Abstract
The paper analyzes a two-stage oligopoly game of semi-collusion in production described by a system with a symmetric structure. We examine the local stability of a Nash equilibrium and the presence of bifurcations. We discover that the model is capable of exhibiting extremely complicated dynamic behaviors.
Highlights
Research and development (R&D) are critical to a company’s growth
We considered a continuous-time version with delays of a discrete model with R&D competition
Our modification of the discrete model was suggested by real economic situations where there are always time delays between the times when information is obtained and when the decisions are implemented
Summary
Research and development (R&D) are critical to a company’s growth. They enable the development of lower manufacturing costs, increase production productivity, and improve the quality of goods. Both companies reduce the expense of R&D acquisitions by the use of Research Joint Ventures (RJVs) or R&D cartelization Following that, they commit themselves to compete in the product market through a Bertrand or Cournot game. Zhang et al [14] built a dynamical two-stage duopoly game based on Fershtman and Gandal’s research results, assuming that the business has a linear inverse demand function and the firms are bounded rational. They believed that companies compete in the R&D stage and allowed for spillover at this stage.
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