  This paper presents a comprehensive analytical study of two competitive
cognitive operators' spectrum leasing and pricing strategies, taking into
account operators' heterogeneity in leasing costs and users' heterogeneity in
transmission power and channel conditions. We model the interactions between
operators and users as a three-stage dynamic game, where operators make
simultaneous spectrum leasing and pricing decisions in Stages I and II, and
users make purchase decisions in Stage III. Using backward induction, we are
able to completely characterize the game's equilibria. We show that both
operators make the equilibrium leasing and pricing decisions based on simple
threshold policies. Moreover, two operators always choose the same equilibrium
price despite their difference in leasing costs. Each user receives the same
signal-to-noise-ratio (SNR) at the equilibrium, and the obtained payoff is
linear in its transmission power and channel gain. We also compare the duopoly
equilibrium with the coordinated case where two operators cooperate to maximize
their total profit. We show that the maximum loss of total profit due to
operators' competition is no larger than 25%. The users, however, always
benefit from operators' competition in terms of their payoffs. We show that
most of these insights are robust in the general SNR regime.
