قیمت گذاری بهینه و سیاست های تبلیغاتی برای یک رویداد سرگرمی

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.

The aim of the paper is to determine optimal advertising and pricing policies for a one-time entertainment event (a classical or a rock concert, a ballet, a theater performance, a soccer match or another sports event). A basic assumption of the paper is that the organizers of the event can forecast with good precision the demand for tickets to the event, when a particular pricing and advertising strategy has been chosen. This aims to motivate our choice of a deterministic setup. The model of ticket sales that we suggest incorporates the following features: (1) The supply of capacity is fixed. By capacity we mean the maximum number of tickets that can be offered for sale. Additional capacity in terms of staff, heating, refreshments, etc. are also needed, but will be disregarded here. The major part of the cost of providing and utilizing the capacity is sunk when the decision to have the event has been made. Thus, the capacity cost is independent of the number of tickets offered or sold and in what follows we disregard this cost. (2) The assumption is that the event is unique. Some events may be duplicated, e.g., a concert or a ballet, and some events are organized in series. In other cases it may, however, be impossible because the performers or the location are no longer available. It is such an one-time event we have in mind here. (3) The organizers have the option to sell tickets for the event in two distinct markets. During a first interval of time, tickets are sold in what we call the regular market at a fixed price p1p1. Organizers have the option to sell tickets at a different price p2p2 during a second, and terminal, interval of time. This is referred to as the last-minute market. Depending on the context, the last-minute price can be higher or lower than the price in the regular market. Some attendees may, in a last-minute market, be willing to pay more than the regular price. On the other hand, some theaters, for instance, offer last-minute tickets at significantly lower price than the regular price.

The paper has analyzed pricing and advertising policies for an event, taking into account demand learning effects and a last-minute market. The setup combines period-by-period constant prices and with continuous advertising in the first period. The organizers can sell tickets at a regular price and advertise during an initial period of time. If all tickets are not sold by the end of this period, there is a last, and short, period in which tickets are sold at a reduced price and no advertising is done. The reader should be aware that we do not claim that the optimization model suggested above is a ‘realistic’ representation of real-life entertainment ticket sales. The model is no better than its assumptions and it may apply in some instances, not in others. One particularly limiting assumption is that of deterministic demand. Although simple specifications for advertising cost and demand functions were employed, the determination of optimal policies is not trivial. We found that advertising should be decreased over time, as the number of sold tickets increases. Depending on the values of the model parameters, it may be optimal not to advertise, to advertise at a positive rate until the end of the regular selling period, or to stop advertising at some earlier instant of time. If demand learning effects are absent, advertising (if any) should be done at a uniform rate. In the last-minute market, the organizers implement a feedback pricing policy such that the selected price depends on the number of tickets already sold in the regular market. Finally, we stated conditions for when it is optimal to switch from regular sales to last-minute sales.