SQUIDS Seminar: Numerical Computation of Mean Field Games Using Cole-Hopf Transformation and Fictitious Play
| Dates: | 12 November 2025 |
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| Times: | 13:00 - 14:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, Current University students |
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| Speaker: | Daisuke Inoue |
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Speaker: Daisuke Inoue (Imperial College London)
Abstract: Controlling large-scale multi-agent systems (MAS) is a critical challenge in today’s highly interconnected society. In this presentation, we present methods based on Mean Field Games (MFG) to address the computational challenges associated with MAS control problems. By combining the Cole–Hopf transformation and fictitious play, we first derive a linear iterative MFG (LIMFG), which resolves the nonlinearity and coupling problems inherent in MFG. Numerical schemes for LIMFG ensure ease of implementation while guaranteeing convergence of the solution. We discretize the LIMFG using two approaches: a finite difference method and a Monte Carlo method. The former uses an explicit Euler scheme for time discretization, which allows convergence analysis by tracking the error through discretization and iteration. The latter uses the Feynman–Kac formula to express the PDE solution as the expected value of the solution to an SDE, enabling efficient computation for problems that mesh-based methods cannot handle.
Speaker
Daisuke Inoue
Organisation: Imperial College London
Travel and Contact Information
Find event
Frank Adams Room 2
Alan Turing Building
Manchester
