Convergence of self-play dynamics to a strict equilibrium

Determine whether the coupled self-play dynamics and self-tuned scale schedule converge to a strict pure equilibrium for specified classes of finite games, rather than cycling or settling at an interior equilibrium.

Background

The paper proves bounded intrinsic time and an O(1/T)O(1/T) CCE rate conditional on convergence to a strict pure Nash profile. It also notes that nonconvergent multiplicative-weights behavior and interior equilibria can occur. The convergence of the coupled dynamics and schedule itself is not established and is explicitly left as an open question.

References

One level up remains open: whether the coupled dynamics-and-schedule system converges to a strict profile at all, for a given class of games, or instead cycles or settles on an interior equilibrium.

— The concentration game: Bayesian updating, regret, and information  (2608.18061 - Balsubramani, 18 Aug 2026) in Section 6.2, General-sum play and equilibrium consequences; Appendix, Section \ref{app:proofs-games}