A Consensus-Based Algorithm for Non-Convex Multiplayer Games: Numerical Experiments
by OligopolyJuly 10th, 2024
Too Long; Didn't Read
In this section, we present our numerical experiments, which are performed in Python on a 12thGen. Intel(R) Core(TM) i7–1255U, 1.70–4.70 GHz laptop with 16 Gb of RAM. As usual in CBO schemes, we discretize the interacting particle system in (1.2) with a Euler– Maruyama time discretization scheme 34.
Authors:
(1) Enis Chenchene, Department of Mathematics and Scientific Computing, University of Graz;
(2) Hui Huang, Department of Mathematics and Scientific Computing, University of Graz;
(3) Jinniao Qiu, Department of Mathematics and Statistics, University of Calgary.
Table of Links
2.1 Quantitative Laplace principle
2.2 Global convergence in mean-field law
3 Numerical experiments and 3.1 One-dimensional illustrative example
3.2 Nonlinear oligopoly games with several goods
4 Conclusion, Acknowledgments, Appendix, and References
3 Numerical experiments
In this section, we present our numerical experiments, which are performed in Python on a 12thGen. Intel(R) Core(TM) i7–1255U, 1.70–4.70 GHz laptop with 16 Gb of RAM and are available for reproducibility at https://github.com/echnen/CBO-multiplayer. As usual in CBO schemes, we discretize the interacting particle system in (1.2) with a Euler– Maruyama time discretization scheme [34], resulting in the method depicted in Algorithm 1.
3.1 One-dimensional illustrative example
3.1.1 Experimental setup
3.1.2 Results and discussion
This paper is available on arxiv under CC BY 4.0 DEED license.
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