Sep. 2, 2013 — With new insights into the
classical game theory match-up known as the
"Prisoner's Dilemma," University of
Pennsylvania biologists offer a mathematically
based explanation for why cooperation and
generosity have evolved in nature.
Their work builds upon the seminal findings of
economist John Nash, who advanced the field
of game theory in the 1950s, as well as those
of computational biologist William Press and
physicist-mathematician Freeman Dyson, who
last year identified a new class of strategies for
succeeding in the Prisoner's Dilemma.
Postdoctoral researcher Alexander J. Stewart
and associate professor Joshua B. Plotkin, both
of Penn's Department of Biology in the School
of Arts and Sciences, examined the outcome of
the Prisoner's Dilemma as played repeatedly by
a large, evolving population of players. While
other researchers have previously suggested
that cooperative strategies can be successful in
such a scenario, Stewart and Plotkin offer
mathematical proof that the only strategies
that succeed in the long term are generous
ones. They report their findings in the
Proceedings of the National Academy of
Sciences the week of Sept. 2.
"Ever since Darwin," Plotkin said, "biologists
have been puzzled about why there is so much
apparent cooperation, and even flat-out
generosity and altruism, in nature. The
literature on game theory has worked to
explain why generosity arises. Our paper
provides such an explanation for why we see
so much generosity in front of us."
The Prisoner's Dilemma is a way of studying
how individuals choose whether or not to
cooperate. In the game, if both players
cooperate, they both receive a payoff. If one
cooperates and the other does not, the
cooperating player receives the smallest
possible payoff, and the defecting player the
largest. If both players do not cooperate, they
receive a payoff, but it is less than what they
would gain if both had cooperated. In other
words, it pays to cooperate, but it can pay
even more to be selfish.
In the Iterated Prisoner's Dilemma, two players
repeatedly face off against one another and can
employ different strategies to beat their
opponent. In 2012, Press and Dyson "shocked
the world of game theory," Plotkin said, by
identifying a group of strategies for playing
this version of the game. They called this class
of approaches "zero determinant" strategies
because the score of one player is related
linearly to the other. What's more, they
focused on a subset of zero determinant
approaches they deemed to be extortion
strategies. If a player employed an extortion
strategy against an unwitting opponent, that
player could force the opponent into receiving
a lower score or payoff.
Stewart and Plotkin became intrigued with this
finding, and last year wrote a commentary in
PNAS about the Press and Dyson work. They
began to explore a different approach to the
Prisoner's Dilemma. Instead of a head-to-head
competition, they envisioned a population of
players matching up against one another, as
might occur in a human or animal society in
nature. The most successful players would get
to "reproduce" more, passing on their
strategies to the next generation of players.
It quickly became clear to the Penn biologists
that extortion strategies wouldn't do well if
played within a large, evolving population
because an extortion strategy doesn't succeed
if played against itself.
"The fact that there are extortion strategies
immediately suggests that, at the other end of
the scale, there might also be generous
strategies," Stewart said. "You might think
being generous would be a stupid thing to do,
and it is if there are only two players in the
game, but, if there are many players and they
all play generously, they all benefit from each
other's generosity."
In generous strategies, which are essentially
the opposite of extortion strategies, players
tend to cooperate with their opponents, but, if
they don't, they suffer more than their
opponents do over the long term.
"Forgiveness" is also a feature of these
strategies. A player who encounters a defector
may punish the defector a bit but after a time
may cooperate with the defector again.
Stewart noticed the first of these generous
approaches among the zero determinant
strategies that Press and Dyson had defined.
After simulating how some generous strategies
would fare in an evolving population, he and
Plotkin crafted a mathematical proof showing
that, not only can generous strategies succeed
in the evolutionary version of the Prisoner's
Dilemma, in fact these are the only approaches
that resist defectors over the long term.
"Our paper shows that no selfish strategies will
succeed in evolution," Plotkin said. "The only
strategies that are evolutionarily robust are
generous ones."
The discovery, while abstract, helps explain the
presence of generosity in nature, an inclination
that can sometimes seem counter to the
Darwinian notion of survival of the fittest.
"When people act generously they feel it is
almost instinctual, and indeed a large
literature in evolutionary psychology shows
that people derive happiness from being
generous," Plotkin said. "It's not just in
humans. Of course social insects behave this
way, but even bacteria and viruses share gene
products and behave in ways that can't be
described as anything but generous."
"We find that in evolution, a population that
encourages cooperation does well," Stewart
said. "To maintain cooperation over the long
term, it is best to be generous."
Story Source:
The above story is based on materials provided
by University of Pennsylvania , via
EurekAlert!, a service of AAAS.
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