The evolution of cooperation

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The evolution of cooperation

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Altruism and the selfish gene

• Altruism benefit b to recipient at cost -c to
  the donor

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Altruism and the selfish gene

• Altruism benefit b to recipient at cost -c to
  the donor
• get the altruism out of altruism... (Trivers)

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Altruism and the selfish gene

• Altruism benefit b to recipient at cost -c to
  the donor
• get the altruism out of altruism... (Trivers)
• kin selection
• Hamiltons rule clt b.r

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Altruism and the selfish gene

• Altruism benefit b to recipient at cost -c to
  the donor
• get the altruism out of altruism... (Trivers)
• kin selection
• Hamiltons rule clt b.r
• in humans co-operation among non-relatives

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Darwin

• The small strength and speed of man, his want of
  natural weapons, etc., are more than
  counterbalanced ... by his social qualities,
  which led him to give and receive aid from his
  fellow men.

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Cooperation among non-relatives

• Direct reciprocation and the Prisoners Dilemma
• Indirect reciprocation
• Public Goods

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• Consequently, theories of evolution which, in
  accordance with the philosophies inspiring them,
  consider the mind as emerging from the forces of
  living matter, or as a mere epiphenomenon of this
  matter, are incompatible with the truth about
  man. Nor are they able to ground the dignity of
  the person.

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Reciprocity

• Reciprocal altruism...the trading of altruistic
  acts in which benefit is larger than cost, so
  that over a period of time both parties enjoy a
  net gain.
• (Trivers)

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The Prisoners Dilemma game

• To cooperate or to defect
• (example cooperate means to give a gift of value
  b at cost -c)

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Prisoners Dilemma

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Prisoners Dilemma

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The iterated Prisoners Dilemma

• probability w for another round
• (for instance, toss a coin, stop game if 6)
• shadow of the future (Axelrod)

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

• Generous Tit For Tat
• p close to 1
• q sizeable
• two zones

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

• Heteroclinic network
• A Tit or Tat
• B Firm But Fair
• C Bully
• D AllD

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The iterated Prisoners Dilemma

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The iterated Prisoners Dilemma

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Pavlov

• Cooperate if other player used same move as
  yourself in previous round
• reinforcement principle repeat former move after
  high payoff
• Pavlov is error-correcting
• Pavlov is stable
• Pavlov cannot invade population of defectors

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Pavlov

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Pavlov

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Pavlov

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Pavlov

• Simple learning rule
• stable, error-correcting
• but needs retaliator to prepare the ground

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Indirect reciprocity

• few rounds, as donor or receiver
• never with the same partner twice

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Indirect reciprocity

• R. Alexander
• Indirect reciprocity .. involves reputation and
  status, and results in everyone in the group
  continually being assessed and reassessed.

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Indirect reciprocity

• R. Alexander
• Indirect reciprocity .. involves reputation and
  status, and results in everyone in the group
  continually being assessed and reassessed.
• Cooperation channelled towards cooperative members

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Indirect reciprocity

• score increases by 1 if help is given, decreases
  by 1 if help is withheld
• score 0 at birth

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Indirect reciprocity

• score increases by 1 if help is given, decreases
  by 1 if help is withheld
• score 0 at birth
• strategy k give only if recipient has score at
  least k
• kgt5 always defect
• klt-5 always help

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Indirect reciprocity

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Indirect reciprocity

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Indirect reciprocity

• cooperation based on discrimination
• but not stable (can occasionally break down)

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Indirect reciprocity

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Indirect Reciprocity

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William D. Hamilton

• The theory of many-person games may
• seem to stand to that of two-person games
• in the relation
• of sea-sickness to a head-ache!