A mathematical model for personalized advertisement in virtual reality environments
The authors consider a personalized advertisement assignment problem faced by 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. The objective of the manager is to find an optimal dynamic ad display policy in order to maximize her expected revenue. They 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. The authors construct the successive approximations for the value function. Also, they investigate the smoothness of the value function in the remaining time until the end of the time horizon. Finally, they provide a numerical example with two users and two advertisers to illustrate how the optimal policy is implemented in practice. The appendix includes auxiliary results and proofs.
scientific article; zbMATH DE number 6759769