P2P INCENTIVES Dror Marcus

YoniDeny Confess

Hadas

Deny Redo the test Yoni is freeHadas is expelled from school

Confess Yoni is expelled from schoolHadas is free

Both fail this course

YoniDeny Confess

Hadas

Deny Hadas : 2

Yoni : 2

Hadas : 0

Yoni : 3

Confess Hadas : 3

Yoni : 0

Hadas : 1

Yoni : 1 Nash Equilibrium

OUTLINE Optimizing Scrip Systems[1][2]

Modeling the problem Finding optimal solutions

One hop reputation for BitTorrent[3] Improving Tit-For-Tat

OPTIMIZING SCRIP SYSTEMS What is Scrip?

Non-governmental currency Users pay other users for service with scrip Free riding is prevented through the need to earn

scrip

OPTIMIZING SCRIP SYSTEMS How to model the problem? Determine the amount of money in the

system How to set the pricing in the systems How do newcomers effect the system

OPTIMIZING SCRIP SYSTEMS:MODEL Game of rounds Each agent i:

a: cost of satisfying a request b: probability of being able to satisfy a request g: value of having a request satisfied d: discount rate r: relative request rate (cost $1 if granted) : agent i‘s utility in round r

Total utility of an agent:

riu

/

0

r n ri

r

ud

OPTIMIZING SCRIP SYSTEMS:INITIAL INTERESTING RESULT Altruism & Hoarders

There exists an value C, that depends only on a, b and d such that, in G(n, d, b, a) with at least C altruists, not volunteering is a dominant strategy Set C > log1-b (a (1-d))

0

(1 )(1 )1

CC r

r

bb dd

--

-

Player’s request get satisfied for free with prob.

Most additional expected utility to gain by having money is:

1 (1 )Cb- -

OPTIMIZING SCRIP SYSTEMS:INITIAL INTERESTING RESULT - CONT Example:

b 0.01 (each player can satisfy 1% of requests) a 0.1 d 0.9999/day (≈ 0.95 per year) r = 1 per day Only need C > 1145

Therefore, adding reputation system on top of existing P2P systems to influence cooperation will have no effect on rational users! Is this a problem?

OPTIMIZING SCRIP SYSTEMS:MODEL REVISED Game of rounds An agent’s type t = (at,bt,gt,dt,rt)

at: cost of satisfying a request bt: probability of being able to satisfy a request gt: value of having a request satisfied dt: discount rate rt: relative request rate (probability to need

something)

OPTIMIZING SCRIP SYSTEMS:STRATEGY Picking a wining strategy for players

Threshold strategy to win Sk Show that this is the best strategy

Threshold Strategy

In some round, I have k dollars and have to decide whether to volunteer. What should I do?Sk: Volunteer if I have less than k dollarsk is your “comfort level,” how much you want to have saved up for future requestsS0 corresponds to never volunteering and S corresponds to always volunteering

OPTIMIZING SCRIP SYSTEMS:PLAYING THE GAME Examining the game

How to describe the state of the system?

OPTIMIZING SCRIP SYSTEMS:PLAYING THE GAME How to describe the state of the system?

Look at the distribution of Money. Each state in the system represents the amount

of money each player has. Specifically:

Each player can have {0,….,k} dollars ($) Let Dk denote the set of probability distributions on {0,

…,k} represents the fraction of people that have each

amount of money Each state s has its own distribution

kd D

s kd D

OPTIMIZING SCRIP SYSTEMS:PLAYING THE GAME The system is analyzed as a Markov Chain

The system always ends up in the same place!

Markov Chain

≈ The probability of moving from the current state to another only depends on the current state of the system. (We don’t care about the past)

OPTIMIZING SCRIP SYSTEMS:PLAYING THE GAME The system is analyzed as a Markov Chain

The system always ends up in the same place*

OPTIMIZING SCRIP SYSTEMS:REACHING EQUILIBRIUM Equilibrium exists

There is an efficient algorithm to find this equilibrium

Agent response : How to set its threshold (k) If dt is not too small, and every agent but i plays

a threshold strategy, then agent i has an e-best response that is a threshold strategy.

Agent i’s best response function is monotone in the strategies of the other agents

OPTIMIZING SCRIP SYSTEMS:RECAP Have a model to describe the system System reaches a steady state (money

distribution) Equilibrium exists What Next?

OPTIMIZING SCRIP SYSTEMS:OPTIMIZE PERFORMANCE Improved performance

Better social welfare i.e. More utility

How to improve performance? Increasing the amount of money in the system

up to a certain point, after which the system experience a monetary crash

The Capitol Hill Babysitting Co-op

OPTIMIZING SCRIP SYSTEMS:OPTIMIZE PERFORMANCE Given an Equilibrium, how good is it?

If a request in satisfied, social welfare increases by gt-at.

What are the chances for a request being satisfied: Requester needs to have money – Probability 1-M0 Need to have a volunteer – Probability ≈1

Total expected welfare summed over all rounds:

Therefore minimizing M0 maximizes utility!

0(1 )( )1

t t

t

M g ad

- --

OPTIMIZING SCRIP SYSTEMS:OPTIMIZE PERFORMANCE

OUTLINE Optimizing Scrip Systems[1][2]

Modeling the problem Finding optimal solutions

One hop reputation for BitTorrent[3] Improving Tit-For-Tat

Incentives for Live P2P streaming (bonus ) Creating incentives to stream video

BITTORRENT REFRESH File is broken to small blocks (32-256 KB) A tracker site keeps track of the active participants

+ extra statistics. Seed – A peer that finished downloading, and has

all the pieces of the file Leecher – A peer that is still downloading pieces of

the file Swarm – tracker sends list of ~40 peers

downloading the file to a new leecher together forming a swarm.

Chocking Algorithm – Choose top k-1 peers from the swarm with highest rates + 1 random peer (optimistic unchoke) to upload to. All k peers receive the same upload rate.

BITTORRENT REFRESH File is broken to small blocks (32-256 KB) A tracker site keeps track of the active participants

+ extra statistics. Seed – A peer that finished downloading, and has

all the pieces of the file Leecher – A peer that is still downloading pieces of

the file Swarm – tracker sends list of ~40 peers

downloading the file to a new leecher together forming a swarm.

Chocking Algorithm – Choose top k-1 peers from the swarm with highest rates + 1 random peer (optimistic unchoke) to upload to. All k peers receive the same upload rate.

HW – Think of at least two different

ways to exploit the current incentives methods in Bittorrent (tit-for-tat, chocking, unchocking) to gain more download rate for

less upload

ONE HOP REPUTATION :SHARING IN THE WILED Large scale measurements of bittorent “in

the wild” More then 14 million peers and 60,000 swarms

studied. Data was collected in two traces BT-1 (~13K

swarms) and BT-2 (~55K Swarms). Measurements were used to analyze both

current BitTorrent performance and the new “one-hop” method effectiveness.

ONE HOP REPUTATION :BITTORRENT PERFORMANCE Performance and availability are extremely

poor Median download rate in swarms is 14 KBps for a

peer contributing 100KBps. 25% of swarms are unavailable.

ONE HOP REPUTATION :BITTORRENT PERFORMANCE - CONT Weak Incentives

Peers at low end of capacity see large returns in contributions

Increase by 100-fold only improves by 2-fold The incentive is the weakest for the peers that

can help the most

ONE HOP REPUTATION :BITTORRENT PERFORMANCE - CONT Altruism

Seeds do not have requests and can’t use tit-for-tat for making decisions.

Too many seeds weakens contribution incentives. Too few seeds also weakens incentives since

peers quickly run out of data to trade. Overall performance is mixed

Some swarms enjoy many altruistic donations (enabling free-riding).

Other swarms are “starved” for data

ONE HOP REPUTATION:WHAT CAN BE DONE? Can long-term history between peers be used

(instead of tit-for-tat)?

ONE HOP REPUTATION:WHAT CAN BE DONE? Can long-term history between peers be used

(instead of tit-for-tat)?

ONE HOP REPUTATION 97% of all peers observed in trace BT-2 are

connected directly or through one of the 2000 most popular peers.

ONE HOP REPUTATIONPROTOCOL Notations and peer state information

ONE HOP REPUTATIONPROTOCOL Each peer selects it’s top K intermediaries. When two peers meet first, they exchange

top K sets and compute intersection. For each intermediate, peers request receipts

of contributions. Multiple peers can serve as intermediaries. Receipt messages are sent periodically from

receiver to sender. Also update messages are sent to intermediaries.

For each peer P request If P interacted with me before use: Otherwise get random subset of joint Top K

mediators and compute reputation according to:

Where:

ONE HOP REPUTATIONDEFAULT POLICY

For each peer P request If reputation is above a threshold, send data

to P at rate proportional to it’s reputation

ONE HOP REPUTATIONDEFAULT POLICY- CONT

My reputation is on the line! Even if a “evil” peer convinces a popular

intermediary to recommend him, his own good standing will reduce and he will no longer be popular.

ONE HOP REPUTATIONREPUTATION

Peers can gain good standings by: 1) Contributing to an intermediary directly 2) Contributing to a peer that satisfied the

intermediary request in the past In (1), there is an increase of reputation in

the intermediary. In (2), reputation of one peer is simply

moved to the other.

ONE HOP REPUTATIONLIQUIDITY

Total reputation (liquidity of intermediary) is limited by its own demand. Solved by inflation factor of 100. Inflation also provide incentive to be

intermediary. Potential for economic inflation.

ONE HOP REPUTATIONLIQUIDITY

ONE HOP REPUTATIONEVALUATION

Data overhead Maximum overhead for popular intermediary of

3MB per day. How good is the one hop coverage (In BT-2

trace)? Median number of shared intermediaries is 83 More than 99% of peers have at least one

common entry in their top K.

ONE HOP REPUTATIONEVALUATION

How quickly can a new peer determine intermediary value? After a few dozen interactions with randomly

chosen peers.

ONE HOP REPUTATIONEVALUATION - NEW USERS

How quickly can a new peer gain reputation? Peers observe popular intermediaries frequently.

New users both encounter opportunity to gain standings and recognize it. What can they exchange?

ONE HOP REPUTATIONEVALUATION - NEW USERS

Evaluation show concrete improved performance, regardless of strengthened incentives.

25 MB file download was tested on PlanetLab Historical information allows peers to find

good tit-for-tat peering. Results show a median reduction in download

time from 972 seconds to 766 seconds

ONE HOP REPUTATIONEVALUATION – PERFORMANCE

QUESTIONS?

[1] Efficientcy and Nash equilibria in a scrip system for P2P networks Ian A. Kash, Eric J. Friedman, Joseph Y. Halpern

[2] Optimizing scrip systems: Eciency, crashes, hoarders, and altruists Ian A. Kash, Eric J. Friedman, Joseph Y. Halpern

[3] One hop Reputations for Peer to Peer File Sharing Workloads Michael Piatek Tomas Isdal Arvind Krishnamurthy

Thomas Anderson.

PAPERS