Attention economy is a rich information management approach in order to get only significant information. In this work, we analyze the problem of optimizing the value of information presented in an electronic device to users who seek information on the web and whose attention is a priori limited and considered as a scarce and valuable resource. The optimization problem is posed as a dynamic and stochastic prioritization problem and is modeled as a dual-speed multi-armed restless bandit problem (RMABP) in a finite state-space and discrete-time setting. In addition, Adaptive-Greedy algorithm (AG) is used to approximate their solution, this algorithm assigns the value of Whittle’s index to each piece of information, which determines whether or not it is favorable to be presented to the user at a given time. Computational experiments based on Monte Carlo modeling are presented, which show that this methodology substantially improves Greedy index policy and asymptotically approximates the optimization solution to Whittle benchmark.