Dynamic analysis of R&D in an oligopoly under general demand and cost functions

Masahiko Hattori () and Yasuhito Tanaka
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Masahiko Hattori: Takasaki City University of Economics

OPSEARCH, 2022, vol. 59, issue 2, No 15, 694-710

Abstract: Abstract This paper presents an analysis of cost reducing R&D investment in a dynamic oligopoly under general demand and cost functions by differential game approach. The steady state value of the R&D investment by each firm is decreasing in the number of firms. If the direct effect of R&D investment is larger (smaller) than the spillover effect, the steady state value of the industry R&D investment is increasing (decreasing) in the number of firms. If the outputs of the firms are strategic substitutes, the R&D investment by each firm given the cost level is decreasing in the number of firms. If there is no spillover effect of R&D investment, and the outputs of the firms are strategic substitutes (or strategic complements), the R&D investment of each firm given the cost level in a memoryless closed-loop solution is larger (smaller) than that in an open-loop solution. Also we show that if there is no spillover effect of R&D investment, a memoryless closed-loop solution and a feedback solution (by the Hamilton–Jacobi–Bellman equation) are equivalent.

Keywords: Differential game theory; Oligopoly; Cost reducing investment; General demand and cost functions; Open-loop; Closed-loop; Feedback (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s12597-021-00556-y

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