Optimal Pricing for Duopoly in Cognitive Radio Networks: Cooperate or Not Cooperate?” Wireless Communications

Abstract—Pricing is an effective approach for spectrum access control in cognitive radio (CR) networks. In this paper, we study the pricing effect on the equilibrium behaviors of selfish secondary users ’ (SUs’) data packets which are served by a CR base station (BS). From the SUs ’ point of view, a spectrum access decision on whether to join the queue of the BS or not is charac-terized through an individual optimal strategy that is joining the queue with a joining probability. This strategy also requires each SU to know the average queueing delay, which is a non-trivial problem. Toward this end, we provide queueing delay analysis by using the M/G/1 queue with breakdown. From the BS’s point of view, we consider a duopoly market based on the two paradigms: the opportunistic dynamic spectrum access (O-DSA) and the mixed O-DSA & dedicated dynamic spectrum access (D-DSA). In the first paradigm, two co-located opportunistic-spectrum BSs utilize freely spectrum-holes to serve SUs. Then, we show the advantages of the cooperative scenario due to the unique solution that can be obtained in a distributed manner by using the dual decomposition algorithms. For the second paradigm, there are one opportunistic-spectrum BS and one dedicated-spectrum BS. We study a price competition between two BSs as a Stackelberg game. The cooperative behavior between two BSs is modeled as a bargaining game. In both paradigms, bargain revenues of the cooperation are always higher than those due to competition in both cases. Extensive numerical analysis is used to validate our derivation. Index Terms—cognitive radio, duopoly, Stackelberg game, bargaining game, M/G/1 queue