BLMA: A Blind Matching Algorithm with Application to Cognitive Radio Networks

We consider a two-sided matching problem with a defined notion of pairwise stability. We propose a distributed blind matching algorithm (BLMA) to solve the problem. We prove the solution produced by BLMA will converge to an $ε$-pairwise stable outcome with probability one. We then consider a matching problem in cognitive radio networks. Secondary users (SUs) are allowed access time to the spectrum belonging to the primary users (PUs) provided that they relay primary messages. We propose a realization of the BLMA to produce an $ε$-pairwise stable solution assuming quasi-convex and quasi-concave utilities. In the case of more general utility forms, we show another BLMA realization to provide a stable solution. Furthermore, we propose negotiation mechanism to bias the algorithm towards one side of the market. We use this mechanism to protect the exclusive rights of the PUs to the spectrum. In all such implementations of the BLMA, we impose a limited information exchange in the network so that agents can only calculate their own utilities, but no information is available about the utilities of any other users in the network.

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