Negotiation with Price-dependent Probability Models

Negotiation and agreement generally require models of the peers who are involved in the negotiation. One typical area where negotiation takes place is in selling and retailing, which is also known as Customer Relationship Management (CRM). Customers and products are usually modelled using previous retailing experiences with similar or dissimilar customers and products. Machine learning is typically used to construct these models, which can be used to design mailing campaigns, to recommend new products, to do cross-selling, etc. Many CRM problems can already be solved through rankers, recommender systems, etc., provided that there are good models of customer and product behaviours available. A related but more general problem is when models are used to negotiate with one or more features of the product (or, less frequently, the customer) such as prices, bonuses, warranties, etc. Additionally, if it is possible to make several bids until an agreement is reached, methods must be devised so that the maximum profit is obtained by the seller. In this work, we present a taxonomy of CRM problems, from which we distinguish those that have already been solved and those whose solutions are still pending. Then, we extend classical purchase probability rankings to the notion of profit probability curves (price-dependent distributions), and we propose a simple negotiation solution for these cases.