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This implies that in the second-to-
last round defection is also a
better choice—anticipating the
future defection of your rival. By
continuing this logic backward,
it seems that defection dominates
in every round so that the sub-
game perfect choice is to defect
on the first round. This result
appears paradoxical, however,
given that the sum of money in
the first round is very small and
hardly worth defecting over.
This idea has been applied
to the situation where there is a
large chain store with outlets all
over the country, and a rival is
preparing to enter the market in
one or more locations. The chain
store could threaten to cut prices
in the location that the new firm
is thinking of entering. This threat
would appear to be both credible
and worthwhile since it would not
cost the chain store too much
profit and would deter the firm
from trying to enter in that area.
The optimal strategy in terms of
Nash equilibrium appears to be
for the chain store to fight a price
war, and for the new firm not to
try to enter the market. However,
according to Selten, if the existing
firm were forced to cut prices every
time a new firm tried to enter one of
its markets, the cumulative losses
would be too great. Thus, by
looking forward and reasoning
backward, the threat of a price war
is irrational. Selten concludes that
the new firm’s entry without a price
war is sub-game perfect.Bounded rationality
These paradoxes come from the
assumption that individuals playing
games are fully rational. Selten
proposed a more realistic theory of
decision making. Although people
do sometimes make decisions
through rational calculation, often
they do so on the basis of past
experience and rules of thumb.
People may not always use rational
calculation. Instead, they may
be what game theorists call
“boundedly rational:” able toPOST-WAR ECONOMICS
In cooperative games players have
the chance to form alliances. In many
of these games, such as a tug of war,
the only chance an individual has of
winning is to cooperate with others.
When I used to theorize
about a nuclear standoff,
I didn’t really have to
understand what was
happening inside the
Soviet Union.
Thomas Schellingchoose the more intuitively
appealing solutions to games that
may not be sub-game perfect.
Game theory is not without its
critics, who say that it tells great
stories but fails the main test of
any scientific theory: it can make
no useful predictions about what
will happen. A game might have
many equilibriums. An industry
resulting in a cartel might be as
rational a result as one that
descends into a price war. Further,
people don’t make decisions based
on “If I do this and they do this
and I do that and they do that”
ad infinitum.
The US economist Thomas
Schelling has addressed this
issue by studying the idea that
the triggers for behavior are not
simply based on mathematical
probabilities. In the “coordination
game,” where both players are
rewarded if they think of the
same playing card, what card in
the pack would you select if you
wanted to try to match with
someone else? Would you pick
the ace of spades? ■