The Tragedy of the Commons
and
The Prisoner’s Dilemma
Thomas Malthus
• 1798, writes critique of Condorcet et al
• Food supplies increase additively (linear)
• Population increases geometrically (nonlinear)
Thomas Malthus
• Malthus argued that two types of checks hold
population within resource
• catastrophic checks: hunger, disease and war
• preventive checks: abortion, birth control,
prostitution, postponement of marriage and
celibacy
• God created this situation deliberately to ensure
our moral development
Herbert Spencer
"A Theory of Population" (1852)
• Malthus proves that welfare to the poor
is like feeding rats: you only get more rats
• Social Darwinism: humanitarian impulses should be
resisted so that the social struggle for existence can
remove the unfit.
The Tragedy of the Commons
Garrett Hardin, 1968
• The class of "No technical solution problems" has
members. My thesis is that the "population
problem," as conventionally conceived, is a member
of this class.
• It is fair to say that most people who anguish over
the population problem are trying to find a way to
avoid the evils of overpopulation without
relinquishing any of the privileges they now enjoy.
They think that farming the seas or developing new
strains of wheat will solve the problem-technologically. I try to show here that the solution
they seek cannot be found.
The Tragedy of the Commons
Garrett Hardin, 1968
• Herders sharing a common parcel of land, on which
they are each entitled to let their cows graze.
• It is in each herder's individual interest to put as
many cows as he acquires onto the land.
• A herders might be aware of overgrazing dangers,
but to limit cows would just further exacerbate the
decrease to income from the overgrazing.
• Modern examples: overfishing of the world's
oceans, timber extraction, etc. Even advertising.
The Tragedy of the Commons
Garrett Hardin, 1968
• Hardin laments this interpretation of The Universal
Declaration of Human Rights (United Nations):
The Universal Declaration of Human Rights describes
the family as the natural and fundamental unit of
society. [Article 16[10]] It follows that any choice and
decision with regard to the size of the family must
irrevocably rest with the family itself, and cannot be
made by anyone else.
The Tragedy of the Commons
Garrett Hardin, 1968
• Hardin essentially repeats the arguments of Hobbs:
• Education is not a solution, humans need higher
authority for coercion
• The authority can be a government dictatorship
that regulates human reproduction (communist
model) or capitalist market that privatizes
ownership of all resources (Spencer’s solution)
Game Theory Approach to the Psychology of the
Commons: The Prisoner’s Dilemma
Hofstadter’s example:
You have diamonds, your dealer has money.
You both agree to leave bags at designated places in forest:
1. You leave a full bag, but his bag is empty. You get ripped off.
2. You leave an empty bag, he leaves a full one. You have
doubled your wealth.
3. You leave an empty bag, and he leaves an empty bag: no
worse off than you are already.
Therefore, economic “rationalism” demands that you leave an
empty bag. Since the dealer is in the same situation, you both
receive nothing.
The Prisoner’s Dilemma
You have both been accused of a crime:
1. You both stay mum, you each get 2 years in jail
2. You rat out your partner: you are free, he gets 5
3. You both rat each other out, you each get 4 years in jail
“Rational self-interest” gives a sub-optimum result!
Origins of Prisoner’s Dilemma
RAND in 1950s: US and USSR each want to eliminate
nukes
• If you both reduce nukes (“mutual cooperation”)
you both get safer world
• If US keeps nukes (“defect”) and USSR gets rid of
them (“cooperates”), US has security, USSR
insecure.
• If you both keep nukes (“mutual defection”), you
both get insecure world
The Prisoner’s Dilemma applies to many situations in
which lack of trust destroys our ability to cooperate
• Human population: why should I have a small family to
prevent over-population, if others do not?
• Renewable resources: why should I limit my (grazing,
hunting, fishing, pollution) if others do not?
• International security: why should I reduce nukes if others
do not?
• Advertisements: why should I make small billboards if
others make larger ones?
• Sleazy crap on TV: why should I offer viewers intelligent
programming if others get more views from sleazy crap?
The Prisoner’s Dilemma is our Race to the Bottom
The Prisoner’s Dilemma: canonical version
Two players have the choice of cooperating or defecting.
Temptation to defect is the highest payoff (5)
Reward for mutual cooperation is second highest payoff (3)
Punishment for mutual defection is third highest (1)
Sucker’s payoff (cooperating during defect) is lowest (0)
T>R>P>S and (T+S)/2 < R are required conditions
More generally, this is
A “Nash Equilibrium”
The Iterated Prisoner’s Dilemma:
Robert Axelrod 1979
• Researchers asked to submit program that makes the
Cooperation/Defect decision
• Programs can keep track of each other, and change in
response to prior moves
• Included random, always cooperate, and always defect
• Every program interacts with every other program 200
times, including a clone of itself
• Scores are cumulative: it doesn’t matter how many times
you “lost”—only the sum of the scores matter
The Iterated Prisoner’s Dilemma winner: Rapoport’s
tit for tat
The first time meeting a program, cooperate
The next time, repeat what it did last time.
If T4T meets itself, they cooperate
If T4T meets defect-only, it only gets fooled once
If T4T meets random chooser (eg JOSS), it will retaliate on the
next move (often when JOSS cooperates)
The Iterated Prisoner’s Dilemma winner: Rapoport’s
Tit for Tat
Axelrod attributes the success to 3 levels of analysis
• Direct effect of a choice: defection earns more
• Indirect effect: you may get punished in retaliation
• “tertiary effect”: unending mutual recrimination—hence
the crucial importance of forgiveness
Spatial prisoner’s dilemma (Martin Nowak)
Runs like cellular automaton
Spatial structure allows “islands” of cooperation to rise in sea
of defectors
Iterated Prisoner’s Dilemma Solves the
problem of Evolutionarily Stable Strategies
Acorn Woodpecker:
Why don’t “freeloaders”
rise in genetic
frequency?
Other Evolutionarily Stable Strategies
The Side-Blotched Lizard (Uta stansburiana) is polymorphic with
three morphs that each pursues a different mating strategy
1) The Orange throat is very aggressive and operates over a large territory attempting to mate with numerous females within this larger area
2) The unaggressive Yellow Throat (called “sneakers”) mimic the markings/behavior of
female lizards and sneakily slip into the Orange Throat's territory to mate with the
females there (thereby overtaking the population), and
3) The Blue Throat who mates with and carefully guards ONE female - making it
impossible for the sneakers to succeed and therefore overtakes their place in a
population…