239
Expensive technology, such as the
Stealth Bomber, was developed during
the Cold War. To avoid the “sucker’s
payoff,” game theory suggested that
both sides should spend this money.payoff”—ending up with a long
sentence—the Nash equilibrium
is always to betray. What is
interesting is that the “dominant”
(best) strategy of mutual betrayal
does not maximize welfare for the
group. If they had both refused to
betray, their total jail time would
have been minimized.
Dresher and Flood tested the
prisoner’s dilemma on two of their
colleagues to see whether Nash’s
prediction would be true. They
made a game where each player
could choose to trust or betray the
other player. The payoffs were
designed so that there was a
sucker’s payoff, but also an option
for a cooperative trade that would
benefit both players, a solution
that reflected von Neumann and
Morgenstern’s earlier work
involving cooperative games.
The experiment was run over
100 rounds. This iterative version
of the game gave players the
chance to punish or reward the
previous behavior of their
partner. The results showed
that the Nash equilibrium of
betrayal was only chosen 14 times
against 68 times for the cooperative
solution. Dresher and Flood
concluded that real people learn
quickly to choose a strategy that
maximizes their benefit. Nash
argued that the experiment was
flawed because it allowed for too
much interaction, and that the
only true equilibrium point
was betrayal.Peace–war game
The iterative version of the
prisoner’s dilemma came to be
known as the peace–war game.
It was used to explain the best
strategy in the Cold War with the
Soviet Union. As new technologies
such as intercontinental ballistic
weapons were developed, each
side had to decide whether to
invest enormous sums of money
to acquire these weapons. The
new technology might lead to
the ability to win a war relatively
painlessly if the other side didn’t
develop the new weapon. The
consequence of not developing ❯❯POST-WAR ECONOMICS
John Nash
Born in 1928 into a middle-
class American family,
John Nash was labeled as
backward at school due to his
poor social skills. However,
his parents recognized his
outstanding academic ability.
In 1948, he won a scholarship
to Princeton University. His
former tutor wrote a one-line
letter of recommendation:
“This man is a genius.”
At Princeton Nash avoided
lectures, preferring to develop
ideas from scratch. It was
there that he developed the
ideas on game theory that
were to earn him his Nobel
Prize. In the 1950s he worked
at the RAND Corporation and
MIT (Massachusetts Institute
of Technology), but by now his
mental state was worsening.
In 1961, his wife committed
him for treatment for his
schizophrenia. Nash battled
with the condition for the next
25 years but never stopped
hoping that he would be able
to add something else of value
to the study of mathematics.Key works1950 Equilibrium Points in
N-person Games
1950 The Bargaining Problem
1952 Real Algebraic ManifoldsEach player’s strategy
is optimal against
those of the others.
John Nash