Despite the extensive literature on product and process innovation within firms, relatively little attention has been paid to how consumer reference perceptions regarding product differentiation dynamically influence the innovation strategies of multi-product firms in markets with network externality. This paper addressed this gap by developing a dynamic optimal control model to analyze the product and process innovation of a multi-product firm in the presence of reference effects about product differentiation and network externality. The key features of this study are as follows: (ⅰ) A multi-product firm offers horizontally differentiated products and engages in both product and process innovation; (ⅱ) the network value depends on both network size and the degree of product substitutability; (ⅲ) market demand incorporates price and, network size, as well as reference perceptions regarding product differentiation; and (ⅳ) a special case was examined where network size evolves proportionally with market demand. The analytical results yielded several propositions and conclusions. The primary findings indicate that: (ⅰ) The saddle-point stability of the steady-state equilibrium, which is crucial for both firm decision-making and government regulation, hinges critically on the discount rate and the consumer memory parameters; (ⅱ) product and process innovation efforts exhibit a complementary relationship; (ⅲ) both types of innovation efforts increase with the proportional coefficient governing network expansion; and (ⅳ) as market demand decreases, the firm intensifies its efforts in both product and process innovation. These findings contribute to the literature by clarifying the dynamic interactions among multi-product innovation strategies, consumer reference perceptions about the product differentiation, and network externality.
Citation: Huiquan Li, Ran Jiang, Lijia Ge. Dynamic control of a multi-product firm's product and process innovation in a market with network externality[J]. Journal of Industrial and Management Optimization, 2026, 22(6): 2598-2623. doi: 10.3934/jimo.2026095
Despite the extensive literature on product and process innovation within firms, relatively little attention has been paid to how consumer reference perceptions regarding product differentiation dynamically influence the innovation strategies of multi-product firms in markets with network externality. This paper addressed this gap by developing a dynamic optimal control model to analyze the product and process innovation of a multi-product firm in the presence of reference effects about product differentiation and network externality. The key features of this study are as follows: (ⅰ) A multi-product firm offers horizontally differentiated products and engages in both product and process innovation; (ⅱ) the network value depends on both network size and the degree of product substitutability; (ⅲ) market demand incorporates price and, network size, as well as reference perceptions regarding product differentiation; and (ⅳ) a special case was examined where network size evolves proportionally with market demand. The analytical results yielded several propositions and conclusions. The primary findings indicate that: (ⅰ) The saddle-point stability of the steady-state equilibrium, which is crucial for both firm decision-making and government regulation, hinges critically on the discount rate and the consumer memory parameters; (ⅱ) product and process innovation efforts exhibit a complementary relationship; (ⅲ) both types of innovation efforts increase with the proportional coefficient governing network expansion; and (ⅳ) as market demand decreases, the firm intensifies its efforts in both product and process innovation. These findings contribute to the literature by clarifying the dynamic interactions among multi-product innovation strategies, consumer reference perceptions about the product differentiation, and network externality.
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Huiquan Li, Ran Jiang, Lijia Ge. Dynamic control of a multi-product firm's product and process innovation in a market with network externality[J]. Journal of Industrial and Management Optimization, 2026, 22(6): 2598-2623. doi: 10.3934/jimo.2026095
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