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

Written by oligopoly | Published 2024/07/10
Tech Story Tags: games | consensus-based-optimization | numerical-experiments | zeroth-order-algorithm | nonconvex-multiplayer-games | global-nash-equilibria | swarm-intelligence | metaheuristics

TLDRIn 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.via the TL;DR App

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.


Written by oligopoly | Interconnected players, shaping market dynamics, fostering competition and cooperation in delicate balance.
Published by HackerNoon on 2024/07/10