Coalitions in Congested Networks By Shai Roitman & Jeffrey Rosenschein
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/