Analysis and Design of Cognitive Radio Networks Using Game Theory
	previous	next	home

Game theory

Desirability of NE

Example : Pareto optimality

Consider the Cognitive Radios’ Dilemma whose game matrix is reproduced in Figure 4.4. This game has three Pareto optimal outcomes – (n,N), (w,N), and (n,W) – and only the NE is not Pareto optimal. This highlights a key implication for NE and optimality an NE is not necessarily optimal nor are optimal points necessarily NE. Pareto optimality is not particularly useful as a tool to aid cognitive radio algorithm design, especially in light of the assumption that the network designer will always have some specific design function, J: A-->R in mind. In general, when designing a cognitive radio network, it is possible to ensure that the associated NE are Pareto optimal or maximizers of J.

Example : SINR maximizing power control

Consider a single cluster DSSS (Direct Sequence Spread Spectrum) network with a centralized receiver where all of the radios are running power control algorithms in an attempt to maximize their signals’ SINR at the receiver. A normal form game, G =<N, A, {ui}> , for this network can formed with the cognitive radios as the players, the available power levels as the action sets and the utility functions given by:

where K is the statistical cross-correlation of the signals.the unique NE for this game is the power vector where all radios transmit at maximum power. This outcome can be verified to be Pareto optimal as any more equitable power allocation will reduce the utility of the radio closest to the receiver, and any less equitable allocation will reduce the utility of the disadvantaged nodes. However, this is not a network we would want to implement because of the following:
(1) This state greatly reduces capacity from its potential maximum due to near-far problems
(2) The resulting SINRs are unfairly distributed (the closest node will have a far superior SINR to the furthest node).
(3) Battery life is greatly shortened.