A Consensus-Based Algorithm for Non-Convex Multiplayer Games: Numerical Experiments

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10 Jul 2024

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.

Abstract and 1 Introduction

2 Global convergence

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.