Cs286r Victor Chan

Scrip Systems

Victor Chan

CS286 Victor Chan

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 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

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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@home, Einstein@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 ISP’s 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:

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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 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

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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

𝑝𝑡

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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 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.

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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 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

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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 M< kn dollars

State of the game can be represented as:

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

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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 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

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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(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

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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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That’s it!

Q & A

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