A Bayesian negotiation model for quality and price in a multi-consumer context

•A general sequential Bayesian model of decision has been developed.•Product price and reliability/quality testing have been considered.•An original approach is implemented in order to obtain appropriate optimal values.•Distributions widely used in reliability and quality contexts have been taken.

Bayesian decision theory plays a significant role in a large number of applications that have as main aim decision making. At the same time, negotiation is a process of making joint decisions that has one of its main foundations in decision theory. In this context, an important issue involved in industrial and commercial applications is product reliability/quality demonstration. The goal is, among others, product commercialization with the best possible price. This paper provides a Bayesian sequential negotiation model in the context of sale of a product based on two characteristics: product price and reliability/quality testing. The model assumes several parties, a manufacturer and different consumers, who could be considered adversaries. In addition, a general setting for which the manufacturer offers a product batch to the consumers is taken. Both the manufacturer and the consumers have to use their prior beliefs as well as their preferences. Sometimes, the model will require to update the previous beliefs. This can be made through the corresponding posterior distribution. Anyway, the main aim is that at least one consumer accepts the product batch based on either product price or product price and reliability/quality. The general model is solved from the manufacturer viewpoint. Thus a general approach that allows us to calculate an optimal price and sample size for testing is provided. Finally, two applications show how the proposed technique can be applied in practice.