Incentive to Innovate: Dynamic Optimization Strategy in the Case of a Symmetric Duopoly

Technological dominance and spillovers play important roles in a firm’s decision to investment in innovated products. It is intuitive to think that a firm which is technologically ahead will dominate the market for innovated products. However, the question of the spillover advantage a firm gets when they are technologically behind makes the decision to invest in new technology more complex. Therefore, in this paper, I consider the investment in new product and cost of doing research, along with capital and level of technology, to be primary factors affecting a firm’s profit. I ask, when is it a good time to invest in new product and when is it appropriate for a firm to allocate more funding for research? I find that firms tend to do more research when they have more market share and invest less when the total capital in the market increases. They tend to invest more when they are technologically ahead and do more research when they are behind. This is a dynamic game because a firm’s decision to invest depends not only on its own level of technology but also on the rival firm’s level of technology and market share. The presence of technological spillovers also adds onto the dynamics of the game since it discourages the firm, which is technologically ahead, from investing in technological advances