The Evolution of Cooperation

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The Evolution of Cooperation

• Robert Axelrod, 1984

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Abstract

• When to cooperate, when to be selfish?
• In an ongoing interaction with another
  person/entity
• Prisoners Dilemma
• Allows players to achieve mutual gains from
  cooperation
• Allows for possibility that one player might
  exploit the other
• Allows for possibility that neither player may
  cooperate
• Computer Prisoners Dilemma Tournament
• Entries from game theorists in economics,
  psychology, sociology, political science,
  mathematics, biology, physics, computer science
• To discover under what conditions will
  cooperation emerge in a world of egoists without
  central authority?
• TIT FOR TAT
• Properties of successful strategy
• Conditions for successful strategy

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Prisoners Dilemma
Player B
Player A
R Reward for mutual cooperation S Suckers
payoff T Temptation to defect P Punishment
for mutual defection

• No communication between players therefore no
  way for A to make enforceable threats or
  commitments with B
• Only info available to the players about each
  other is the history of their interaction so far
  no reputation analysis
• No way to eliminate other players or run away
  from interaction
• No way to change the other players payoffs

T gt R gt P gt S R gt (T S)/2
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TIT FOR TAT

• TIT FOR TAT
• Cooperates on first move
• Do whatever the other player did on the previous
  move
• TIT FOR TAT vs ALL D (always defect)
• TIT FOR TAT Cooperate
• ALL D Defect
• Outcome T 0, A 5
• TIT FOR TAT Defect
• ALL D Defect
• Outcome T 1, A 1
• TIT FOR TAT Defect
• ALL D Defect
• Outcome T 1, A 1
• etc

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Strategy

• What is the best strategy?
• What strategy will yield a player the highest
  possible score?
• NOT how can I win and you lose?
• Not like chess, zero-sum game
• A can safely assume that B will use the most
  feared move
• Interests of the players are completely
  antagonistic
• Non-zero-sum games
• Interests of players not in total conflict
• Both players can do well by getting reward R for
  mutual cooperation, or both can do poorly by
  getting punishment P for mutual defection
• Using the assumption that the other player will
  always make the move you fear most (defection)
  will lead you to expect that the other will never
  cooperate, leading you to defect leads to
  unending punishment P
• If the discount parameter is sufficiently high,
  no best rule exists independently of the strategy
  being used by the other player
• Strategy which works best depends directly on the
  other players strategy, and whether this
  strategy leaves room for development of mutual
  cooperation (ALL D does not)
• Based on discount parameter after all, if you
  are unlikely to meet the other person again or if
  you care little about future payoffs, then you
  might as well defect now and not worry about the
  consequences for the future

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Good strategy when confronted with an iterated
Prisoners Dilemma

• Computer Tournament
• Round-robin each strategy was paired with each
  other entry, as well as with its own twin and
  with RANDOM (randomly cooperates and defects with
  equal probability)
• 1st round winner TIT FOR TAT
• 2nd round all players aware of results from 1st
  round, and still TIT FOR TAT won
• Analysis from tournament properties which tend
  to make a decision rule successful/robust
• Niceness
• Retaliatory
• Forgiveness
• Clarity
• Evolution of cooperation requires that
  individuals have sufficiently large chance to
  meet again, so that they have a stake in their
  future interaction. If this is true, cooperation
  can evolve in three stages
• Cooperation can get started even in a world of
  unconditional defection small clusters of
  individuals who base their cooperation on
  reciprocity and have even a small proportion of
  their interactions with each other
• Strategy based on reciprocity can thrive in a
  world where many different kinds of strategies
  are being tried
• Cooperation, once established on the basis of
  reciprocity, can protect itself from less
  cooperative strategies
• Advice for participants of iterated Prisoners
  Dilemma
• Do not be envious
• Do not be the first to defect

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Live-and-Let-Live WWI

• Cooperation emerged despite great antagonism
  between the players
• During trench warfare, cooperation flourished
  despite
• Best efforts of senior officers to stop it
• Passions aroused by combat
• Military logic of kill or be killed
• Ease of high command to repress any local efforts
  to arrange a direct truce
• Use Prisoners Dilemma theory to explain
• How could the live-and-let-live system have
  gotten started?
• How was it sustained?
• Why did it break down toward the end of the war?
• Why was it characteristic of trench warfare in
  WWI, but of few other wars?

Germany
France/UK
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How to promote cooperation

• Enlarge the shadow of the future
• Mutual cooperation becomes more stable if the
  future is sufficiently important relative to the
  present
• Use large discount parameter
• Or make interactions more durable (prolong
  interaction)
• Or make interactions more frequent
• Change the payoffs
• Make the long-term incentive for mutual
  cooperation greater than the short-term incentive
  for defection
• Or If the punishment for defection is so great
  that cooperation is the best choice in the short
  run, no matter what the other player does, then
  there is no longer a dilemma
• Teach people to care about each other
• Teach reciprocity
• TIT FOR TAT is eye for an eye, which is pretty
  rough justice
• But, in situations where there is no central
  authority to enforce community standards, players
  must rely upon themselves to give each other the
  necessary incentives to elicit cooperation rather
  than defection
• Improve recognition abilities
• Ability to recognize the other player from past
  interactions and to remember the relevant
  features of those interactions is necessary to
  sustain cooperation
• Without these abilities, a player could not use
  any form of reciprocity and hence could not
  encourage the other to cooperate