Abstract

Defining prices and in which consumers' segments to put the company's efforts within competitive markets selling bundles is challenging. On the one hand, methodologies focused on competition are usually appropriate for analyzing market dynamics but not for helping decision makers in specific tasks regarding pricing. On the other hand, simplistic cost-oriented methods may fail to capture consumer behavior. We see these characteristics in such markets as telecommunications, retail, and financial service providers, among others. We propose a framework to support pricing decisions for products with multiple attributes in competitive markets, considering consumers' willingness to pay and multiple segments. The proposed model is a nonlinear profit maximization probabilistic problem. We represent the demands for products and services through a multinomial logit model and then include consumers' maximum willingness to pay through soft constraints within the demand function. Since the profit function is non-concave, we deal with the nonlinearity and the multiple optima to solve the model through an equivalent nonlinear model and a particle swarm optimization (PSO) heuristic. This setting allows us to find the prices that achieve equilibrium for the game among the firms that maximize their profits. Including the features shown, our approach enables decision makers to set prices optimally. Estimating the parameters needed to run our model requires more effort than traditional multinomial approaches. Nevertheless, we show that it is essential to include these aspects because the optimal prices are different from those obtained with more simplified models that do not have them. Additionally, there are well-established methodologies available to estimate those parameters. Both the determination of the first-order optimality conditions and the PSO implementation allow to find equilibria, quantify the effect of the consumers' maximum willingness to pay, and assess the competition's relevance. As complementary material, we analyze a case from a Chilean telecommunications company and show the results regarding price decisions and market share effects. According to our literature review, these aspects have not been handled and quantified jointly, as we do to support pricing.