Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos
We study the long-term behavior of the Multiplicative Weights Update (MWU) algorithm in game settings where learning dynamics frequently fail to converge to Nash equilibria and instead exhibit Li-Yorke chaos. While such chaos precludes the prediction of specific long-term strategy profiles, it does not imply a lack of statistical structure. We demonstrate that natural invariant measures - a fundamental concept from ergodic theory - provide the rigorous framework necessary to find order within this chaos. Focusing on a two-strategy congestion game, we prove that these measures allow for a comprehensive statistical characterization of the dynamics. Crucially, we show that this framework ext...
| Authors | Jakub Bielawski, Thiparat Chotibut, Fryderyk Falniowski et al. |
|---|---|
| Primary category | math.DS |
| Published | 23 July 2026 |
| Last updated at source | 23 July 2026 |
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