Game Theory in Topology Control

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Game Theory in Topology Control

• 10/27/04

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Outline

• Definition
• Prior work and formulation
• How Game Theory fits
• Example Games
• Properties
• Practical problems
• Relation to node participation and Interference
• Conclusion (MANETs, improvements)

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What is Topology Control

• G(V,E)- graph induced by
• nodes using maximal power

Topology Control Algorithm
Topology T(V,E) that preserves
(atleast) connectivity of G(V,E)
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Definition

• Determine min transmission power collaboratively
  (other nodes act as relays) so as to
  achieve/maintain network connectivity
• Problem of minimizing overall power consumption
  while maintaining network connectivity
• Typically formulated as optimization problem

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Performance Measures

• Network connectivity
• Network Lifetime
• Energy efficiency (routing)
• Throughput
• Robustness to node mobility

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Why Topology Control (1/2)

• Need appropriate topology on which routing
  protocols can be implemented
• too large a power gtinterference
• too small gtdisconnected network
• Mitigating MAC level interference
• Bad Topology gtreduced capacity, high end-end
  delays etc.
• Proper TC must be in place!

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Why Topology Control (2/2)

• Conserve Energy
• Reduce Interference

Trade-off
Network Connectivity Spanner Property
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Existing TC Algorithms

• CONNECT, BICONNECT- minimize max Power per node
• COMPOW- each node uses smallest common power.
  Network capacity maximized, battery life
  extended.
• CBTC-2 phase, find min power p such that some
  node in every cone( ), lt guarantees
  network connectivity.
• Several MST based Algos.

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Game Theory (1/2)

• Network formation related to TC
• To form a network requires cooperation
• Nodes are power constrained so must rely on
  intermediary nodes.
• Relaying nodes selfish
• Network connectivity and power control trade off
• Inherent conflict- A Game

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Game Theory (2/2)

• Eidenbenz et al applied GT to TC
• Strong connectivity Game- NE exists
• Connectivity Game- No NE
• Reachability Game- No NE (for )

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Example Games

• Players nodes, Actions power level
• Strong Connectivity Game Every node needs to
  connect to every other node
• Connectivity Game Node pairs (si, ti) need to
  connect (directly or multi-hop)
• Reachability Game A node must reach some number
  of nodes fi(p)

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Game Characterization (1/3)

• Strong connectivity game is a Potential Game
  (trivial)
• Potential P(p) exists (sum of all utilities)
• NE is the power tuple that produces minimum
  overall cost C(p)- social optimum

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Game Characterization (2/3)

• Reachability Game
• fi is the number of nodes reached by node i (over
  multiple hops possible)
• Suppose fi , fj monotonic in pi (p-i fixed)
• If then OPG with OPF being sum of the
  utilities

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Game Characterization (3/3)

• Need final topology (T) to be a sub-graph of
  G(V,E)
• T(V,E) must be a Nash Network
• Multiple Nash Networks exist

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Practical Problems

• Usually TC assumes topology produced minimizes
  interference -not always true!
• Increasing the hop distance may cause network
  disintegration (if atleast one link fails)
• High node degree causes interference

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Improvement to TC Algorithms

• Study TC in conjunction with interference
• Heterogeneous network with asymmetric
  (uni-directional) links
• Node mobility, MANETs

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Do we need connectivity ?

• Existence of path between two nodes
• O (log n) neighbors -gtfull connectivity (Santi)
• TC assumes need for maintaining network
  connectivity (too strict)
• Efficient network may result by ignoring outlier
  nodes
• Graph connectivity (stronger condition)
• Path connectivity (path between any two can be
  found, if needed, with high probability)