Optimal pricing and advertising policies for an entertainment event

We find that advertising should be decreased over time during the first period. There are three different advertising scenarios: it may be optimal not to advertise at all, to advertise at a positive rate until the end of the first period, or to stop advertising at an earlier instant of time. In the last-minute sales, the organizers implement a feedback pricing policy such that the selected price depends on the number of tickets that have been sold in the regular sales period. Finally, we establish optimality conditions for the time instant where to switch to last-minute sales.