Product line design considering competition by bilevel optimization of a Stackelberg-Nash game

Product Line Design (PLD) is one of the most critical decisions to be made by a firm for it to be successful in a competitive business environment. Existing conjoint models for PLD optimization either have not accounted for the retaliatory reactions by incumbent firms to the introduction of new products or have focused on the Nash game to model such competitive interactions, in which all firms are treated equally. However, one firm may own more information on the rivals' behavior, more resources to pre-commit, or a first-mover advantage. This article formulates a Stackelberg-Nash game-theoretic model for the Competitive Product Line Design (CPLD) problem, in which a new entrant wants to enter a competitive market by offering new products where there are existing products belonging to several incumbent firms. A bilevel 0-1 integer nonlinear programming model is developed based on the Stackelberg-Nash game where the new entrant is a leader and the incumbent firms are followers. Consistent with the bilevel optimization model, a nested bilevel genetic algorithm with sequential tatonnement is implemented to find the corresponding Stackelberg-Nash equilibrium for CPLD. An industrial case of mobile phone product is also presented to illustrate the feasibility and potential of the proposed leader-followers model and algorithm.