Spectrum investment with uncertainty based on prospect theory

We study a secondary wireless operator's spectrum investment problem under spectrum supply uncertainty using prospect theory. In order to meet the demands of its users, the secondary operator can either sense for the unused spectrum in a licensed band, or lease spectrum from a spectrum owner. Sensing is usually cheaper than leasing, but the amount of spectrum obtained by sensing is uncertain. We formulate such a hybrid spectrum investment problem as a two-stage optimization problem, and compute the optimal sensing and leasing decisions using backward induction. To model the realistic investment behaviors under uncertainty, we apply prospect theory to overcome the limitations of the widely adopted expected utility theory. We show that the investment decision model based on prospect theory leads to a non-convex optimization problem, which is challenging to solve in closed-form. However, we characterize the uniqueness of the optimal solution analytically, and compute it through a simple line search. Comparing with the expected utility theory benchmark, the analysis based on prospect theory shows that the operator will be more conservative in sensing, in order to reduce the investment risk and to avoid a large possible loss. In other words, the operator is both risk averse and loss averse.