Computing stable limit cycles of learning in games

Researchers have developed a polynomial-time algorithm to determine which cycles in multi-agent learning games are stable, answering a central question open since Shapley's 1964 work. The paper shows a periodic sequence is stable under both fictitious play and replicator dynamics if it passes their new spectral stability test. It also provides a structural sufficient condition linking stability to the game's preference graph, generalizing foundational theorems and extending recent work on replicator attractors.