Manipulating Scrip Systems Sybils and Collusion Ian Kash
Manipulating Scrip Systems: Sybils and Collusion Ian Kash Cornell University Joint work with Eric Friedman and Joe Halpern May 8, 2009 1
What is Scrip? May 8, 2009 2
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] Ant. Farm [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] May 8, 2009 3
Big Question May 8, 2009 4
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? May 8, 2009 5
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? May 8, 2009 6
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: May 8, 2009 7
Agent Strategies In some round, I have k dollars and have to decide whether to volunteer. What should I do? May 8, 2009 8
Why Do I Want to Satisfy? May 8, 2009 9
Why Do I Not Want to Satisfy? May 8, 2009 10
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 May 8, 2009 11
Main Results of Prior Work [Friedman 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. May 8, 2009 12
Results in this Work • Sybils are generally bad. • Collusion is generally good. • Generalization of previous results using relative entropy. May 8, 2009 13
What Can I Do With Sybils? May 8, 2009 14
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 May 8, 2009 15
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 Ø Increasing pe with sybils increases utility. May 8, 2009 16
Proof … 0 1 2 k-1 k Consider the Markov chain whose states are the wealth of an agent May 8, 2009 17
Proof … 0 1 2 k-1 k Probability = pe / (pe + ps) Probability = ps / (pe + ps) Consider the Markov chain whose states are the wealth of an agent May 8, 2009 18
Proof … 0 1 Satisfied Unsatisfied 2 k-1 k Probability = pe / (pe + ps) Probability = ps / (pe + ps) Consider the Markov chain whose states are the wealth of an agent May 8, 2009 19
Proof … 0 1 2 k-1 k This gives the stationary distribution: di = ri (1 – r) / (1 – rk+1). The fraction of requests satisfied is: 1 – d 0 = (r – rk+1) / (1 – rk+1). May 8, 2009 20
Diminishing Returns For Sybils May 8, 2009 21
Sybils Are Typically Bad May 8, 2009 22
Sybils Can Be Good May 8, 2009 23
Sybils Reduce Stability May 8, 2009 24
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. May 8, 2009 25
Not True With Two Types May 8, 2009 26
What To Do About Sybils? • Impose a modest cost to discourage agents with pe close to ps. • Bias the volunteer selection mechanism. May 8, 2009 27
Advertising • Analysis assumed that agents increased pe by creating sybils. • Could also increase pe by advertising their capabilities. For example: – Connection Type – Name Choice May 8, 2009 28
What Can Colluders Do? May 8, 2009 29
Collusion May 8, 2009 30
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. May 8, 2009 31
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