Microeconomia
David A. Besanko, Ronald R. Braeutigam
Copyright © 2009 – The McGraw-Hill Companies srl
546
CHAPTER 14
A P P L I C A T I O N
G A M E T H E O R Y A N D S T R AT E G I C B E H A V I O R
14.3
Bank Runs
If you have ever seen the movie It’s a Wonderful Life,
you probably remember the scene just after George
and Mary Bailey (Jimmy Stewart and Donna Reed) get
married. They are about to catch their train for their
honeymoon, when someone tells George: “There’s a run
on the bank!” In the ensuing scene, George goes to his
family’s business (the Bailey Brothers Building and Loan)
and is confronted with a mob of anxious depositors
who are demanding to withdraw their money. Rather
than locking the doors as many real banks did during
the Great Depression of the 1930s, George does his best
to keep the Building and Loan open. He does so by
pleading with his depositors to not withdraw their
money, or at least, to withdraw only as much as they
need to pay their bills.
Bank runs seem to be a thing of the past in the United
States, but they are nevertheless an intriguing phenomenon. Why do they occur? Are they the result of irrational
fear and hysteria, a sort of dysfunctional mass psychology? It might seem so. After all, if all depositors remained
clear-sighted and level-headed, they would realize that
everyone would be better off if there was no run on the
bank. The bank would remain open, and depositors would
eventually get their money. Or is something else going
on? Could bank runs be consistent with rational maximizing behavior by depositors? Game theory suggests that
the answer to the last question could be yes.
Table 14.9 presents a simple game theoretic analysis
of a bank run. Two individuals have deposited $100 in
the Bailey Building and Loan. The Building and Loan has
taken this money and invested it (perhaps lending
money for houses). If both depositors keep their money
in the bank (“don’t withdraw”), they will eventually get
their deposit back with an interest payment of $10, for a
S
total payoff of $110. If both withdraw their money at
the same time (a bank run), though, the bank must liquidate its investment and then close its doors. In this
case, each depositor gets 25 cents on the dollar. If one
depositor withdraws her money but the other doesn’t,
the bank again must liquidate its investment and close.
The depositor who withdraws her money gets $50, but
the unlucky depositor who left her money in the bank
loses everything.
Like the game of Chicken, the bank run game has two
Nash equilibria. The first is that both depositors keep
their money in the bank. If Depositor 2 chooses “don’t
withdraw,” Depositor 1 is better off choosing “don’t withdraw” as well (a payoff of 110 versus a payoff of 50). The
same holds true for Depositor 1. The second Nash equilibrium is for both players to withdraw their money. If
Depositor 2 chooses “withdraw,” Depositor 1’s best response is to choose “withdraw” as well (and vice versa).
As in the game of Chicken, game theory cannot
tell us which equilibrium will occur, but it does teach us
that bank runs can occur. This is so even though we
assume that all depositors behave rationally and that a
bank run makes all depositors worse off. Thus, as in the
prisoners’ dilemma game, purposeful utility-maximizing
behavior by individuals will not necessarily result in an
outcome that maximizes the collective well-being of
all the players in the game.
TABLE 14.9
The Bank Run Game*
Depositor 2
Don’t
Withdraw Withdraw
Depositor 1
Withdraw
Don’t Withdraw
25, 25
0, 50
50, 0
110, 110
*Payoffs are in dollars.
L E A R N I N G - BY- D O I N G E X E RC I S E
14.2
D
E
Finding All of the Nash Equilibria in a Game
Problem What are the Nash equilibria
in the game in Table 14.10?
Solution Generally speaking, the first step in finding
the Nash equilibria in a game should be to identify
dominant or dominated strategies and attempt to simplify
the game, as we did in Learning-By-Doing Exercise 14.1.
But in this game, neither player has a dominant strategy or
any dominated strategies. (You should verify this before
going further.) Thus, we cannot use this approach.
Instead, to find all the Nash equilibria in this game,
we proceed in three steps.