Bandwidth-constrained multistage Bayesian game for spectrum trading in cognitive radio networks

In this paper, we study the problem of spectrum trading in cognitive radio (CR) networks from a game theoretical perspective. Particularly, we consider the CR network with multiple primary services (PS´s) and a single secondary service (SS), where all PS´s are sellers competing in the prices and the SS is the buyer deciding how much spectrum is demanded from each PS in the trading game. Aiming at dealing with the trading behaviors, we propose using a multistage Bayesian game based trading model to account for possible unknown private information in each player, and obtain the perfect Bayesian equilibrium (PBE) sequentially under a bandwidth constraint. By the backward induction principle, we translate the Karush-Kuhn-Tucker (KKT) condition of the SS to form a joint KKT conditions with PS in order to solve the optimization problem. Finally, in the simulations, we compare the proposed approach with that, and numerically study the convergence behaviors of the proposed multistage game.