Scrip Systems Victor Chan Cs 286 r Victor

Scrip Systems Victor Chan Cs 286 r Victor Chan

Agenda § Scrip Systems § Peer to Peer Systems § Scrip Systems for P 2 P Networks CS 286 Victor Chan 2 § Adobe

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 CS 286 Victor Chan 3 § Adobe

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, with 12, 000 Hours in circulation CS 286 Victor Chan 4 § Adobe

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 CS 286 Victor Chan

Moving on § Any further thoughts on group decision or yootopia? CS 286 Victor Chan

Peer to Peer Networks § Filesharing § § Online discussion § § Bit. Torrent, Kazaa, Gnutella, Napster Slashdot, Digg, etc. Distributed computing § Seti@home, Einstein@home CS 286 Victor Chan

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” p 2 p 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 CS 286 Victor Chan

Barter like approaches: § § Bit. Torrent § Tit for Tat algorithm (Optimistic Unchoking) § Exchange upload bandwidth for download bandwidth § New peers lose out, nothing to offer e. Mule § Track history of previous interactions with other users § Give priority to users with good history § With large n, hard to match up CS 286 Victor Chan

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) CS 286 Victor Chan 1 0 § Adobe

Scrip system for P 2 P § Benefits of having a Scrip System § In history based reputation systems, no longer need to meet same peers § In Bit. Torrent, 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! CS 286 Victor Chan

Scrip System in P 2 P networks § Efficiency and Nash Equilibria in a Scrip System for P 2 P Networks § Friedman, Halpern and Kash (2006) § Model for evaluating Scrip Systems in P 2 P Networks § Nash Equilibrium with threshold strategies § Money supply to maximize efficiency CS 286 Victor Chan

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 CS 286 Victor Chan

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 : agent i’s utility at round t CS 286 Victor Chan and able

Utility functions § Standard User: § Altruistic User: § Total utility: CS 286 Victor Chan

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. CS 286 Victor Chan

How many altruists? § 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: Users will not want to pay the cost and will never choose to volunteer CS 286 Victor Chan

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 P 2 P network § In Bit. Torrent 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 CS 286 Victor Chan

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: CS 286 Victor Chan

Nonstrategic play of the game § System “converges” to a distribution over money § Assume everyone plays § State of the game can be represented as: Total amount of money in state s CS 286 Victor Chan and system has M< kn dollars Player has value in this set

( 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 § There is a unique distribution in § Markov Chain, , then with large n, such that ds will be close to d* § that has, where m = M/n d*, with maximum entropy will likely be in a state s, Closeness is defined as the Euclidean distance between two distributions: CS 286 Victor Chan

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. CS 286 Victor Chan

Simulation Results CS 286 Victor Chan

Simulation Results CS 286 Victor Chan

Simulation Results CS 286 Victor Chan

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. CS 286 Victor Chan

Make the strategies continuous § Look at a strategy pair will play § , with probability and consider a mix strategy and with where § This essentially produces as continuous set of strategies by mixing adjacent threshold strategies. CS 286 Victor Chan

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. CS 286 Victor Chan

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. CS 286 Victor Chan

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 CS 286 Victor Chan

Simulation Results CS 286 Victor Chan

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 CS 286 Victor Chan

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 CS 286 Victor Chan

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 CS 286 Victor Chan

That’s it! Q&A CS 286 Victor Chan 3 5 § Adobe