Optimal Prices in the Presence of Discounts: A New Economic Application of Choquet Integrals

In many real-life situations, there are “package deals”, when customers who buy two or more different items get a special discount. For example, when planning a trip, a deal including airfare and hotel costs less than the airfare and hotel on their own; there are often also special deals when we combine airfare with car rental, and deals that cover all three items plus tickets to local tourist attractions, etc. Usually, there are several such deals with different combinations and different discounts. What if we plan to buy several different copies of each item: e.g., we plan a group tour in which some tourists want to rent car, some want to visit certain tourist attractions, etc. What is the best way to use all available discounts? We show that, under reasonable assumptions, the optimal price is provided by the Choquet integral. 1 Practical Problem and Its Reformulation in Precise Terms Practical situation: discounts. In many real-life situations, there is a “package deal”: customers who buy two or more different items get a special discount. For example: • when planning a trip, a deal including airfare and hotel costs less than the airfare and hotel on their own; • there are often also special deals when we combine airfare with car rental, and deals that cover all three items plus tickets to local attractions, etc.; • when a customer buys a house, there are often package deals which enable the customer to also buy the original furniture and/or car at a special discount;