In this study, we develop a series of consumer-valuation-based models to investigate the pricing and return policies of the sellers in a competitive e-commerce market. Differing from the competition models in literature, a novel two-dimensional valuation structure is built, which considers the valuations of a consumer on two products and the valuation differentiation of all consumers on each product. We consider both monopoly and duopoly (competitive) markets. In each market, two models are respectively developed, one with and one without the return policies. We derive the solutions for the four models, and conduct some analytical and numerical investigations. The results show that return policy with a partial refund is always chosen by the sellers in both monopoly and duopoly markets. Return policy benefits the seller in a monopoly market, but may not benefit the sellers in a duopoly market. In the duopoly models, one seller can be considered as a monopoly seller who meets a new competitor. Our results show that the monopoly seller will reduce its price by no more than 20% when there comes a competitor, and, counter-intuitively, it will meanwhile adopt a severer return policy to the consumers.
Hierarchical competition models with the Allee effect III: multispecies