A multi-level hierarchical game-theoretical approach for cognitive networks

This paper considers a game theoretical approach to study the problem of energy-efficient power control in cognitive wireless networks where some hierarchy exists between cognitive devices. This hierarchical structure is introduced either to model cognitive networks where some transmitters have more sensing capabilities than the others (they can observe more transmitters) or networks for which the degrees of knowledge about the network are different. The optimum selfish power control policy under consideration is determined in two scenarios: 1. K transmitters with K hierarchy levels; 2. two hierarchy levels comprising K₁ non-cognitive terminals and K - K₁ cognitive terminals. For both scenarios, it is shown that the derived equilibria Pareto-dominate the one obtained without hierarchy. Interestingly, in scenario 1 we show that following is better than leading in terms of individual energy-efficiency. In scenario 2, considering the global network efficiency, we show that there exists an optimum number of cognitive terminals to put in the network.