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Research and Development with Stock-Dependent Spillovers and Price Competition in a Duopoly

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Abstract

This paper investigates the research and development accumulation and pricing strategies of two firms competing for consumer demand in a dynamic framework. A firm’s research and development is production-cost-reducing and can benefit from part of the competitor’s research and development stock without payment. We consider decisions in a game characterized by Nash equilibrium. In this dynamic game, a player’s action depends on whether the competitor’s current research and development stock are observable. If the competitor’s current research and development stock are not observable or observable only after a certain time lag, a player’s action can be solely based on the information on the current period t (open-loop strategy). In the converse case, it can also include the information on the competitor’s reaction to a change in the current value of the state vector (closed-loop strategy), which allows for strategic interaction to take place throughout the game. Given the cumulative nature of research and development activities, a primary goal of this paper is to determine whether, regardless of the observability of the competitor’s current research and development stock, free research and development spillovers generate a lower level of scientific knowledge than research and development appropriability. A second objective of the paper is to determine how the observability of the rival’s current research and development stock affects a firm’s research and development and pricing decisions and payoffs under imperfect research and development appropriability.

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Notes

  1. R&D spillovers can arise through channels such as R&D personnel movement, formal and informal networks and meetings, publications related to research output, patent applications and reverse engineering.

  2. See also [12–16]. A supportive empirical evaluation of this theory can be found in [17].

  3. As noted in [18], “common assets create common interests, and common interests make it more likely that firms will noncooperatively refrain from rivalling behaviour”.

  4. Prior studies simultaneously combining R&D with pricing in dynamical setting have been limited to a monopoly context, e.g. [22–26].

  5. Open-loop strategies provide a useful benchmark for assessing the strategic effects related to Markovian strategies [30].

  6. In contrast, in tournament games without R&D accumulation, the timing of new technology adoption plays a central role. In the relevant literature, technological competition may take the form of a pre-emption game (i.e., first-mover advantage) due to rivalry in the product market, or a waiting game (i.e., late-mover advantage) resulting from technological uncertainty and informational spillovers; e.g., [31–35].

  7. A related stream of literature, not discussed here, investigates the impact of R&D competition on market structure; e.g., [36–40].

  8. Cohen and Levinthal [43] introduced the concept of absorptive capacity in R&D, which is defined as the ratio of “usable” to “actual” rival R&D and depends on a firm’s own level of investment in R&D.

  9. Dockner et al. [48] show that closed-loop strategies can be implemented as a subgame-perfect equilibrium in Reinganum’s [19] model.

  10. Fudenberg and Tirole [33] note that an open-loop solution reflects infinitely long information lags, and a first-mover advantage is not supported by subgame-perfect strategies if firms are unable to pre-commit to future actions. Assuming negligible information lags (closed-loop solution), the authors obtain two equilibria: a maturation equilibrium, in which a later innovation yields a higher payoff, and a pre-emption equilibrium, in which the two firms invest on two different dates but their rents are equalized. Therefore, when firms cannot pre-commit themselves to adopt technology on specific dates, timing competition reduces the initial delay in new technology adoption.

  11. Notable exceptions to symmetric spillovers are those presented in [50, 51].

  12. Note that the demand function above can be easily rewritten in a Cournot setting [55].

  13. Intuitively, one would expect the costate variable associated with the rival’s stock of R&D to be zero, and hence a change in such a stock would have no impact on firm i’s optimal profit.

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Acknowledgements

The authors are grateful to Gary Erickson and Steffen Jørgensen for constructive suggestions on an early draft. The paper was written while the first author was visiting the Department of Logistics and Operations Management at HEC-Montreal in Canada.

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Authors and Affiliations

  1. ESSEC Business School, Cergy Pontoise, France

    Fouad El Ouardighi

  2. Bar-Ilan University, Ramat-Gan, Israel

    Matan Shnaiderman

  3. HEC Montréal, Montréal, Canada

    Federico Pasin

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  1. Fouad El Ouardighi
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Correspondence to Fouad El Ouardighi.

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Communicated by Gustav Feichtinger.

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El Ouardighi, F., Shnaiderman, M. & Pasin, F. Research and Development with Stock-Dependent Spillovers and Price Competition in a Duopoly. J Optim Theory Appl 161, 626–647 (2014). https://doi.org/10.1007/s10957-013-0433-2

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