Imitation and Inequity in Avoiding the Tragedy of the Commons

1
Imitation and Inequityin Avoiding theTragedy of
the Commons

• Terry Van Belle and David H. Ackley
• September 14, 2004

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The Tragedy of the Commons

• Model of social interaction, pitting
• Short-term, individual gains vs
• Long-term, collective gains
• Modeled on the old English village commons
• Collective restraint vs Depletion of resources
• Typically, modeled with rational agents
• We studied transmission of memes
• Poorer agents imitated the richer agents
• New outcome -- Inequity

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Modeling the Tragedy
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Modeling the Tragedy, contd.

• Take
• Neural net, characterized by 3 weights
• 3 inputs (bias, resources, wealth), 1 output
  (take)
• Kinder, gentler Tragedy of the Commons
• Tax
• Fixed tax and spoilage
• Imitate
• Move weights to be more like your richer neighbor
• Noise added to weights
• Grow
• Resources increase exponentially until carrying
  capacity
• Minimum resources

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Tragedy of the Commons

• Investigated several different commons sizes
• 1x1, 2x1, 2x2, 4x4
• For anything greater than 2x1, the Tragedy occurs
• Take increases up to legal amount
• Wealth increases, then plummets
• Resources deplete to minimal values
• If each person owns their own commons (1x1),
  result is stable
• Agents who are too stingy or too greedy become
  poor, imitate successful neighbors
• Agents develop a farming strategy

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Inequity in the 2x1 Case
Take
Wealth
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The Folly of Imitating the Wealthy

• Most 2x1 commons contain one rich, greedy agent
  and one poor, altruistic agent
• Common strategy
• High resources Take more
• High wealth Take more
• High negative bias weight to restrain taking
• This strategy works well for rich agents, but is
  a disaster for poor ones

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Sharing in Larger Commons Sizes

• To restrain the Tragedy for larger commons, added
  a sharing step
• Take a portion of each agents wealth and
  distribute it among its neighbors
• 2x2 stabilized with 10 sharing
• 4x4 stabilized with 60 sharing

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Inequity in the 2x2 Case
Take
Wealth
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Inequity in the 4x4 Case
Take
Wealth
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Conclusions

• Not sharing, not depletion, but inequity
• Can occur when agents imitate entire
  philosophies of richer neighbors, rather than
  making rational decisions
• Requires agents to be restrained
• No agent can take 100 of resources
• Sharing required for larger commons sizes