A mathematical model for personalized advertisement in virtual reality environments

We consider a personalized advertisement assignment problem faced by the manager of a virtual reality environment. In this online environment, users log in/out, and they spend time in different virtual locations while they are online. Every time a user visits a new virtual location, the site manager can show the ad of an advertiser. At the end of a fixed time horizon, the manager collects revenues from all of the advertisers, and the total revenue depends on the number of ads of different advertisers she displays to different users. In this setup, the objective of the manager is to find an optimal dynamic ad display policy in order to maximize her expected revenue. In the current paper, we formulate this problem as a continuous time stochastic optimization problem in which the actions of users are represented with two-state Markov processes and the manager makes display decisions at the transition times of these processes. To our best knowledge, no formal stochastic model and rigorous analysis has been given for this practical problem. Such a model and its analysis are the major contributions of this paper along with an optimal solution.