[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

and still be better off. However, these side payments are also illegal, and thus must
be subtle and hard to detect if they occur at all. While perfect coordination is seldom
possible, some industries have found a partial solution by allowing one firm to play
the role of the price leader. In the airline industry, American Airlines for a long time
acted as a price leader. As it increased or decreased prices, others followed suit.
Using Game Theory to Model Collusion Economists apply a branch of
mathematics called game theory to study collusion among oligopolists. Its basic
aim is to shed light on strategic choices—that is, on how people or organizations
behave when they expect their actions to influence the behavior of others. For
instance, when executives at a major airline decide to change fares for flights on a
certain route, they have to consider how their competitors might respond to the
price change. And the competitors, when deciding how to respond, have to consider
how the first airline might answer in turn. These are strategic decisions, just like
those typical of players in various sorts of games, such as chess, football, or poker.
Using game theory, the economist views the participants in a given situation as
players in a game, whose rules define certain moves. The outcomes of the game—
what each participant receives—are referred to as its payoffs, and they depend
on what each player does. Each participant in the game chooses a strategy; he decides
what moves to make. In games in which each player has the chance to make more
than one move (there is more than one round, or period), moves can depend on what
has happened in previous periods. Game theory begins with the assumption that
each player in the game is rational and knows that her rival is rational. Each is trying
to maximize his own payoff. The theory then tries to predict what each player will
do. The actions depend on the rules of the game and the payoffs.
One example of such a game is called the prisoner’s dilemma. Two prisoners, A
and B, alleged to be conspirators in a crime, are put into separate rooms. A police
officer goes into each room and makes a little speech: “Now here’s the
situation. If your partner confesses and you remain silent, you’ll get
five years in prison. But if your partner confesses and you confess
also, you’ll only get three years. On the other hand, perhaps your partner
remains silent. If you’re quiet also, we can send you to prison for
only one year. But if your partner remains silent and you confess, we’ll
let you out in three months. So if your partner confesses, you are
better off confessing, and if your partner doesn’t confess, you
are better off confessing. Why not confess?” This deal is offered to
both prisoners.
Figure 12.9 shows the results of this deal. The upper left box, for
example, shows the result if both A and B confess. The upper right
box shows the result if prisoner A confesses but prisoner B remains
silent. And so on.
From the combined standpoint of the two prisoners, the best
option is clearly that they both remain silent and each serves one
year. But the self-interest of each individual prisoner says that confession
is best, whether his partner confesses or not. However, if
they both follow their self-interest and confess, they both end up
Prisoner
A
Figure 12.9
Confesses
Remains
silent
Confesses
A gets
3 years
Prisoner B
B gets
3 years
B gets
3 months
A gets
5 years
THE PRISONER’S DILEMMA
Remains silent
B gets
5 years
A gets
3 months
A gets
1 year
B gets
1 year
Both prisoners would be better off if both remained silent,
but their individual incentives lead each one to confess.
From the standpoint of prisoner A, confessing is the better
strategy if prisoner B confesses, and confessing is the better
strategy if prisoner B remains silent. The same holds for
prisoner B.
OLIGOPOLIES ∂ 277