Econ 101
Lecture 19
Games and Strategic Behavior
Thus far, we have viewed economic decision makers as confronting an environment that is essentially
passive.
But there exist many cases in which relevant costs and benefits depend not only on the behavior of the
decision makers themselves but also on the behavior of others.
Example 19.1.
Should the prisoners confess?
Two prisoners, X and Y, are held in separate cells for a serious crime that they did, in fact, commit.
The
prosecutor, however, has only enough hard evidence to convict them of a minor offense, for which the penalty is,
say, a year in jail.
Each prisoner is told that if one confesses while the other remains silent, the confessor will go
scot free while the other spends 20 years in prison.
If both confess, they will get an intermediate sentence, say five
years.
These payoffs are summarized in the payoff matrix below.
The two prisoners are not allowed to
communicate with one another.
If the prisoners are rational and narrowly self-interested, what will they do?
Prisoner Y
Prisoner X
Confess
Remain Silent
Remain Silent
Confess
5 years
for each
1 year
for each
0 years for X
20 years for Y
20 years for X
0 years for Y
Their
dominant strategy
is to confess.
No matter what Y does, X gets a lighter sentence by speaking
out-- if Y too confesses, X gets five years instead of 20;
and if Y remains silent, X goes free instead of spending a
year in jail.
The payoffs are perfectly symmetric, so Y also does better to confess, no matter what X does.
The
difficulty is that when each behaves in a self-interested way, both do worse than if each had shown restraint.
Thus,
when both confess, they get five years, instead of the one year they could have gotten by remaining silent.
And
hence the name of this game,
prisoner's dilemma
.
Example 19.2.
Why do students have to wait in line overnight to buy Cornell hockey tickets?
Each year Cornell announces a time at which its ticket window will open for the sale of a limited number
of hockey tickets for students.
Students show up more than 24 hours in advance to wait in line for these tickets,
even though no more tickets are available that way than if everyone had shown up only 1 hour in advance.
Suppose that if everyone shows up one hour in advance, everyone has a 50-50 chance of getting a ticket, and that
the odds of getting a ticket are the same if everyone shows up 24 hours in advance.
If you show up 24 hours in
advance and everyone else shows up one hour in advance, you are sure to get a ticket.
But if you show up 1 hour
in advance and others show up 24 hours in advance, you have no chance to get a ticket.
The same applies to other
students.
Waiting only one hour has no cost to you.
But you would be willing to pay $40 to avoid having to wait
24 hours.
A 50-50 chance of getting a ticket is worth $50 to you and a 100 percent chance of getting a ticket is