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A mean field game model of firm-level innovation

Barker, Matt, Degond, Pierre, Martin, Ralf and Muûls, Mirabelle (2023) A mean field game model of firm-level innovation. Mathematical Models and Methods in Applied Sciences, 33 (5). 929 - 970. ISSN 0218-2025

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Identification Number: 10.1142/S0218202523500203


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.

Item Type: Article
Official URL:
Additional Information: © 2023 World Scientific Publishing Company.
Divisions: Centre for Economic Performance
Subjects: Q Science > QA Mathematics
Date Deposited: 24 Apr 2023 11:21
Last Modified: 19 May 2024 05:18

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