Prisoners Dilemma and Axelrod Experiment

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Prisoners’ Dilemma and Axelrod’s
Experiment
Amit Sinha
(www.indicus.net)
This blog is about the Prisoners’ Dilemma and Dr
Axelrod’s experiments around it.
The basic description of the Dilemma
Two suspects, A and B, are arrested by the police. The
police have insufficient evidence for a conviction. They
visit each of them to offer the same deal to both - if one
testifies for the prosecution against the other and the
other remains silent, the betrayer goes free and the silent
accomplice receives the full sentence of 10 years. If both
stay silent, the police can sentence both prisoners to only
six months in jail for a minor charge. If each betrays the
other, each will receive a two-year sentence. Each of the
two prisoners must make the choice of whether to betray
the other or to remain silent. Neither prisoner knows
what choice the other prisoner will make. And hence the
dilemma
The dilemma, in summary
1. Both Stay Silent - Both serve six months
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2. Prisoner A Stays Silent and Prisoner B Betrays -
Prisoner A serves ten years, Prisoner B goes free
3. Prisoner A Betrays and Prisoner B Stays Silent -
Prisoner A goes free, Prisoner B serves ten years
4. Both Betray - Both serve two years
Each prisoner has two options: to cooperate with his
accomplice and stay quiet, or to defect and betray his
accomplice in return for a lighter sentence. The outcome
of each choice depends on the choice of the accomplice,
but the player must choose without knowing what their
accomplice has chosen to do.
If my partner stays quiet, my best move is to betray as I
then walk free instead of receiving the minor sentence. If
my partner betrays, my best move is still to betray, as by
doing it I receive a relatively lesser sentence than staying
silent. At the same time, the other prisoner’s thinking
would also have arrived at the same conclusion and
would therefore also betray. So going from the best
outcome for an individual, we would both betray.
However, from the perspective of the optimal outcome
for the group (of two), the correct choice would be for
both to cooperate with each other, as this would reduce
the total jail time served by the group to one year total.
Any other decision would be worse for the two prisoners
considered together. When the prisoners both betray each
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other, each prisoner achieves a worse outcome than if
they had cooperated.
The above game interested game theorists a lot, and from
the basic construct a more general form of the game
emerged.
There are two players (1 and 2). Each player has two
choices in an interaction - “Cooperate” or “Defect”. Each
player makes his choice simultaneously, ie., they know
each others moves only post facto. At the end of a turn,
each player receives the amount as described below,
depending on what each of them did (cooperate or
defect) -
1. If player 1 defects and player 2 cooperates, player 1
gets the Temptation to Defect for a payoff of 5 points
while player 2 receives the Sucker’s payoff of 0 points.
2. If the reverse happens, the exact reverse in terms of
score happen.
3. If both cooperate they get the Reward for Mutual
Cooperation payoff of 3 points each
4. If they both defect they get the Punishment for Mutual
Defection payoff of 1 point.
This is basically same as the original game without the
same terminologies. Here positive points are scored in
every case (or zero), which gives the players an illusion
that they are not losing. This simulates real life better.
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From this the next step is the iterative prisoners dilemma.
Here a set of two players play each other repeatedly. This
means that players have memories of what the other did
last time, and that influences his strategy against the
particular player.
Finally the big step was a tournament of several players,
each playing the above game with everyone else
simultaneously and iteritively. For example if there are
100 players, each is playing the game individually
against each of the other 99 repeatedly, say 20-25 rounds
or more.
What strategy is best under these circumstances –
cooperate or defect? Moreover, in a society where every
interaction has a potential to cooperate or defect, what
strategy would finally emerge in life? Would people
defect from each other to maximize individual gains or
would they end up cooperating? These questions had
immense value.
Dr. Robert Axelrod, a game theorist got interested in the
above, and back in 1984 he decided to conduct a
tournament. He invited many players to give their
strategies, which were fed in a computer. Each player
had to play other players with a strategy for over 100
rounds. The strategies had to be programmed. He
received several computer programs, some of which
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were very complex. Some were very simple such as
always cooperate or always defect. Some had random
moves, and so on. On the day of the tournament, the
strategies were fed in and the computer flagged off.
There were over 70 participants with individual
strategies.
The end result was startling. The winner was a simple
strategy developed by a person called Anatole Rapoport
called Tit for Tat. This strategy was to cooperate on the
first move and then with each opponent do exactly what
the opponent did on the last move. If he cooperated,
cooperate, if he defected, defect.
This was a surprise. This simple strategy beat all the
complex strategies which tried to look at various patterns
in each opponent.
Axelrod concluded that the lessons were that the
strategies needed to be:
1) Nice - It will not defect before its opponent does.
Almost all of the top-scoring strategies were nice.
Defecting strategies faced heavy retaliation, except for
the very few “always nice” strategies.
2) Punishing - The successful strategy, though nice,
needed to punish dissenting behavior. A non-retaliating
strategy is Always Cooperate. This is a very bad choice,
as “nasty” strategies will ruthlessly exploit such softies
like parasites.
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3) Forgiving - Another quality of successful strategies is
that they must be forgiving. Tit for tat, for example,
punishes dissent, but when the other comes back with
cooperation, it again cooperates. This stops long runs of
revenge and counter-revenge, which reduce points.
4) Consistent – Strategies that had random elemnts,
tended to elicit retaliatory behavior. Consistent strategies
worked well in getting cooperation from other strategies.
Axelrod then started thinking of other strategies such as
Tit for tat that starts with defect instead of cooperate, tit
for two tats, and others. He published his analysis and
asked for another participation in a tournament. Once
again he got great response, except that now the
participants had full report of the last tournamnet. Once
again the tournamnet was flagged off. Axelrod himself
was looking for new successful strategies.
However, once again Tit for tat came up trumps over all
other strategies. It was an overwhelming evidence in
favor of Tit for tat.
The whole exercise has direct relevance to life. In life
and in business, we are dealing with hundreds of people
and we are cooperating or defecting all the time and
building a track record and history with each interaction.
Hence everyone else is also reacting to our moves. The
success of Tit for tat strategies and the lessons drawn by
Axelrod provide a guideline for us. To succeed in life we
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need to elicit cooperative behavior from others, which Tit
for tat does beautifully.
Kindly note that one needs to be non-envious, that is not
strive to score more than the opponent. Tit for tat will not
score more than its opponent. At best they will both be
equal. In fact Tit for tat treats them as partners not
opponents. That is the secret of its success.
I would encourage the reader to google on prisoner’s
dilemma and derive more insights into it.
I would recommend the following links to readers
Robert Axelrod’s Home Page
Evolutionarily Stable Strategy
Tit-for-Tat was long considered to be the most effective
strategy. However, a team from Southampton University
in England introduced a new strategy at the 20th-
anniversary Iterated Prisoner’s Dilemma competition
held in 2004, which proved to be more successful. This
strategy relied on cooperation between programs to
achieve the highest number of points for a single
program. The University submitted 60 programs to the
competition, which were designed to recognize each
other through a series of five to ten moves at the start.
Once this recognition was made, one program would
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always cooperate and the other would always defect,
assuring the maximum number of points for the defector.
If the program realized that it was playing a non-
Southampton player, it would continuously defect in an
attempt to minimize the score of the competing program.
There is a key point to be remembered - It requires
connivance and collusion of a significant proportion of
players to beat strategies that have the characteristics of
“Tit for Tat” – nice, retaliatory, forgiving and non-
envious. This is possible in many cases such as oil cartel,
monopolies and cartels in limited geographies, uneven
power equation, etc.
However, for most individuals living in society and
having a large number of interactions with many people,
there needs to be no fear of a large number of them
ganging up.
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Prisoners Dilemma and Axelrod Experiment

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Prisoners Dilemma and Axelrod Experiment