Scrip Systems

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Scrip Systems
Victor Chan
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Agenda

• Scrip Systems
• Peer to Peer Systems
• Scrip Systems for P2P Networks

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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

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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

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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 isnt 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

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Moving on

• Any further thoughts on group decision or
  yootopia?

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Peer to Peer Networks

• Filesharing
• BitTorrent, Kazaa, Gnutella, Napster
• Online discussion
• Slashdot, Digg, etc.
• Distributed computing
• Seti_at_home, Einstein_at_home

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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 ISPs are trying to remove them
• Fair sharing does not happen since these users
  exist

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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

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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)

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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!

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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

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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 ß 0
  probability of fulfilling a request
• Assumption Time independence
• Agent fulfilling request will pay cost a
• A discount factor of d
• Time steps are in 1/n

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More definitions

• G(n,d,a,ß) represents a game with n agents
• agent chosen in round t to make request
• whether a given agent can
  satisfy request, dependent on ß
• whether a given agent will
  satisfy the request
• the agent
  chosen to satisfy request.
• Chosen at random from willing
  and able
• agent is utility at round t

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Utility functions

• Standard User
• Altruistic User
• Total utility

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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 d,a,ß such that in G(n, d,a,ß) with at least a
  altruistic users not volunteering is the dominant
  strategy for all standard users.

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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
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What does this mean?

• Example with ß 0.01, a 0.1, d 0.9999/day
  then need a1145
• 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 doesnt depend on n?
• In order to establish a useful scrip system, need
  to remove altruistic users, or standard users
  will all become free riders

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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

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Nonstrategic play of the game

• System converges to a distribution over money
• Assume everyone plays and system has Mdollars
• State of the game can be represented as

Player has value in this set
Total amount of money in state s
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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

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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.

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Simulation Results
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Simulation Results
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Simulation Results
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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.

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Make the strategies continuous

• 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.

where
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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.

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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.

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Theorem 4.2

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

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Simulation Results
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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(d,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

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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

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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

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Thats it!

• Q A

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