Journal article
Equilibria in the Large-Scale Competition for Market Share in a Commodity with Resource-Buying
Dynamic games and applications
06 May 2024
Abstract
We study a mean field game model of Cournot/Bertrand competition between firms. Chan and Sircar introduced such a mean field model of competition in natural resource extraction. In their model, each firm has a finite reserve of a commodity and may choose to extract a positive quantity per unit time. We instead treat the situation in which firms compete to purchase raw materials, rather than produce the raw material. With this change, we arrive at the same nonlinear system of partial differential equations, but what corresponds to the positive rate of resource extraction in the Chan-Sircar model is instead negative in our setting. We prove existence of stationary solutions, using a Lyapunov-Schmidt decomposition and multiple applications of the implicit function theorem.
Metrics
Details
- Title
- Equilibria in the Large-Scale Competition for Market Share in a Commodity with Resource-Buying
- Creators
- Luke C. Brown - Drexel UniversityDavid M. Ambrose - Drexel University
- Publication Details
- Dynamic games and applications
- Publisher
- Springer Nature
- Number of pages
- 26
- Grant note
- DMS-1907684; DMS-2307638 / Division of Mathematical Sciences; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001214079800001
- Scopus ID
- 2-s2.0-85192073194
- Other Identifier
- 991021880201404721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Interdisciplinary Applications