Optimal pricing and advertising policies for an entertainment event

The paper suggests an optimal control model to determine optimal pricing and advertising policies for a one-time entertainment event. There are two periods, an initial period of regular price sales and a terminal period of last-minute sales at a (possibly) reduced price. The price in a period is constant over time. In the initial period, the organizers of the event advertise the event to potential attendees. If tickets are sold out by the end of the first period, there will be no last-minute sales. 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