Advertising an event

The paper considers a problem of how to minimize advertising costs to sell seats for a particular event, for instance, a sports game, a rock concert or a ballet performance. We take into consideration a word-of-mouth effect, which means that people buying a ticket tell their friends about it, so that advertising is unnecessary to inform those people.The problem is one of optimal control and the number of seats sold and the advertising effort of the organizers are the state and control variables, respectively. We show that, besides being dependent on the cost and revenue parameters, the optimal advertising policy is also affected by the length of the planning period and the relation between the number of seats and the total number of potential attendees.