Mean Field Games
The Road That Made Everyone Late
Close a busy road and the traffic gets faster. Cities have done it and been surprised. The reason is arithmetic, it needs every driver to be perfectly selfish and perfectly informed, and in the smallest version a free new road costs everybody fifteen minutes. Then it turns out the most destructive road of all is not the free one.
Read more →Everybody Wants the Cheap Plug
Ten thousand vehicles, two cheap places to charge and one hour. A mean field game — Hamilton–Jacobi–Bellman backwards, Fokker–Planck forwards — solved on a torus and animated, and the 1.60% that nobody's mistake accounts for.
Read more →From Plasma to Game Theory: The Unlikely Journey of an SDE
McKean-Vlasov SDEs emerged from plasma physics in the 1960s. Mean field games arrived from economics in 2006. They converged on the same equation from opposite directions.
Read more →The Mean Field Game of Mediocrity
Mean field game theory gives mediocracy a precise formulation: when conformity pressure exceeds rank incentive, the coupled HJB–Fokker–Planck system has a concentrated Nash equilibrium. A phase transition separates dispersed outcomes from universal indistinction.
Read more →ABM or MFG? The Cases Where the Answer Is Not Clear
Agent-based models and mean field games are often presented as alternatives. In practice, a significant share of real problems sit between them — and recognizing that grey zone is the first step toward modeling it correctly.
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