Abstract
Ye [¿Competitive Communication Spectrum Economy and Equilibrium,¿ 2008, working paper] and Lin [¿Budget Allocation in a Competitive Communication Spectrum Economy,¿ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EURASIP J. Adv. Signal Process.</i> , Article ID: 963717, vol. 2009, p. 12, Sep. 2009] have shown that dynamic spectrum management (DSM) using the market competitive equilibrium (CE), which sets a price for transmission power on each channel, leads to better system performance in terms of the total data transmission rate (by reducing cross talk), than using the Nash equilibrium (NE). But how to achieve such a CE is an open problem. We show that the CE is the solution of a linear complementarity problem (LCP) and can be computed efficiently. We propose a decentralized tatonnement process for adjusting the prices to achieve a CE. We show that under reasonable conditions, any tatonnement process converges to the CE. The conditions are that users of a channel experience the same noise levels and that the crosstalk effects between users are low-rank and weak.
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