May 8, 2009 1

Manipulating Scrip Systems:Sybils and Collusion

Ian KashCornell University

Joint work with Eric Friedmanand Joe Halpern

May 8, 2009 2

What is Scrip?

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Related Work:Uses 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 Work:Analysis 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 – and earns $1, and everyone else gets 0.

• Total utility for an agent is the discounted sum of round payoffs:

u rir

r

,0

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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 Work[Friedman et al ’06, Kash et al ’07]

• Maximum entropy characterizes the distribution of wealth.

• There is an -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 agent’s 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 agent’s requests get satisfied is:

(r − rk+1)/(1 − rk+1) if r ≠ 1

and k/(k + 1) if r = 1

Increasing pe with sybils increases utility.

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Proof

0 1 kk-12

Consider the Markov chain whose states are the wealth of an agent

…

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Proof

0 1 kk-12

Consider the Markov chain whose states are the wealth of an agent

Probability = pe / (pe + ps)

Probability = ps / (pe + ps)

…

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Proof

0 1 kk-12

Consider the Markov chain whose states are the wealth of an agent

Probability = pe / (pe + ps)

Probability = ps / (pe + ps)

…

Unsatisfied

Satisfied

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Proof

0 1 kk-12

…

This gives the stationary distribution:

di = ri (1 – r) / (1 – rk+1).

The fraction of requests satisfied is:

1 – d0 = (r – rk+1) / (1 – rk+1).

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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.