Effect of Selfish Nodes on Topology Control

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Effect of Selfish Nodes on Topology Control

• Ramakant Komali
• ECON 5984

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Outline

• Motivation
• Game-theoretic model
• Propositions
• Future work

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Why consider selfish nodes in TC?

• Traditional TC algorithms
• focus on achieving connectivity related
  properties at minimum power
• Assume that nodes fully cooperate to achieve a
  global objective
• Unrealistic when nodes are owned by different
  entities
• Will perform poorly in presence of even a single
  selfish node
• Top reason for a node to be selfish
• Conserve energy consumption
• nodes do not need to be active for the entire
  session duration
• cost of node cooperation may exceed benefit
• nodes may reject relay requests to extend
  lifetime

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Effect of a single selfish node

• S.Eidenbenz, P. Santi,A Framework for Incentive
  Compatible Topology Control in Non-Cooperative
  Wireless Multi-Hop Networks, Tech. report
• Final outcome may not be globally optimal!

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Why consider selfish nodes in TC?

• Need to account for such nodes (and behavior) to
  form network which
• Is connected at minimum power
• Common approaches
• Stimulating nodes to cooperate
• Modeling incentives
• Reputation mechanism

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Game-theoretic model

• Consider
• A
• Power vector p induces g(p) assume g(p)
  undirected graph
• Payoffs where
• Assume
• f is the number of nodes that can be reached
  (multi-hop).

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The M2M algorithm

• Initialization Phase
• Each node i transmits at pi,max.
• Construct a topology gmaxg(pmax). Note that by
  assumption gmax is connected
• Update Phase
• Select nodes in a random manner to update their
  power levels
• Update rule
• for every node i
• Update topology g(pi,p-i,max)
• Return to step 3
• Stop, when no node makes any more update to their
  pi

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Energy Efficiency

• A network gp is locally energy efficient if no
  node can reduce its transmission power without
  disconnecting the network.
• A network gp is globally energy efficient if the
  sum of transmission powers (of all nodes) is
  minimum.

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Previous results

• This game is an ordinal potential game (OPG) with
  potential function given by
• The M2M algorithm, converges to NE (gp)
• The M2M algorithm converges to a topology that is
  locally energy efficient and preserves
  connectivity of gmax.

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New results

• The M2M algorithm converges in exactly n steps n
  is the number of nodes in the topology.
• Each node chooses a min power level required to
  be connected
• The set of global potential maximizers coincide
  exactly with the set of connected topologies
  which are globally energy efficient
• Suppose p maximizer but g(p) not efficient
• Suppose g(p) not connected
• contradiction

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New results

• Continued.
• Thus g(p) is always connected
• Suppose pi not minimum for some i i.e
• contradiction
• Thus g(p) connected and locally energy
  efficient!
• Proving other way
• Suppose g(p) locally energy efficient
• fi(p)n and pi min for all i gt min
• max

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New results

• Aliter
• To show global potential maximizers are globally
  efficient
• First potential maximizers lead to connected
  topologies
• Let p be the maximizer
• g(p) is globally efficient!

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Future work

• Node selfishness may lead to non-optimal
  topologies
• M2M algorithm doesnt achieve global optimality
• Sorted node pairs in increasing order of
  distances node farthest updates first gt
  simulation suggests steady state quite close to
  global optimum
• Implemented random better response gt hits global
  optimum with greater frequency
• Noisy best response?
• What is the closest we can get?
• Optimistic price of anarchy
• M2M biased towards nodes updating first
• Appropriate fairness metric?
• Random better response fairer
• What is best fairness we can achieve?
• M2M is a global algorithm
• Implemented localized algorithm, all results hold
  true (except convergence)