A static approximation for dynamic demand substitution with applications in a competitive market.

*(English)* Zbl 1167.90330
Summary: We propose a static approximation of dynamic demand substitution behavior based on a fluid network model and a service-inventory mapping. This approximation greatly enhances our ability to analyze the interdependent inventory/service, price, and product assortment decisions in noncompetitive and competitive scenarios with demand substitution. We demonstrate that the approximation is well behaved and then apply it to two previously intractable applications. First, we study a price and service competition between single-product retailers. After establishing a unique pure-strategy Nash equilibrium, we find that competition results in lower price, higher demand, and a higher level of inventory. We also observe that the aggregate profit and inventory level increase to positive constants as the number of retailers goes to infinity. Second, we study a duopolistic competition on price, service, and product assortment. We establish a pure-strategy Nash equilibrium for the product assortment competition and identify a condition for uniqueness. We find that competition on both price and product assortment results in lower price and less variety for each competitor, but the total number of products and the aggregate inventory level in a duopoly market are both likely to be higher than in a monopolistic market.

##### MSC:

90B05 | Inventory, storage, reservoirs |

90B15 | Network models, stochastic (optimization) |