors them by borrowing $200. On day 2, another two players withdraw. Unable to borrow enough to honor these withdrawals, the bank fails. It liquidates its investment (receiving $350), and has $150 left after repaying the loans it took to honor day-one withdrawals. It returns $75 to each of the day-two withrawals, and nothing to the six who did not withdraw.

By default, Group Size is 6, the bank returns $150 on a $100 Deposit not withdrawn after three days (Rate of Return (%)=50 and Days to Maturity=3), and the Liquidation Rate is 60%. Keeping these default parameters but setting Periods greater than 1 (i.e., groups remain fixed over multiple periods) will generally result in some groups converging to day-one withdrawals and others finding the equilibrium where nobody withdraws.

The Online section discusses how to set up a game where each student plays only with automated players (robots).

Key Treatment Variations

Forced Withdrawals (%) determines the likelihood that a depositor with be forced to withdraw in the current round. After completing a game, choose to Replay with Fixed Groups and set Forced Withdrawals to 10: many groups that were previously in a no-withdrawal equilibrium will now start to fail.

Deposit Insurance (%) is the percent of a deposit that will be returned, at minimum, in the event of bank failure. If set to 80, almost all groups will likely converge to the no-withdrawal equilibrium.

Results

For each period, we present a summary table, as well as two graphs showing the distribution of outcomes across groups. You can switch between periods using the Go To: drop-down menu.

Figure 1: Summary Table (Click to expand)

The table (Figure 1) summarizes across all groups the number of withdrawals in each round. Importantly, these averages may mask outcome heterogeneity across groups.

Figure 2: Distribution of Outcomes

The first graph (Figure 2) depicts the number of groups failing in each round, as well as the number not failing. Without deposit insurance, in later periods, you will likely see that most groups will either not have failed or will have failed in round one.

Figure 3: Per-group Outcome

The final set of charts displays the withdrawal history of each group (Figure 3). For each group, you see for each day (horizontal axis) the number of new and cumulative withdrawals (vertical axis). In early periods, it is often easy to see early withdrawals leading to bank runs and later bank failure.

Use In An Online Class

As robots follow a very human strategy (more likely to withdraw as the number of previous withdrawals increases), you can configure for out of class play in a way that introduces students to bank run psychology and shows that both bank run and no bank run are equilibria.

To set up, check All Play Only Robots. Setting Liquidation Rate (%) to 50 and Rate of Return (%) to 70 gives a good balance between risk and reward when Group Size is set to 11, while a large number of Periods (e.g., 12) encourages learning. As a result of these choices and robot strategy, a player whose withdrawal choice depends on the choices of other depositors earns more (on average) than both the player always withdrawing on the first day and the player never withdrawing.

Robot Play

A robot (i.e., an automated player) does not withdraw its deposit if insurance is ≥80%. Otherwise, it withdraws with probability .10 × (n+1), where n is the number of other group members who have already withdrawn their deposits.

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