A stackelberg game approach to distributed spectrum management

Meisam Razaviyayn, Zhi Quan Luo, Paul Tseng, Jong Shi Pang

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We consider a cognitive radio system with one primary (licensed) user and multiple secondary (unlicensed) users. Given the interference temperature constraint, the secondary users compete for the available spectrum to fulfill their own communication need. Borrowing the concept of price from market theory, we develop a decentralized Stackelberg game formulation for power allocation. In this scheme, the primary user (leader) announces prices for the available tones such that a system utility is maximized. Using the announced prices, secondary users (followers) compete for the available bandwidth to maximize their own utilities. We show that this Stackelberg game is polynomial time solvable under certain channel conditions. When the individual power constraints of secondary users are inactive (due to strict interference temperature constraint), the proposed distributed power controlmethod is decomposable across the tones and unlike normal water-filling it respects the interference temperature constraints of the primary user. When individual power constraints are active, we propose a distributed approach that solves the problem under an aggregate interference temperature constraint. Moreover, we propose a dual decomposition based power control method and show that it solves the Stackelberg game asymptotically when the number of tones becomes large.

Original languageEnglish (US)
Pages (from-to)197-224
Number of pages28
JournalMathematical Programming
Issue number2
StatePublished - Oct 1 2011


  • Cognitive radio network
  • Linear complementarity problem (LCP)
  • Mathematical program with equilibrium constraint (MPEC)
  • Stackelberg game


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