G401
September 24, 1998
Professor Rasmusen
NOTES ON THE PRISONER'S DILEMMA
In ``The Prisoner's Dilemma'', two
prisoners, Messrs
Row and Column, are being
interrogated separately. If
both confess, each is sentenced to eight
years in
prison; if both deny their involvement, each is
sentenced to
one year. If just one
confesses, he is
released but the other prisoner is sentenced to ten
years.
Table 1.1 ``The Prisoner's Dilemma''
Column
Deny Confess
Deny -1,-1 -10, 0
Row:
Confess 0,-10 -8,-8
Payoffs to: (Row,Column).
Each player has a dominant strategy. Consider Row. Row
does
not know which action Column is choosing, but if
Column chooses
Deny , Row faces a Deny payoff of -1 and a
Confess
payoff of 0, whereas if Column chooses Confess ,
Row faces a
Deny payoff of -10 and a Confess payoff of -8 .
In
either case Row does better with Confess . Since the
game is
symmetric, Column's incentives are the same.
The dominant strategy
equilibrium is (Confess,
Confess ), and the equilibrium
payoffs are (-8,-8) ,
which is worse for both players than
(-1,-1) . Sixteen,
in fact, is the greatest possible combined total
of
years in prison.
The result is even stronger than it seems, because it is
robust to
substantial changes in the model. Because the
equilibrium is a
dominant strategy equilibrium, the
information structure of the game
does not matter. If
Column is allowed to know Row's move before
taking his
own, the equilibrium is unchanged. Row still chooses
Confess , knowing that Column will surely choose Confess
afterwards.
``The Prisoner's Dilemma'' crops up in many different
situations, including oligopoly pricing, auction bidding, salesman
effort, political bargaining, and arms races. Whenever you observe
individuals in a conflict that hurts them all, your first thought
should be of ``The Prisoner's Dilemma''.
(What is above is an excerpt adapted from Eric Rasmusen, Games and Information,
2nd edition, Chapter 1).
SPECIAL TO G401.
1. Each player's action has an externality for the other. If Row chooses
Confess, that hurts Column, a negative externality. If Row chooses Deny, that
helps Column, a positive externality.
2. The Prisoner's Dilemma can be adapted to N players instead of 2, to
illustrate the Free Rider problem. In the adapted form, each of N players must
decide whether to Cooperate or Grab, where to Grab reduces everybody else's
payoff.
3. With either 2 or N players, the Prisoner's Dilemma can illustrate the
Teams problem. Row and Column choose Work or Slack on their joint project. Work
is like Deny; Slack is like Confess. The project is evaluated jointly, so if Row
Works and Column Slacks, Column gets half the credit, but Row gets all the
cost.
4. The Prisoner's Dilemma also illustrates the Oligopoly problem. Firms Row
and Column each choose High Output or Low Output.
5. The Prisoner's Dilemma also illustrates political lobbying. Shipping
lines Row and Column each choose High Lobbying Effort or Low Lobbying Effort in
trying to get legalization of cartels.
6. The Prisoner's Dilemma is not inescapable, but to escape it, the players
have to change the rules of the game. The Mafia used to change the rules by
committing to a policy of killing anyone who chose Confess. This amounts to
subtracting 100 from the payoff of anybody who chooses Confess. The FBI's
Witness Protection Program has wrecked this policy, however, in recent years.
(Still somewhat effective is for Row to kill Column before the games even
starts.)
7. Another escape may be to have a repeated relationship--repeat the game
each year for 20 years.
8. Another escape is legal contracts--Row and Column sign a legal contract to
both Deny. Contracts are, of course, illegal for criminals (obstruction of
justice) and for cartels (conspiracy in restraint of trade).
9. Another escape is to have a reputation for doing what you say you'll do.
If Row has a reputation as a moral person, he can tell Column,"I'll Deny" and be
believed. This, too, is problematic for criminals.
10. Other examples of the Prisoner's Dilemma:
A. Two cola companies each must decide whether or not to introduce caffeine-
free cola.
B. Two countries must each decide whether to raise import tariffs.