On Selfish Behavior in CSMACA Networks

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On Selfish Behavior in CSMA/CA Networks
Mario Cagalj, Saurabh Ganeriwal, Imad Aad,
Jean-Pierre Hubaux
Paper appeared in Infocom 2005
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CSMA/CA in 802.11 networks

• Protocol to solve contention at the MAC layer
• Transmit only if channel is idle for a
  distributed inter-frame space (DIFS) time period
• DATA and ACK separated by a short interframe
  space SIFS lt DIFS
• Channel busy
• Transmission deferment until the channel is
  sensed idle for a DIFS period
• Further random deferment (backoff time)
• Possible use of RTS/CTS mechanism

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Exponential backoff procedure

• Extract a random number in (0, w)
• Decrement backoff counter every time slot
• If the backoff counter reaches 0, transmit
• If the channel is sensed busy
• freeze the backoff counter
• restart the backoff counter after the channel is
  sensed idle for a DIFS period
• First attempt-gt wCW
• Next m attempts -gt w2mx(CW1)-1, m 1

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Selfish behavior

• Wireless nodes may control their random deferment
• Simple cheating technique
• initializing the contention window CW to a lower
  value to gain a higher throughput
• keeping the CW value fixed after an unsuccessful
  transmission attempt
• Game theory approach
• game players -gt cheater nodes
• player i payoff function Ui -gt throughput ri
• player i strategy -gt cheater i sets the CW size
  Wi to maximize the throughput ri

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Payoff/Throughput evaluation
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Important property of cheater throughput
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Non-cooperative static game

• C -gt number of cheater players
• Si(1,2,,Wmax) -gt strategy set of player i
• Wi Si -gt strategy of player i
• For every Nash equilibrium W(W1,W2,,WC) at
  least one Wi has to be 1
• There are (WmaxC (Wmax -1)C) Nash equilibria
• Two families of Nash equilibria
• Only one selfish node i plays Wi1 and receives
  throughput rigt0, while the other players receive
  0 -gtunfair solution
• More than one selfish node sets its contention
  window to unity and all the C players receive
  throughput 0 -gt inefficient solution
• The tragedy of commons

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Cooperative static game (1)
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Cooperative static game (2)

• R is neither compact nor convex in CSMA/CA game
• i1,2,,C
  is a non-Nash, but unique, fair and
• Pareto-optimal solution
• Simulative results
• 10 cheater nodes
• 10 good nodes
• cheater nodes choose
• the same CW size

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Feasibility of Pareto-optimal solution r/W

• r/W dependence on the cheaters number C
• Unawareness of the node number in the network
• ?Idea dynamic repeated non-cooperative game
• to turn the non-Nash Pareto-optimal solution
  r/W into a Nash equilibrium
• to allow cheaters to converge to the Nash
  equilibrium point r/W

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Dynamic repeated non-cooperative game
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Nash equilibrium (1)

• Fundamental role of the amount
• At Nash equilibrium
• ? Any strategy profile t(t1, t2,, tC) with 0lt
  tilt1, i1,2,,C, can be made a Nash equilibrium
  point
• no network collapse

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Nash equilibrium (2)

• allows the Nash equilibrium point control
• Convenient choice
  
• 
  -gt penalty that the player with the lowest
  access probability inflicts on player i
• by the
  gradient method

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How does the game evolve?

• Cheaters set their access probabilities in such a
  way that ti(0)lt1 i1,2,,C
• Running the gradient method until all the
  cheaters stabilize at Nash equilibrium point
• A cheater i decreases its to the value
• Running the gradient method again and reaching
  the new Nash equilibrium point
• Each cheater j compares its current payoff
  with the previous step payoff
• if , stop
• otherwise repeat the previous steps

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More about the penalty function

• Dependence on the access probabilities of all the
  nodes
• Sufficient conditions for payoff functions
  Ji(ti)ri(ti)-Pi(ti) having a unique maximizer
  ti te
• tilt1 i1,2,,C
• A more convenient penalty function is
• Advantages
• Detection and penalizing of deviating cheaters
  need only throughput related knowledge
• Property of throughput equalization when the
  cheater j inflicts a punishment to the cheater i,
  Jiri-Pirj

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Detection mechanism

• Each cheater measures the throughput of each
  other node for Tobs seconds
• If the measured throughput ri and rj of nodes i
  and j are such that rj/ri gt (1e) with e
  tolerance margin, i classifies j as deviating
  cheater

• Short-term unfairness of 802.11 MAC protocol
• Possibility of false positives

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Penalizing mechanism

• Each cheater jams the packets of the detected
  non-cooperative cheaters for Tjam seconds
• Throughput equalization property is used to set
  the Tjam value
• If cheater i has to punish cheater j, riTobs
  riTjam rjTobs 0Tjam
  -gtTjam (rj / ri-1)Tobs
• To avoid Tjam-gt8 when ri-gt0, TjamminTjam,(rj/ri
  -1)Tobs

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Adaptive strategy

• If a cheater detects itself being jammed during a
  period ?, it gradually increases its contention
  window by steps of size ?
• ? -gt tradeoff between convergence speed and
  efficiency
• Higher fairness and efficiency also in case of
  multiple misbehavior levels

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Distributed coordination protocol

• Assumption WiWiin for all the cheaters at the
  onset of the system
• Every cheater sets a random timer to increase its
  contention window by a step of size ?
• The cheater x with the shortest timer increases
  the contention window to (Wxin ?)
• Based on the detection mechanism, cheater x
  activates the penalizing mechanism
• If a cheater observes that it is being jammed, it
  stops the timer
• Eventually the system stabilizes and Wi Wxin
  ? for all the cheaters
• Every cheater compares its throughput at Wiin
  with the throughput at Wxin ?
• in case of throughput decrease, it will stop the
  search for the optimal point of operation
• otherwise it will start a new timer to increase
  the size of its contention window and repeat the
  previous steps