Coalitions in Congested Networks

By Shai Roitman & Jeffrey Rosenschein

General Scenario

Users sharing a pool of shared resources Users sharing a communication network Users can choose their own strategy No central control can be enforced Users can communicate with each other

Problems emerging from the scenario

Lack of co-operations and greedy individual behavior leads to

1. Global loss of utility – All users suffer loss of utility due to congestion

2. Individual user loss of utility – Individual users suffer loss of utility.

3. Loss of utility which could have been gained by using more of the network

Social welfare and central managementVs.Users rationality and lack of central control

Reasons for loss of utility

Local optimization of each user regardless of global optimization

Greedy behavior and lack of central management

Instable global optimization points

Due to congestion and non cooperative behavior

Agenda

Model of congested networks Model of Peer to Peer Networks Suggested improvements

– Coalition formation– Cooperative Nodes

Current solutions Summary Further extensions

Model of Congested Networks

Physical Model User Model Strategy Model Flow Model Cost / Utility Model User Optimization Nash Equilibrium Coalitions Formation

Physical Model

Let G be a graph. (V,E) For each e in E let L(e) be the latency

function ( G,{L(e)} ) are the physical setting

Latency functions

General attributes– Continuous– Non decreasing– Differentiable

Constant Linear Queue Theory Other

User model

U – the user group. n the number of users

ST = {Si,Ti} i=1…k (Source Target)

– Si , Ti in V r(i) – the rate of user “i” in

R^kR^k >=0

R = Matrix of k x n (G , L(e) , U , ST ,R )

instance problem

Strategy Model

Given an instance problem(G , L(e) , U , ST ,R)

Pi the simple paths from Si to Ti P The union of all Paths A strategy for a user “i” is a function

f: P-> R Feasibility of function f

Flow model

F – the total flow in the network F(p) – the flow in the path p For each edge e we can define F(e) The latency of a path given a flow is Lp(f) = Sum Le(Fe) (e is in P)

Cost / Utility model

User cost over a flow f:

Sum ( Lp(f)*f(i,p) )

The total cost of a fixed flow fSum (Le(e)*F(e)

User Optimization and Individual rationality

Given a flow F each user seeks out a strategy f such that

Ci(F+f) is minimized

Subject to feasibility

Nash Equilibrium points

A flow F is in Nash Equilibrium point if for every user i Ci(fi) <= Ci(f*i) for each f*I

Coalition formation

S subset of U Rs = Sum Ri (i in S) CoaliationValue (S) = Cs(f) – Sum (Ci(f*))

Theoretical results

The existence of Nash Equilibrium points The Worst case ratio between Nash

Equilibrium points and global optimization The super additive structure of the problem

-> The grand coalition = central control

Peer to Peer usages

Sharing of Information Software distribution Media distribution Computational Tasks Peer to Peer networks

Peer to Peer Model

Special case of the general model Peer to peer networks which are currently

used– Kazaa– eMule– FreeNet– Grid computing

Peer to Peer - Settings

Loosely controlled networks Users Pursue their own utility – no social awareness Most users are cooperative Some users may be malicious No Side payments / Side payments are allowed Some key users may which to care about social

welfare

Peer to Peer - Physical Model

Clusters of users joined by the ISP nodes – Fast internal communication– Slow external communication

Upload / Download bandwidth can be asymmetrical Clusters of the ISP joined by high bandwidth links

– Supporting many users

Number of open connections are limited per user

Peer to Peer Model – User Model

Users have supply and demand of information / files

Upload / Download bandwidth Users support a limited number of upload /

download slots Allocate resources for social benefit

– Disk Space (Cache)– Network bandwidth

Peer to Peer Model – Strategy

Users wish to maximize their gain – Satisfy their demand as quickly as possible

Users choose from who they wish to download – the route is chosen to maximize the bandwidth

Greedy strategy Users can act as mediators and have some social

awareness Users are mostly cooperative Some Users are malicious

Peer to Peer Model – Flow

Users share the connections of the ISPs ISP is using equal shares for the users

requests Every link is not fully used Users use a single route for information

transfers

Peer to Peer – Utility Model

Users wish to satisfy their demand as quickly as possible

Credit system can be used Some Users are there to help the social

welfare (ISP nodes / cache nodes) Users who are not active can help others Some users are malicious – wish to minimize

others utility

Peer to Peer Model – User Optimization

Users wish to maximize their utility – satisfy their demand

Users will evaluate the preferred route for their requests and use the fastest single route

Complete knowledge is assumed

Social Welfare and Private Utility

Nash Equilibrium Total competitiveness –> form of congestion

and inefficient network usage

=> Coalition formation – Sharing of information– Social awareness

Coalition Formation – Types

Coordinate downloads of files that have mutual interest for both of the clients

Have a pool of the credits -> Share the credits Users will upload files

– For gaining higher credit value – For participating in downloading hordes

Users will download popular files to increase their social value

ISP – Social welfare coordinators Malicious – Detecting them (Reputation System)

Peer to Peer – Simulation

Analysis Architecture Design Problems Concrete implementation

Peer to Peer – An Example

1 Supply Node – 2 slots 2 Demand Nodes – 2 Slots All are connected via ISP by a 2 kb/s link

(download and upload) The Supply is generated with 10 files Coordinated Vs Non Coordinated value

Peer to Peer – Suggested Twicking

eMule (Server Based) eMule - Kademlia (Distributed) FreeNet

Peer to Peer – More Issues

Security– Anonymously– Secretly– Authentication

Legal Aspects Protocols

Related work

eMule – Credit System eDonkey – Horde Downloading FreeNet – Secure Information distribution HTTP Proxies – File Caching

Conclusions

Extending the protocols to enable cooperative behavior may benefit the users

Coalitions may Increase the utilization of the network and loosen congestion

May be extended to other settings - computational tasks

Future Expansions

More simulation and extended protocols Reputation Systems

– Improve Credit System– External Credit / Utility System

Resource Allocation usages Coordinators – Users who coordinate efforts

Bibliography

How Bad is Selfish Routing? By Tim Roughgarden and Eva Tardos , 2000

Competitive Routing in Multi-User Communication NetworksBy Ariel Orda, Raphael Rom, Nahum Shimki

Worst-case EquilibriaBy Elias Koutsoupias and Christos Papadimitrio ,1999

Tight Bounds for Worst-Case EquilibriaBy Tight Bounds for Worst-Case Equilibria, 2002

Game Theory – 3rd edition, By Guillermo Owen, 1995

Related Sites

eMule– http://www.emule-project.net/

FreeNet– http://freenet.sourceforge.net/

Boost– http://www.boost.org/