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

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 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. 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. Authors: 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 Abstract and 1 Introduction Abstract and 1 Introduction 2 Global convergence 2 Global convergence 2.1 Quantitative Laplace principle 2.1 Quantitative Laplace principle 2.2 Global convergence in mean-field law 2.2 Global convergence in mean-field law 3 Numerical experiments and 3.1 One-dimensional illustrative example 3 Numerical experiments and 3.1 One-dimensional illustrative example 3.2 Nonlinear oligopoly games with several goods 3.2 Nonlinear oligopoly games with several goods 4 Conclusion, Acknowledgments, Appendix, and References 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 3.1.1 Experimental setup 3.1.2 Results and discussion 3.1.2 Results and discussion This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

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

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