TCP Connection Game: A Study on the Selfish Behavior of TCP Users

1
TCP Connection GameA Study on the Selfish
Behavior of TCP Users
Honggang Zhang, Don Towsley, Weibo Gong Univ. of
Massachusetts Amherst

• Presented by
• Honggang Zhang

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Outline

• General TCP connection game formulation
• System optimization problem
• Different games capturing different user
  behaviors
• Conclusions and future work

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TCP Connection Game
bottleneck link

• Assumptions
• all connections experience the same loss rate
• aggregate goodput bottleneck link capacity

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TCP Connection Game
bottleneck link

• m users compete for congested bottleneck link
• User i strategy number of connections (ni)
• User i adjusts number of connections to search
  for maximum goodput or other utilities

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Problems to be studied

• Existence, uniqueness of Nash equilibrium
• Nash equilibrium
• a vector n(n1, n2, , nm) such that no
  user can benefit by deviating from it

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What is cost ?
bottleneck link
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System Optimization
minimize aggregate offered rate from all
users while keeping bottleneck link fully utilized
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Results of System Optimization

• Loss rate p is increasing function of number of
  connections

Example. Assume all users have same RTT.

• System optimal cost uniquely achieved when each
  user opens one connection

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TCP Connection Game

• Different games to capture different user
  behaviors
• Two most important games
• Game 1 aggressive users
• Game 2 resource constrained
• Strategy space of user i

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Game 1 Aggressive Users

• Utility of user i goodput

Number of connections of user i
Per connection goodout of user i
Round Trip Time of user i
Bottleneck link capacity

• Nash equilibrium nNE(n1max, , nmmax)
• Reason users not resource constrained

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Game 1 Aggressive Users

• Efficiency loss unbounded as nimax increase

Example. Total goodput of user i given other
users having 5 connections.
As nimax increases, loss rate approaches 1
congestion collapse !
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Game 2 Resource Constrained Users

• Users utility function

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Game 2 Resource Constrained Users

• Theorem there exists a unique Nash equilibrium
  (NE) in m (mgt2) user TCP connection game.

Two-player game example

• Illustrate Nash equilibrium using best response
  curves
• Best Response of player i
• The optimal number of connections given the
  number of connections of all other players.

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1
3
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Game 2 Resource Constrained Users
System cost of Nash equilibrium
Loss of Efficiency
System cost of optimal point

• Loss of efficiency is bounded
• The upper bound is function of network
  parameters and

NO congestion collapse!
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How users play TCP connection game?

• Best-response dynamics or algorithm
• Users take moves alternatively, each move is the
  best response to the number of connections of all
  other players

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2
Number of connections of player 2
3
1
Number of connections of player 1
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Stability of Nash equilibrium in Game 2

• Nash equilibrium (NE) of two-player game locally
  stable for best response dynamics
• Within some neighborhood of NE, if there is
  deviation from Nash equilibrium and each player
  takes best response alternatively, then this
  interaction process converges back to Nash
  equilibrium
• Result follows from Banach contraction mapping
  theorem

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Local Stability
Player 1 deviates from Nash equilibrium
Nash equilibrium
1
4
Number of connections of player 2
3
2
Local Stability Region
Number of connections of player 1
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Conjecture Global Stability
Nash equilibrium
4
2
Number of connections of player 2
3
1
Number of connections of player 1
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Conclusions

• Nash equilibrium exists in all variants of TCP
  connection games
• Efficiency loss bounded if users resource limited
• More powerful users have higher utility at Nash
  equilibrium
• Nash equilibrium locally stable for two-player
  version of game 2
• Selfish behavior of TCP users will NOT lead to
  congestion collapse in TCP connection games

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Thank you!Questions ?