Manipulating Scrip Systems: Sybils and Collusion

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Manipulating Scrip SystemsSybils and Collusion

• Ian Kash
• Cornell University
• Joint work with Eric Friedman
• and Joe Halpern

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What is Scrip?
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Related WorkUses of Scrip Systems

• Preventing Free Riding
• Babysitting Coop Sweeney and Sweeney 77
• Karma Vishnumurthy et al 03
• Brownie Points Belenkiy et al 07
• Dandelion Sirivianos el al 07
• AntFarm Peterson and Sirer 09
• Resource Allocation
• Agoric Systems Miller and Drexler 88
• Mariposa Stonebraker et al 94
• Yootles Reeves et al
• Mirage Chun et al 05
• Egg Brunelle et al 06

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Big Question
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Big Question

• How robust are the economies of scrip systems
• and what should the system designer do to
• optimize performance?
• What happens when people have multiple identities
  (sybils)?
• What happens when people collude?

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Related WorkAnalysis of Scrip Systems

• Friedman et al 06, Kash et al 07
• Aperjis and Johari 06
• Hens et al 07
• Implicitly assumes each agent is separate.
• What happens when people work together?

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Modeling a Scrip System

• n agents
• In round r, an agent is randomly chosen to make a
  request
• Each other agent decides whether to volunteer
• One volunteer is randomly chosen to satisfy the
  request
• For round r, requester gets a payoff of 1 (if
  someone volunteered) and pays 1, volunteer pays
  a small utility cost of a and earns 1, and
  everyone else gets 0.
• Total utility for an agent is the discounted sum
  of round payoffs

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Agent Strategies

• In some round, I have k dollars and have to
  decide whether to volunteer. What should I do?

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Why Do I Want to Satisfy?
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Why Do I Not Want to Satisfy?
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Threshold Strategies

• Sk Volunteer if I have less than k dollars
• k is your comfort level how much you want to
  have saved up for future requests

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Main Results of Prior WorkFriedman et al 06,
Kash et al 07

• Maximum entropy characterizes the distribution of
  wealth.
• There is an e-Nash Equilibrium where all agents
  play threshold strategies.
• More money is good, until the system crashes.

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Results in this Work

• Sybils are generally bad.
• Collusion is generally good.
• Generalization of previous results using relative
  entropy.

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What Can I Do With Sybils?
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Some Notation

• Consider the perspective of a single agent
• ps probability of being able to spend a dollar
  in the current round
• pe probability of being able to earn a dollar in
  the current round
• Sybils increase this
• r pe/ps
• Linear in pe
• k the agents threshold

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How does being chosen help?

• Theorem In the limit as the number of rounds
  goes to infinity, the fraction of the agents
  requests get satisfied is
• (r - rk1)/(1 - rk1) if r ? 1
• and k/(k 1) if r 1
• Increasing pe with sybils increases utility.

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Proof

0
1
k
k-1
2
Consider the Markov chain whose states are the
wealth of an agent
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Proof

0
1
k
k-1
2
Probability pe / (pe ps)
Probability ps / (pe ps)
Consider the Markov chain whose states are the
wealth of an agent
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Proof

0
1
k
k-1
2
Satisfied
Probability pe / (pe ps)
Probability ps / (pe ps)
Unsatisfied
Consider the Markov chain whose states are the
wealth of an agent
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Proof

0
1
k
k-1
2
This gives the stationary distribution di ri
(1 r) / (1 rk1). The fraction of requests
satisfied is 1 d0 (r rk1) / (1 rk1).
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Diminishing Returns For Sybils
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Sybils Are Typically Bad
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Sybils Can Be Good
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Sybils Reduce Stability
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Sybils Are Not Needed(With One Type)

• Theorem With one type of agent, if there exists
  an equilibrium with social welfare x that relies
  on some agents having sybils then there exists an
  equilibrium with social welfare approximately x
  where no agents have sybils.

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Not True With Two Types
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What To Do About Sybils?

• Impose a modest cost to discourage agents with pe
  close to ps.
• Bias the volunteer selection mechanism.

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Advertising

• Analysis assumed that agents increased pe by
  creating sybils.
• Could also increase pe by advertising their
  capabilities. For example
• Connection Type
• Name Choice

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What Can Colluders Do?
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Collusion
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Conclusion

• Sybils are generally bad.
• Can be discouraged using modest costs.
• Bias selection to help poor agents.
• Also applies to advertising.
• Collusion is generally good.
• Also applies to creating the ability to loan
  money.