Innova-Sim: Modeling Firm Competition in Innovation as a Multi-Stage Game with Agent-Based Simulation

Markets for technology products often experience intense innovation and competition between firms. We propose a model, represented as a multi-stage game, for firm-level innovation through the mechanisms of R&D investment, knowledge spillover, and quality differentiation. At the start of each game period, firms make an R&D investment to increase their probability of gaining knowledge units. This knowledge delta isscaled by a fraction of the knowledge share of the most innovative firm according to the spillover rate. Market demand and the resulting profits are dependent on firms’ product quality, as a function of their knowledge, and their quantity produced. Using an object-oriented simulation framework with computational agents representing firms, we explore the impact of different R&D investment strategies on net profits and knowledge produced. The best performing strategy leverages a finite-horizon approximation of future net profits to adapt its investment choice for market scenarios. It considers relative quality positions, the effect of spillover, and the incremental value of a unit of knowledge to determine the near-optimal R&D budget allocation. Results from innovative duopoly simulations demonstrate that quality competition between firms catalyzes greater R&D investment, more knowledge produced, and lower net profits compared to markets without innovation. Analysis shows that future net profits per dollar of R&D investment decrease as firms expand their knowledge bases. This implies emergent incentives to seek methods of differentiation beyond product quality once technologies reach maturity. The ease and extensibility of the model and simulation framework enable the study of other innovation mechanisms in future works.

Keywords: Innovation economics, agent-based simulation, quality differentiation, knowledge spillover