A mean field game model of firm-level innovation
File(s)
Accepted version
Author(s)
Barker, Matt
Degond, Pierre
Martin, Ralf
Muûls, Mirabelle
Type
Journal Article
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. The model developed is a mean field game model, which allows for heterogeneity in the productivity of a firm and allows for a novel approach to describing sector-level spillovers. The model is constructed from a network of interacting firms, whose connections represent knowledge transfers. 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.
Date Issued
2023-05
Date Acceptance
2022-11-27
Citation
Mathematical Models and Methods in Applied Sciences, 2023, 33 (5), pp.929-970
ISSN
0218-2025
Publisher
World Scientific Pub Co Pte Ltd
Start Page
929
End Page
970
Journal / Book Title
Mathematical Models and Methods in Applied Sciences
Volume
33
Issue
5
Copyright Statement
Electronic version of an article published as Mathematical Models and Methods in Applied Sciences Vol. 33, No. 05, pp. 929-970 (2023) © World Scientific Publishing Company https://doi.org/10.1142/S0218202523500203
Identifier
http://dx.doi.org/10.1142/s0218202523500203
Publication Status
Published
Date Publish Online
2023-03-29