Scrip Systems

1. Scrip Systems Victor Chan

2. Agenda Scrip Systems Peer to Peer Systems Scrip Systems for P2P Networks Adobe Internal

3. What is a scrip? A scrip is a non governmental currency used to pay for services from others. The need to earn scrip prevents freeloading Adobe Internal

4. Where is scrip systems used? • Capitol Hill Baby Sitting Co-op (Sweeney ‘77) • Couples babysitting for each other • Paid in scrips, each worth one hour of babysitting time • Low circulation of scrips resulted in “recession” • Eventually too much scrip was issued • Ithaca Hours (started in 1991) • Local currency used at Ithaca New York • 500 business participating, including libraries, banks, medical centers, landlords • Used to promote local economic development, with12,000 Hours in circulation Adobe Internal

5. Yootopia! (Reeves et al 2006) • Yootle, a local currency created at Yahoo! • Used in prediction markets • Used to buy favors from people • Used where cold hard cash isn’t the best idea • All transactions are recorded in a ledger system • Group decision with a scrip system (Where to go for dinner?) • Voting with compensation • Vickery-Clarke-Groves (VCG) Mechanism • General Decision Auction (DAUC) • Iterative Decision Auction • SMS and web interface for users

6. Moving on Any further thoughts on group decision or yootopia?

7. Peer to Peer Networks • Filesharing • BitTorrent, Kazaa, Gnutella, Napster • Online discussion • Slashdot, Digg, etc. • Distributed computing • Seti@home, Einstein@home

8. Peer to Peer Networks in Files Sharing • Increased social welfare • Costs still exist, leading to free riding users • Gnutella 70% users do not share, and 50% requests filled by top 1% users • There exist “altruistic” users that have become vital to the “health” p2p systems • However these users are expensive to host on a network and ISP’s are trying to remove them • Fair sharing does not happen since these users exist

9. Barter like approaches: • BitTorrent • Tit for Tat algorithm (Optimistic Unchoking) • Exchange upload bandwidth for download bandwidth • New peers lose out, nothing to offer • eMule • Track history of previous interactions with other users • Give priority to users with good history • With large n, hard to match up

10. Reputation based approaches: • Internet Relay Chat (IRC) • Direct client to client sharing • Set up using private messaging/negotiation • Slow for new users to gain enough “rep” • Kazaa • Measure ratios of upload vs. download • To help new users, everyone is given “avg” rating • Free ride until “bad” rating, and create a new account (sybil attack) Adobe Internal

11. Scrip system for P2P • Benefits of having a Scrip System • In history based reputation systems, no longer need to meet same peers • In BitTorrent, tit for tat can be extended to an exchange between multiple users • “The Role of Prices in Peer-Assisted Content Distribution” Johari et al • New users can be given scrip right away to participate • Problems of having a Scrip System • Still vulnerable to sybil attacks • How much money to have in the system? • Inflation, bubbles, recessions just like the real economy!

12. Scrip System in P2P networks • Efficiency and Nash Equilibria in a Scrip System for P2P Networks • Friedman, Halpern and Kash (2006) • Model for evaluating Scrip Systems in P2P Networks • Nash Equilibrium with threshold strategies • Money supply to maximize efficiency

13. The Model • Model Asymmetric interactions in a file sharing network • Unlike previous models of random matching between users • Each round uniformly select an agent to request and match with provider • Providers in the system each with β > 0 probability of fulfilling a request • Assumption: Time independence • Agent fulfilling request will pay cost α < 1 • A discount factor of δ < 1 is used • Time steps are in 1/n

14. More definitions • G(n,δ,α,β) represents a game with n agents • : agent chosen in round t to make request • : whether a given agent can satisfy request, dependent on β • : whether a given agent will satisfy the request • : the agent chosen to satisfy request. • Chosen at random from willing and able • : agent i’s utility at round t

15. Utility functions • Standard User: • Altruistic User: • Total utility:

16. Altruistic Users: Closer look • Always happy to upload, since cost is positive and their strategy is • for all t • If enough of these users, others become free riders and play • for all t • How many altruists do you need to make everyone a freeloader? • Proposition 2.1: There is an a that depends only on δ,α,β such that in G(n, δ,α,β) with at least a altruistic users not volunteering is the dominant strategy for all standard users.

17. How many altruists? Users will not want to pay the cost and will never choose to volunteer With no money, users have their requests filled with probability: So even with money, their total additional utility gain is: But if this gain is less than the cost to get money:

18. What does this mean? • Example with β = 0.01, α = 0.1, δ = 0.9999/day then need a>1145 • Relatively small size compared to a large P2P network • In BitTorrent having 1145 Seeds (altruist) is unlikely, so we still see many leechers uploading. • Any thoughts on why amount doesn’t depend on n? • In order to establish a useful scrip system, need to remove altruistic users, or standard users will all become free riders

19. Finding the equilibrium in a Scrip System • Users pay those that satisfy their requests $1 • Total amount of money in system M • Agents using threshold strategies:

20. Nonstrategic play of the game Player has value in this set Total amount of money in state s System “converges” to a distribution over money Assume everyone plays and system has M< kn dollars State of the game can be represented as:

21. Distributions of Money in the System ( • Let be the distribution on {0,….,k} • Not very useful by itself, since not all distributions can be achieved • Look at the distributions that has, where m = M/n • There is a unique distribution in d*, with maximum entropy • Markov Chain, , then with large n, will likely be in a state s, such that ds will be close to d* • Closeness is defined as the Euclidean distance between two distributions:

22. Theorem X is the random variable that the Markov Chain is in a state S at time t After some time t, the Pr(X is in state S where ds will be close to d*) is very high.

23. Simulation Results

24. Simulation Results

25. Simulation Results

26. Game under strategic play Goal: Show that there is a non trivial Nash Equilibrium where all agents play a threshold strategy First show for all k, if all other agents play Sk there is a Sk’ for agent i that is also the best response.

27. Make the strategies continuous where Look at a strategy pair , and consider a mix strategy will play with probability and with This essentially produces as continuous set of strategies by mixing adjacent threshold strategies.

28. Theorem 4.1 If every other agent is playing then the best response is either a unique or a mix of playing two adjacent threshold strategies.

29. Proof of 4.1 Consider agent i with probability of making a request and receiving a request constant i decides at each iteration whether to satisfy a request based on its strategy So to i, the system is a Markov Decision Process, with i having the choice to move between various states i will compute the optimal policy for this MDP, and there is a optimal policy that is a threshold policy.

30. Theorem 4.2 • There should be a Nash Equilibrium that is in the space of threshold strategies • Fixing δ , we get a best response function that is a step function. • Any point where the br(δ,γ) = γ then there is a Nash Equilibrium

31. Simulation Results

32. Social Welfare and Scalability • How much money M should be in the system? • Theorem 5.1: Most efficient equilibrium only depends on the ratio of M to n. • Proof, from Theorem 3.1, the d* depends only on M/n and k, and since br(δ,k) depends on only d*, the Nash Equilibrium is only depend on M/n • In practice, it will be easier to adjust the price of a transaction rather than injecting or removing money from the system. • New comers can be added by changing the price of transactions

33. Sybils and Collusion • Sybils can be used to increase the likelihood of being chosen to fulfill a request • Set a lower k threshold strategy, offer to work more often • Sybils can also be used to drive down the price of requests • Or make sybils leave and drive up the price • Price of fulfilling a request depends on n

34. Extensions The current system is Homogenous, relax these assumptions Cost of joining the network, could deter sybil attacks The current system does not take into account of altruistic users Effect of hoarders, people who work but never spend (stocking up) Any scrip system will require a centralized accounting system, and users will likely have to reveal their identities

35. That’s it! Q & A Adobe Internal