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

We consider a two-sided one-to-one abstract matching problem with a defined notion of pairwise stability. The formulated problem is shown to encompass the ordinal and cardinal utility markets. We propose a distributed blind matching algorithm (BLMA) to solve the problem. The BLMA is characterized by random activations of agents, and by generic negotiation and aspiration (utility) update processes. We prove that the solution produced by the BLMA will converge to an <inline-formula> <tex-math notation="LaTeX">$\epsilon$ </tex-math></inline-formula>-pairwise stable, equivalently <inline-formula> <tex-math notation="LaTeX">$\epsilon$ </tex-math></inline-formula>-core, outcome with probability one. We then consider three BLMA applications in cognitive radio networks. We propose a simple BLMA negotiation and aspiration update dynamic to produce an <inline-formula> <tex-math notation="LaTeX">$\epsilon$ </tex-math></inline-formula>-pairwise stable solution for the case of quasi-convex and quasi-concave utilities. In the case of more general utility forms, we show another BLMA process to provide equilibrium. We also consider the use of the BLMA in an ordinal utility market. In all applications 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 user in the network.