This content originally appeared on HackerNoon and was authored by Oligopoly
:::info 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.
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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
3.2 Nonlinear oligopoly games with several goods
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\ Figure 2: Studying the dependence of Algorithm 1 with respect to the algorithm’s parameters to solve (3.5).
\ of good produced, namely
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\ 3.2.1 Experimental setup
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\ 3.2.2 Results and discussio
\ In Figure 3, which shows the results corresponding to the experiment in case 1, as observed for instance in [28], we see that the anisotropic case does indeed show a faster convergence rate especially in the initial iterations and for λ which is of the order of σ 2 . If λ increases, though, we see no significant differences in the convergence behavior of anisotropic or isotropic dynamics, both for the residual and for the variance decrease.
\ Figure 4 shows the results of the comparisons in cases 3 and 2. Regarding case 2, we can see that indeed as the dimension increases, we need exponentially many particles (quantified by N) to reach high accuracy of order 10−9 . This indicates that Algorithm 1, while being quite reliable, and sometimes the only available solver for low-dimensional problems, might need further improvement in high-dimensional settings.
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:::info This paper is available on arxiv under CC BY 4.0 DEED license.
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This content originally appeared on HackerNoon and was authored by Oligopoly
Oligopoly | Sciencx (2024-07-10T21:00:14+00:00) A Consensus-Based Algorithm for Non-Convex Multiplayer Games: Nonlinear Oligopoly Games. Retrieved from https://www.scien.cx/2024/07/10/a-consensus-based-algorithm-for-non-convex-multiplayer-games-nonlinear-oligopoly-games/
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