A mean field game model of firm--level innovation

TL;DR

This paper develops a mean field game model to analyze firm-level innovation and knowledge spillovers, providing insights into under-investment in research and potential policy implications.

Contribution

It introduces a new mean field game model of spillovers, proving existence and uniqueness of solutions, and explores how spillovers impact sector productivity.

Findings

Model demonstrates how indirect spillovers enhance productivity

Proves existence and uniqueness of solutions to the model

Initial simulations show the impact of spillovers on innovation

Abstract

Knowledge spillovers occur when a firm researches a new technology and that technology is adapted or adopted by another firm, resulting in a social value of the technology that is larger than the initially predicted private value. As a result, firms systematically under--invest in research compared with the socially optimal investment strategy. Understanding the level of under--investment, as well as policies to correct it, is an area of active economic research. In this paper, we develop a new model of spillovers, taking inspiration from the available microeconomic data. We prove existence and uniqueness of solutions to the model, and we conduct some initial simulations to understand how indirect spillovers contribute to the productivity of a sector.