Process and product innovation: A differential game approach to product life cycle

Abstract

We investigate the timing of adoption of product and process innovation by using a differential game in which firms may invest in both activities. We consider horizontal product innovation that reduces product substitutability, and process innovation that reduces marginal cost. First, we demonstrate that the incentive for cost-reducing investment is relatively higher than the incentive to increase product differentiation. Second, depending on initial conditions, (i) firms activate both types of investment from the very outset to the steady state; (ii) firms initially invest only in one R&D activity and then reach the steady state either carrying out only such activity or carrying out both; (iii) firms do not invest at all in either type of innovation.JEL classification: C73, D43, D92, O31.

Endogenous specialization of heterogeneous innovative activities of firms under the technological spillovers

“…The most recent paper on product and process innovations in differential games framework is the work (Lambertini and Mantovani 2010). This paper assumes fully dynamical model of the duopoly competition of innovating firms.…”

“…First, it contributes to the line of literature on strategic interactions between innovating agents in the spirit of (Reinganum 1982), (Judd 2003) and late (Lambertini and Mantovani 2010). These approaches are extended by considering the distributed parameter model and formulating the fully dynamical differential game with richer strategic sets for both players.…”

Research and Development Cooperatives and Market Collusion: A Global Dynamic Approach

“…This can be read off the optimization problem (30)-(31) obtained after the second scaling (29). Let α 1 = 1/9 and α 2 = 1/8 be the respective partial and full collusion values of α.…”

“…The related literature [24,[27][28][29][30] has not considered initial marginal cost levels that exceed the choke price nor has it carried out a global analysis. In all these papers, any of the initial (permissible) technologies will be developed to full materialization; technologies that are only developed under specific regimes (i.e., product market collusion) remain hidden.…”

R&D competition versus R&D cooperation in oligopolistic markets with evolving structure

“…Furthermore, cooperative R&D efforts over time are higher than in the fully noncooperative game. Lambertini and Mantovani (2010) study R&D activities, process or product R&D, in Cournot and Bertrand oligopolies. They demonstrate that in a dynamic setting, the two types of innovation are not necessarily complementary.…”